Omar Jamal they don't just play around with abstract things, they construct incredible abstract structures, from the the top to the foundation. A foundation that is absolute truth made out of logic (let's just ignore the mess that is set theory for the sake of my argument). It is the most pure science. Physics, biology and chemistry simply tries observing the world and attempts fitting a theory that only necessarily fits the observation. Social science, HA, it is simply making assumptions on assumptions. These amazing structures, that can say constructive things about what would seem to be nonsensical at face value, such as infinity , turns out to also be really useful in all fields. Even if something doesn't find an application now it might be extremely useful for the next generation. So yes they are basically just messing about with random abstract things, and that is what is the most glorious aspect regarding the wonder that is mathematics.
@@buffendene9996 please explain to me how you know what i don't know. if what i said is wrong please try to disprove me instead of asking stupid questions.
Tao is a very good communicator. Modest, fluent, responsive, considered, honest, and humorous. Very good person, a great scholar and a gentleman to the core.
Not sure on the "good communicator". He does stutter frequently but I must say he is nonetheless one of the greatest mathematician and I do love his books on analysis. His passion really shows
he is as beautiful as the mathematics he talks about. The key the learning mathematics is to listen to someone who speaks with such passion. That passion is contagious, wakes up the natural curiosity that is dormant inside of us. Just beautiful.
I was at office hours for one of my math classes here at ucla, and I turn around and just this guy (Terence Tao) just casually walking around. It was pretty crazy to think about all that he's accomplished and to go to a university where people like him work at!
Probably one of the best lectures I've ever watched, it's amazing how he can state the elegance of pure mathematics to his target audience with ease. Thank you. Things that I will continue to explore/learn/appreciate more into the future: *The Reimann Hypothesis *Goldbach conjecture *All primes except 2 are adjacent to a multiple of 6 *trillions of dollars is kept safe by prime number randomness. *There are musical "chords" of primes. *Sieve theory is like a sculpture that you carve out prime numbers from. *The arithmetic progressions of the primes and almost primes. *There are many unsolved prime number problems and most mathematicians work on the problems that are closest to being solved. This has encouraged me to try to study number theory as a hobby... Why not?
Hope you went ahead with Maths as a hobby! Its not unheard of to be pursuing Mathematics as separate from a primary career: en.m.wikipedia.org/wiki/List_of_amateur_mathematicians You've got names like Fermat, Mersenne and Pascal in the list above; amongst many more. Hell, even Benjamin Franklin is on that list!
@@ryanh1013 Could you please define what "adjacent" means? 2 is not adjacent to 6 because it cannot be described as 6n+1 or 6n-1, where n is a positive integer. This is the pattern I deduced from Matthew's statement. In that case, 3 cannot be either, which is why I wrote my comment. 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, etc are can be expressed in the form of 6n+1 or 6n-1. Why is 3 adjacent to 6 but 2 isn't?
He stutters and says “um” a lot but still managed to give a concise, interesting, and clearly understandable presentation. So called “public speaking skills” only matter when you really don’t have anything of substance to say.
The reason he stutters is because he is trying to talk fast without stuttering but fails to ,if he instead just speaks slowly with pronouncing each word clearly he won't stutter. I mean if he practices it a bit then boom no stuttering but i guess he has better things to do. That is why he doesn't put efforts not to stutter.
@@ritvikreddy3959he stutters cause his brain is processing things faster than he can speak, elon musk is another example... Its not something you can just 'fix'.
@@MTran0708 Not really processing is one thing and conveying is different. I have had a problem of stuttering while i was having brain fog. I didn't pay attention to what i was and was talking at a faster pace. What helped me was keeping a calm mind and saying words slowly. You can definitely fix it.
I don't know anything about maths; but I find this strangely therapeutic. It reminds me of how stupid and insignificant my life is, and it is very humbling.
I'm supposed to know 'something' about maths, since it's by farrr the main thing I do in life and I'm doing a degree in maths at a top university. But Terence Tao as a mathematician reminds me how stupid and insignificant my life is too. In fact, any genuinely good mathematician makes me realise how stupid and worthless my piece of sh*t brain is. Oh well. I have nothing else anyway lol.
I dont pretend to understand more than a small percentage of what he says here... but, dont you find he has a wonderfully clear and simple way of explaining such high-end stuff? is that just me? I find him very easy to listen to and attempt to learn from somehow? to me, its just further proof of his truly towering genius!
He's such a great explainer for both technical and non-technical audiences. A mathematician not afraid to use metaphors and analogies in explanation? Yes please. So humble, so brilliant. Love Professor Tao.
As someone who has been a Math guy, I love the great ones such as Terence who are so humorous. We love this subject and it brings joy that cannot be described. Number theory is deceptively simple in the sense of making statements, but notoriously difficult to prove. The proof of Fermat's last theorem is a canonical example. Taniyama, Shimura (also Weil) conjecture... What the hell have Modular forms have to do with a seemingly simple statement about some integer power sums. They do! Another example is from my thesis adviser's thesis adviser (Feit) ... Groups of Odd Order are Solvable (Feit - Thompson). This is beautiful. Once the commutator descends, one can apply induction and prove all kinds of things. This why the whole subject is so spiritual. Love it!
This presentation really opened my eyes and mind to prime numbers. I now wish I had taken a life path in mathematics. There is SO much in the pattern of primes that I wish I knew how to express mathematically.
Indeed, we can only speculate! :) There were some parts in the video where he would find something funny but no one else would, it seems most people were laughing at things which relate to normal life, whereas he found mathematical formulas funny. A difference in humour, and humour is all about unsaid truths.
Given the subject point out here my research, in Italian, in which I show that a law for prime numbers does not exist, even in an algebraic version. I have also proofed the non primality of number 1. For now there is in English the algebraic version of my demonstration with an informal introduction : tesisuinumeriprimi.blogspot.it/
There is actually a much more satisfying reason for not including 1 as a prime. If you define a prime as being a number with exactly four unique divisors, 1 and itself and minus 1 and minus itself, then the number 1 does not fill that bill. As far as I know no one uses this definition, but it seems to me that it would eliminate a common student confusion about the role of 1, and the role of 2 for that matter.
A memorable lecture that shows the "lumpyness" of the Number Line via the concept of Prime occurring in the unit cycle of "counting", which is a particular identification of ePi connection multiples.. And if you stare at the blank page or black board, the context in which we visualize Numberness condensed from Mathematical Imagination and Intuition, the omnidirectional-dimensional Origin of Superspin preceeds all function cause-effect of form, In-form-ation formulae. So the reference to the logarithmic relationships with Prime Number, the fact of the inherent-implied processes of Differentiation and Integration "Interfere" as numberness in potential possibility, of time-duration = calculation manifestation, substantiates the Mathematical holistic conditions of Polar-Cartesian Coordination and Geometry in Spacetime, by which observation in Methodology self-defining difference in Principle produce these Proof/Disproof circumstances. This lecture also promoted the idea of pseudo random fields of Uncertainty in otherwise specific resonance interference positioning Image condensation and certain vertices in vortices of e-Pi-i interference positioning resonance of resonances.., ie "simple", and messy, complexity. Mathematicians may prefer Spinfoam Totality of Superspin, a Modulation conception, to "resonances"? Terminology is the real problem of further Education, in my worthless opinion. The antilog "Chord of Superspin" Modulation Totality, (could be an opening to a "Music of Prime", Eternity-now Interval of Vector, Temporal Opera?). There's another well defined concept, pseudo random conglomerations of primes and cofactors, either in a lump of Granite conglomerate, or box of unsifted Sand, the idea is reducible to mathematical expressions. Same applies to "fluid" fields of Uncertainty in otherwise specific resonance interference positioning that becomes turbulence and the Navier-Stokes Equations.. The intuitive reason for the properties of numbers is the temporal vectors of time duration timing modulation, by the naturally occurring superimposed probability, in potential possibilities conception, of whole number base logarithms, in the Superspin-calculations=> antilog-> self-definition numberness context of e-Pi-i continuous creation connection QM-TIMESPACE Principle. Time is ONE at zero-infinity, and Timing is the hyperfluid state of zero-infinity sum-of-all-histories wave-package probability ONE, from which all phenomena self-define. (P=nP doesn't seem to define itself from the logarithmic fluid state, intuitively) Put simply, the time duration timing modulation functional probability of Primes and multiples of Primes=> cofactors, are the cause-effect embodiment of the QM-TIMESPACE Principle Universe.., this Mathematical Eternity-now Interval/format. The Kieth Newman book, "God is a Mathematician", is consequently a degree of fact, because "Mathematics has Substance" in Actuality.
It's somehow so hard to imagine him being a mathematical prodigy (in addition, also actually, a child prodigy, if more precise). He is one and it has been proven that he is a genius. But he looks so normal. Like a normal Asian young adult, just like any one of us (except for the fact that not all of us are Asian, lol). What makes him what he is? His physical appearance is also very pleasing and he seems like a sympathetic, honest and a polite person. I really do find him likeable. I watched this lecture some days ago already so I just thought I'd drop by and say what I just said. If I had to say something about this particular lecture, I do not have any strong opinions in one way or another. It was a nice basic presentation without any technical detail. I also stumbled upon Terry's personal blog and saw his mathematical powers in action. I'm a mathematical noob and would like to learn A LOT but, hah, I might never reach the level to even understand any of Terry's mathematical stuff.
and keep note he said we do not grant the number 1 the property of primality, as the primes as a group use the number 1 in axiomizing them as a subset of the integers, thus using the number 1 is a self reference hence circular arguement, ie treating 1 as a prime is equally useful as saying 1/1 = 1, which is the required property of an identity element under the operation of division!
I guarantee this man could fix the budget and point our country in the right direction. He is the type of man that would tackle any problem with cold calculating logic, and be smart enough to recruit any assistance he needs to fix any problems he encounters.
Joshua Bruce Taylor Tao is good at technical problem solving. "Pointing our country in the right direction" is far more difficult and demanding than solving technical problems. Human emotions are very much involved in the job of a powerful leader.
Constance Reid (sister of the brilliant Mathematician who died so tragically young and author of (among other books on popular maths) "Mathematical People") wrote: People have spent more time think-ing about prime numbers than war. A really cool talk. Also, there is an *excellent* popular maths book on the Poincaré conjecture. The part that Professor Tau (great name) left out, was that so many people were try-ing to claim the prize (for make-ing what were (it seems) minor corrections to his 3-part proof) that he refused to have anything to do with the money and returned to teaching and research. This is parallel to Richard Feynman's comment about the Nobel Prize he shared that the reward was to work on the problems and make some headway to *understanding* the universe. thanks, for the post -r.
I spent years searching for the essence of truth through poetry and fiction. Became a lawyer but was miserable every minute I practiced. As I continued searching for that essence, I was led to study mathematics. I feel that math has provided all the solace I had been searching for. If you're reading this and have wondered if mathematics is worth your time and effort, trust me it is. Math is an inexhaustible well of discovery and enlightenment. You will never regret it.
I am not mithered by the fact that there are people in the world more brilliant than me! It doesn't bother me! Nope! Nope! I am quite content! I may try and read a chapter from the book The Identity of Man by J Bronowski, tonight. I find reading difficult! I failed GCE English with a D Grade from college in 1999 at the age of 24.
Thank you, UCLA, for posting this video. Terrence Tao and his work has further inspired me to pursue mathematics, I someday wish to come to UCLA to take courses or go to lectures under Mr. Tao.
Yeah mod functions can change things a lot. It's a simple concept though, which is used a lot in maths but not taught in schools. All you do for mod P is divide by P and keep the remainder. For example, our clocks use mod 12, so if 25 hours have passed, we divide by 12 and keep only the remainder. Thus, the time shows 1 hour later.
+Santiago Arce Of course not, confidence is highly correlated with low intelligence. The more intelligent a person is the more anxiety they will generally have as they realize how many things in the world can go wrong while most people are completely oblivious. Also, most geniuses think they are stupid as unlike most people they are aware of their own ignorance.
I love this stuff. Pure genius. The great ones are very humble. I was fortunate to meet some of them as a young child (Weil, Borel, Atiyah, Bombieri, Godel … all at IAS (Princeton) ) where my dad spent some years.
At age 7 he wrote a Basic programme about Fibonacci numbers in which he first got players to guess the year of birth of Fibonacci and if they were much to late the programme responded _"Fibonacci has gone to heaven."_ In this presentation he talks about _"God does not play dice..."_ I wonder if he has considered the following: Mathematics reveals many patterns in the numbers, why? Answer, patterns mean what we are seeing is a non-random field or fields of concepts which are related to our reality in some way. Non randomness in thermodynamics means *order* and it is possible to show that all order comes from information and all information comes from a mind, (Ref Max Planck). So is this a mathematical proof of Gods existence?
There is a verse in Holy Quran Chapter 59 verse 23 with most number of God's names (Attributes) i.e. 8 names. He is Allah, other than whom there is no deity, the Sovereign,1 the Pure,2 the Perfection,3 the Grantor of Security,4 the Overseer,5 the Exalted in Might,6 the Compeller,7 the Superior.8 Exalted is Allah above whatever they associate with Him. Few prime number facts: 1) 59 is a prime number 2) 23 is a prime number 3) This verse has 19 words in Arabic 19 is another prime number. 4) 8th prime number is 19 5) Concatenate 59, 23 we get 5923 a prime number 6) Sum of the digits 5+9+2+3 = 19 a prime number 7) Add 8 to 23 we get 31 a prime number. 8) Add 8 to 59 we get 67 another prime number. 9) Concatenate 8 with 23 we get 823 a prime number. 10) Concatenate 8 with 59 we get 859 a prime number. 11) Add 59, 23 and 19 we get 101 another prime number. 12) Add 58, 23, 19 and 8 we get 109 another prime number.
This shows that as a number grows faster the density of prime gets lesser?.what one can infer or what about the significance is ,one can draw from this statement
Thank you for this very much for this video. The video shows that pi is approximately 22 / 7. This value is approximately 3.14. Using the properties of this value we can compute prime numbers in sequence, which is based on the existing computing capability. The formula was an algorithm, that was developed by a well known mathematician. Using his formula and the method that I discovered, I can compute prime numbers in sequence using 22 / 7 .
Terrence, a brilliant mathematician. 7:51, Euclid proved (by contradiction) that 2, 3, 5 were not the only prime by multiplying then adding or subtracting one (2x3x5+1 or -1) thus creating 31 and 29 which are two prime numbers since if 31 and 29 WERE NOT PRIME, then by the fundamental theorem of arithmetic which states that every positive integer can be expressed as a product of at least one prime then 31 and 29 should have been, but they could not. That is, if 31 and 29 were not prime then they could be expressed as a product using 2 or 3 or 5 or DIVISIBLE BY 2,3, OR 5. Since they can't then the fundamental theorem of arithmetic would have been violated. Therefore 2, 3, and 5 were not the only prime.
I think I was channeling a little Douglas Adams with that thought. But I'm not even exaggerating: math is beyond comprehension in it's beauty and complexity. There's symmetry, fractals, recurring themes and hidden spaces everywhere. It's like an infinite cathedral built at the height of the late medieval. My apologies if you already know this; I'm taking some classes on modular forms and I'm just beginning to wrap my head around the symmetries and relationships.
He's such a great teacher in a way that, despite his problems with the idiom (also he speaks too fast) and his obvious shyness, he can make very difficult math problems sound easier than they really are, also he makes you want to know more...
Because I am also a programmer, I wrote 2 applications to demonstrate how Diffie-Hellman works and how RSA works. I wrote my own large integer math library in C to aid with the effort. I also used a large prime generator based on a Rabin Miller test. It can handle 100 digits easily.
Actually, 10, ten, is very special in number theory-there are constructions that work only for radixes 2 and 5 whence 10, e.g. dragon curves by 90°, (radix 3 works at 60°),... (P.S. I tested radixes 2 and 5 but not radices 2 and 5 together..., and radix 4 closed up...)
Pedro Fernandez you are too stupid to appreciate a genius such as his. Please stop breathing the precious oxygen that should be saved for those who aren't grossly immoral narcissistic schizophrenic ignoramuses
42:30 k^k Would be the inefficient bound given large k, as lim (trash^k)/(k^k) as k->∞ is 0. The trash^k is still interesting despite being terrible for small values of k.
In fact progressions of seven seems to be very easy... It's in fact already shown as progression of 6 at the end like 7, 157, 307, 457, 607, 757 however just attach 907 to it and [7, 157, 307, 457, 607, 757, 907] you have prg. 7
The prime sequence is based off of a sieve from the first 2 primes (2&3) : 2-4-2-4-2....with the only exception being a prime multiplied by a prime. Ex: 5,7,11,13,17,19,23, (25 = 5*5), 29,31,(35 = 5*7),37,41,43,47,(49=7*7),53,(55=5*11).You can use the arctangent of the reciprocal of the prime number to define the azimuth for these exceptions.
I read somewhere that he could be working on proving or disproving the Riemann Hypothesis. Hopefully, I am still around when he eventually accomplished a feat several generations of the most brilliant mathematicians has attempted to do.
Collatz conjecture that oscillate between even number divided by half becoming a odd number follow 3x+1 that follow a reduction towards number 1 skewing seems to be very interesting analogy starting from any infinite number following time stepping can be compared with Kuprekar constant stability at 1694 as even number blocking once for all in between maxima and minima finally reduced to 1694 but not a prime number.Any chemical bonding oscillating along frequency of natural vibration will destruct itself the the very nature of chemical bonding as applicable in cancer therapy.Any chemical bonding oscillating along multiple harmonics of natural bring forth a destructive property. Sankaravelayudhan Nandakumar Sankaravelayudhan Nandakumar
FORMULA OF PRIME NUMBERS Positive integers which are not members of arithmetic progressions: Q(ik)=a(i)+b(i)*k a(i)=6*i^2-1; b(i)=6*i-1 R(ik)=a(i)+c(i)*k c(i)=6*i+1 Are indexes P of all prime numbers in the sequence S1(P)=6*P+5; i=1, 2, 3,…; P=0, 1, 2,…, k=0, 1,2,… Positive integers which are not members of arithmetic progressions: T(ik)=d(i)+b(i)*k d(i)=a(i)-2*i; U(ik)=f(i)+c(i)*k f(i)=a(i)+2*i; Are indexes P of all prime numbers in the sequence S2(P)=6*P+7; i=1, 2, 3,…; P=0, 1, 2,…, k=0, 1,2,…
+lgbtTV5 I have heard of Ramanujan. I was referencing the similarity regarding their math intrests. Also, if you have Netflix you can watch it. ps: please check out my TH-cam channel I do math and science on it
Well, that's a sieve. The problem is that calculating, storing and scanning those arrays is of the order of n^2*log(n). Which is much worse than O(n + n*log(log((n))) that the classical Erasthotenes sieve requires, never mind more efficient sieving methods. It also provides no information whatever on the large-scale _distribution_ (as opposed to computation) of primes. BTW - your link to IJMCR does not work.
This is a "core Mathematical substance" illumination of basic QM manifestation. A confluence-collider of concepts in the general Conception of Time. This distinguishes the "sides" of wave-particle duality that has no absolute sides, the mutual synch-alignment of amplitude and frequency Primes in a superimposed line-of-sight superposition of the concept of material Number, and the empirical timing-synch of precedents, in metastable sustainability.., a coexistence parallel resonance that's mutual simultaneous alignment, and re-evaluation, corresponding active connection existence. So there's also a "physical manifestation" reason not to use 1 as a Prime, which is because of exponential time function active connection, and natural logarithmic condensation wave-particle uncertainty, "designed" by the surrounding wave-field projection+/-, of superimposed Primes. Ie it's the cause-effect of Temporal Superposition Synchronisation shape shifting positioning.., around the instantaneous .dt infinitesimal potential possibilities of the e-Pi-i pivotal Planck Dimension, and zero-infinity Singularity Vanishing Point Perspective Positioning, a structured time duration position differentiation by potentially mathematically pure.., relative timing motion integration functions. Therefore the Minimum Time, motionless in Time trajectory that is the Omni directional and dimensional Origin @.dt, is self-defining infinitely distributed vanishing point positioning, singularity function, probability of constant primary combinations of synchronisation. WYSIWYG Physics of pulsed time duration, Quantitative Mechanism. The rationale and reasoning of the lecture shows that because Primes are calculated from the POV of Mathematical calculations of Idealized Real Numbers, that the existence of the infinite objective, Prime, line of sight analog of ONE P, is the definition of an impossible positioning from outside of the Universe. Ie, the hypothetical Big Bang Singularity. (Which is a "legitimate belief" according to empirical evidence, and an arbitary Mathematical "Accounting" choice within the e-Pi-i format)
This mans IQ is so high, he isn't considered smart, proficient, genius, or even extreme genius. He is in a category all his known named unmeasurable genius (around 230).
I started a project where I'm took the base video and started cutting out ums, uhs, and repeated words. Already got it down to 42:25. Fascinating talk, though.
A few people are missing the point here We consider a "largest" prime, p. Then we examine N, the product of ALL the primes up to and including p, plus 1. N = (2 x 3 x 5 x 7 x ... x p) + 1. If N is prime, it is a prime greater than p and so p is not the largest prime after all. If N is not prime, then it has prime factors. And its prime factors are greater than p, because p and all the smaller primes leave a remainder of 1 when they divide N. So, the prime factors of N are greater than p. QED.
It isn’t always the math material itself which merely makes the subject so fucking scary to people, it’s living breathing talking titans like tao who make his level of expertise incomprehensibly unachievable, but we’re still glad people like him exist to conquer such a universal beast
EinSofQuester Is this a joke? Those two equations couldn't be any less related. The Boltzmann constant k is just a proportionality constant, whereas n obviously varies. Those two quantities are not even proportional.
Reposting and slight editing of recent mathematical ideas into one post: Split-complex numbers relate to the diagonality (like how it's expressed on Anakin's lightsaber) of ring/cylindrical singularities and to why the 6 corner/cusp singularities in dark matter must alternate. The so-called triplex numbers deal with how energy is transferred between particles and bodies and how an increase in energy also increases the apparent mass. Dual numbers relate to Euler's Identity, where the thin mass is cancelling most of the attractive and repulsive forces. The imaginary number is mass in stable particles of any conformation. In Big Bounce physics, dual numbers relate to how the attractive and repulsive forces work together to turn the matter that we normally think of into dark matter. Complex numbers = vertical asymptote. Split-complex numbers = vertical tangent. Dual numbers = vertical line. These algebras can be simply thought of as tensors. Delanges sectrices can be thought of as opposites of vertical asymptotes. Ceva sectrices as opposites of vertical tangents, and Maclaurin sectrices as opposites of vertical lines. The natural logarithm of the imaginary number is pi divided by 2 radians times i. This means that, at whatever point of stable matter other than at a singularity, the attractive or repulsive force being emitted is perpendicular to the "plane" of mass. In Big Bounce physics, this corresponds to how particles "crystalize" into stacks where a central particle is greatly pressured to degenerate by another particle that is in front, another behind, another to the left, another to the right, another on top, and another below. Dark matter is formed quickly afterwards. Ramanujan Infinite Sum (of the natural numbers): during a Big Crunch, the smaller, central black holes, not the dominating black holes, are about a twelfth of the total mass involved. Dark matter has its singularities pressed into existence, while baryonic matter is formed by its singularities. This also relates to 12 stacked surrounding universes that are similar to our own "observable universe" - an infinite number of stacked universes that bleed into each other and maintain an equilibrium of Big Bounce events. i to the i power: the "Big Bang mass", somewhat reminiscent of Swiss cheese, has dark matter flaking off, exerting a spin that mostly cancels out, leaving potential energy, and necessarily in a tangential fashion. This is closely related to what the natural logarithm of the imaginary number represents. Mediants are important to understanding the Big Crunch side of a Big Bounce event. Black holes have locked up, with these "particles" surrounding and pressuring each other. Black holes get flattened into unstable conformations that can be considered fractions, to form the dark matter known from our Inflationary Epoch. Sectrices are inversely related, as they deal with dark matter being broken up, not added like the implosive, flattened "black hole shrapnel" of mediants. Ford circles relate to mediants. Tangential circles, tethered to a line. Sectrices: the families of curves deal with black holes and dark matter. (The Fibonacci spiral deals with how dark matter is degenerated/broken up, with supernovae, and forming black holes. The Golden spiral deals with black holes being flattened into dark matter during a Big Bounce event.) The Archimedean spiral deals with black holes and their spins before and after a reshuffling from cubic to the most dense arrangement, during a Big Crunch. The Dinostratus quadratrix deals with the dark matter being broken up by ripples of energy imparted by outer (of the central mass) black holes, allowing the dark matter to unstack, and the laminar flow of dark matter (the Inflationary Epoch) and dark matter itself being broken up by lingering black holes. Delanges sectrices (family of curves): dark matter has its "bubbles" force a rapid flaking off - the main driving force of the Big Bang. Ceva sectrices (family of curves): spun up dark matter breaks into primordial black holes and smaller, galactic-sized dark matter and other, typically thought of matter. Maclaurin sectrices (family of curves): dark matter gets slowed down, unstable, and broken up by black holes. Jimi Hendrix's "Little Wing". Little wing = Maclaurin sectrix. Butterflies = Ceva sectrix. Zebras = Dinostratus quadratrix. Moonbeams = Delanges sectrix. Jimi was experienced and "tricky". Jimi was commenting on dark matter. How it could be destabilized by being slowed down, spun up, broken up by lingering black holes, or flaked off. (The Delanges trisectrix also corresponds to stable atomic nuclei.) Dark matter, on the stellar scale, are broken up by supernovae. Our solar system was seeded with the heavier elements from a supernova. I'm happily surprised to figure out sectrices. Trisectrices are another thing. More complex (algebras) and I don't know if I have all the curves available to use in analyzing them. I have made some progress, but have more to discern. I can see Fibonacci spirals relating to the trisectrices. The Clausen function of order 2: black holes and rarified singularities are becoming more and more commonplace. Doyle's constant for the potential energy of a Big Bounce event: 21.892876 Also known as e to the (e + 1/e) power. At the eth root of e, the black holes are stacked as densely as possible. I suspect Ramanujan's Infinite Sum connects a reshuffling from the solution to the Basel problem and a transfer of mass to centralized black holes. Other than the relatively small amount of kinetic energy of black holes being flattened into dark matter, the only energy is potential energy, then: 1 (squared)/(e to the e power), dark matter singularities have formed and thus with the help of Ramanujan, again, create "bubbles", leading to the Big Bang part of the Big Bounce event. My constant is the chronological ratio of these events. This ratio applies to potential energy over kinetic energy just before a Big Bang event. Methods of arbitrary angle trisection: Neusis construction relates to how dark matter has its corner/cusp singularities create "bubbles", driving a Big Bang event. Repetitious bisection relates to dark matter spinning so violently that it breaks, leaving smaller dark matter, primordial black holes, and other more familiar matter, and to how black holes can orbit other black holes and then merge. It also relates to how dark matter can be slowed down. Belows method (similar to Sylvester's Link Fan) relates to black holes being locked up in a cubic arrangement just before a positional jostling fitting with Ramanujan's Infinite Sum. General relativity: 8 shapes, as dictated by the equation? 4 general shapes, but with a variation of membranous or a filament? Dark matter mostly flat, with its 6 alternating corner/cusp edge singularities. Neutrons like if a balloon had two ends, for blowing it up. Protons with aligned singularities, and electrons with just a lone cylindrical singularity? Prime numbers in polar coordinates: note the missing arms and the missing radials. Matter spiraling in, degenerating? Matter radiating out - the laminar flow of dark matter in an Inflationary Epoch? Corner/cusp and ring/cylinder types of singularities. Connection to Big Bounce theory? "Operation -- Annihilate!", from the first season of the original Star Trek: was that all about dark matter and the cosmic microwave background radiation? Anakin Skywalker connection?
Either prime numbers being unpredictable is proof that randomness is an inherent characteristic of the universe, or it is yet another example of a problem with our invented numerical system that is not an intrinsic part of nature.
I have though long and hard about that question myself and I think that is our numerical system should not exist in nature. The theory of relativity suggests this
+Jose Diola dimension > there are lots of them > are all nature > exists because you pondered > you pondered because you are outside looking in > which a glimpse of omnipotence > that is GOD..
+Monochromicornicopia I don't think you could have a generally usable number system that allowed for simple, efficient arithmetic (the way digital numbers do) in which prime numbers were orderly and easy to generate. You could imagine a number system where each number is expressed as the product of its prime factors (Ex. p(1)^2 * p(2)^7 * p(4) = 2^2 * 3^7 * 7). Representing primes would become a breeze, but addition and subtraction would become a nightmare.
I smoked some pot and as always meditated upon reality. I could actually grasp the pattern of all the prime numbers but I can not remember nor explain; but at the time it was clear and very easy to understand how and why all prime numbers seems to appear randonmly and how they form everything there is in the material world up to some levels above where it is yet not spiritual but is mid way, for example the part and level of the universe where dreams occur.. I am positive that the insight I had about prime numbers is the final answer to mathematics, but I unfortunately cant recall the main ideas.. I can recall something that was fundamental for this understanding and it has to do with the real nature of numbers itself. I remember realizing the existance of only 3 fundamentals for creating all numbers, something like binary systems where the idea of 1 (one) is to the masculine principle and the idea of 0 (zero) the negative or feminine. the intercourse of both creates the plurality of all existing numbers.. And I also remember I could understand how and in what degree each of this 2 (1 and 0 ) would relate to each other and create "pockets" where each of this "pockets" would be enclosed by a positive prime in the beggining and a negative prime in the end enclosing this pocket.. for example in between the 2 and the 3 is one individual pocket the 3 and the 5 is another pocket and so on for eternity revealing all primes.. I can recall the theoretical part of all but I cant grasp the insight that made me recite primes for almost one hour amazed becouse I didnt know primes.. I actually could tell primes forever without calculating anything, thus I know it was not a pot trip, it was real ... It was really scary and I remember felling shivers all over my spine that felt like jolts of real electricit and my body was somehow numb.. It really felt like an extraordinary degree of inteligence where in the realms of numbers I could understand absolutly everything yet it was something really simple and fundamental.. I wish I could think of this again.. But the more I try when I get high the harder it gets to recall .. I guess it something sponteneous;; But if anyone into mathematics, try to think of the numbers as only 2 "beings" inteligent and living beings habitating higher dimentions of our personal universe. Try to imagine them "having sex" yeas its funny but I remember imagining numbers having sex and really "having a swing party" thats how I can describe my thoughts at the moment, than it was unfolding into understanding and seem where each prime would "give birth " to the created numbers.. It was in other words like looking into a lineage of numbers where the first ones to conceive would first conceive primes and the primes would conceive "lesser beings" . I know it sounds crazy, but at the moment I was really concerned about my sanity upon this thoughts..
Dude I know what you mean, I feel like if more people burned up and did math or science or art or w.e as opposed to just sit there then alot more things will be discovered. Paul Erdos said that when he took amphetamines he will look at a piece of paper and have many ideas. I'm studying Math at University of Toronto and when I took M and went to the club, for some reason my interest and the way the perspectives I saw math opened up, it was weird, but I know what you're sort of saying.
I understand what you're talking about, I was on LSD at the time. It's very difficult to communicate your experience from a different dimension; it's like it's the golden rule (you can feel the truth but not allowed to share it. People have to discover the truth for themselves.) 0 and 1 is the key. The universe is about dualities. When I was in this alternate dimension under the influence of psychedelics I was free from all forces of the physical world. You feel as one with all and everything is clear. I've felt all spectrums of good and bad / high and low whilst under and they go together. At my highest euphoria I discovered the secret and became number 1. One key tip I've learn't that I can share with all is that be 100% with any decision you make in life; whether that decision takes an instant or a lifetime.
+Daniel Pavlovsky Dear Daniel, I didn't have the luck to study Latin in my school years (or on my own), so I'm not sure on which grammatical rule the phrase "reduction ad absurdum" obeys. I just keep it in mind along with a dosen more which are used in science and mathematics (and actually I usually google it to make sure I get it right). A very stupid comment anyways, under such an illuminating video.
You can find interesting facts and puzzles about Prime Numbers and Magic Squares, Smith Numbers, and Arithmetic and Palindromic Primes on Glenn Westmore's blog.
What is prime in terms of matter content is the distribution of matter types. Matter can take any one of the prime forms only and others are molecules or mixture. Usually primes occur as cluster like gold and silver and iron but the low primes are carbon and oxygen.
Randomness in primes are because of sequences are always waves and waves can get to a higher order if a trough meets a trough or amplitudes are in sync. Or frequencies.
Im pretty sure there isn't a finite formula that can describe primes, but i think they can generate a formula F(x) which can determine how another formula G(x) changes, G(x) being the formula for the nth prime.
..Yes, he can. If he lock the box and send it back to Alis before reaching Bob, he read or alternate the message then put his lock and send it to Bob..
This is probably dumb, but could you see the first number as G to the A call it (#1). Then see the number Bob sends back which is G to the AB call it (#2). Then ask to what power do you have to raise #1 to get to #2. This will find B. Then when Alice sends it back (it'll be sent back as G to the B). All you have to do is take the B root, which you know, and you'll get G. Maybe this Mod P, stuff prevents that.
Riemann's-Euclid's zeta function ζ(s) = Σ(1/nˢ) has curious parallel in a disproof of 0.999... = 1.000... because Σ(9/(10-ε)ⁿ) (ε→0) eventually rounds up a carry though in its limit looks okay like the difference between pointwise and uniform convergence...
![[LIVE] BABYMONSTER(베이비몬스터) - DRIP | 두시탈출 컬투쇼](http://i.ytimg.com/vi/UG05pxLGwzc/mqdefault.jpg)
I have so much respect for all of you mathematicians. It is truly unbelievable what you all do. Cheers!
all they do is play around with made up abstract things
Yes, and it's so much fun!
Omar Jamal they don't just play around with abstract things, they construct incredible abstract structures, from the the top to the foundation. A foundation that is absolute truth made out of logic (let's just ignore the mess that is set theory for the sake of my argument). It is the most pure science. Physics, biology and chemistry simply tries observing the world and attempts fitting a theory that only necessarily fits the observation. Social science, HA, it is simply making assumptions on assumptions.
These amazing structures, that can say constructive things about what would seem to be nonsensical at face value, such as infinity , turns out to also be really useful in all fields. Even if something doesn't find an application now it might be extremely useful for the next generation.
So yes they are basically just messing about with random abstract things, and that is what is the most glorious aspect regarding the wonder that is mathematics.
@@omarjamal161 and yet these things have given you the modern world that you know it today
@@buffendene9996 please explain to me how you know what i don't know. if what i said is wrong please try to disprove me instead of asking stupid questions.
Tao is a very good communicator. Modest, fluent, responsive, considered, honest, and humorous. Very good person, a great scholar and a gentleman to the core.
Not sure on the "good communicator". He does stutter frequently but I must say he is nonetheless one of the greatest mathematician and I do love his books on analysis. His passion really shows
@@Fidder492 What is your major? Looks like you are a smart guy. Where are you?
@@Fidder492 Being a brilliant mathematician, Tao must've been thinking far faster than he can speak, that's why he is stuttering
It's a complicated subject and he MUMBLES TOO MUCH !@@kerbodynamicx472
he is as beautiful as the mathematics he talks about. The key the learning mathematics is to listen to someone who speaks with such passion. That passion is contagious, wakes up the natural curiosity that is dormant inside of us. Just beautiful.
I was at office hours for one of my math classes here at ucla, and I turn around and just this guy (Terence Tao) just casually walking around. It was pretty crazy to think about all that he's accomplished and to go to a university where people like him work at!
It's insane how we can listen to this gold while just sitting at home ! Thank you Tao, UCLA, Internet, electricity, etc...
Probably one of the best lectures I've ever watched, it's amazing how he can state the elegance of pure mathematics to his target audience with ease.
Thank you.
Things that I will continue to explore/learn/appreciate more into the future:
*The Reimann Hypothesis
*Goldbach conjecture
*All primes except 2 are adjacent to a multiple of 6
*trillions of dollars is kept safe by prime number randomness.
*There are musical "chords" of primes.
*Sieve theory is like a sculpture that you carve out prime numbers from.
*The arithmetic progressions of the primes and almost primes.
*There are many unsolved prime number problems and most mathematicians work on the problems that are closest to being solved.
This has encouraged me to try to study number theory as a hobby...
Why not?
"All primes except 2 are adjacent to a multiple of 6"
3?
Hope you went ahead with Maths as a hobby! Its not unheard of to be pursuing Mathematics as separate from a primary career: en.m.wikipedia.org/wiki/List_of_amateur_mathematicians
You've got names like Fermat, Mersenne and Pascal in the list above; amongst many more. Hell, even Benjamin Franklin is on that list!
@@wanlitan7406 3 is next to 6 what are you talking about
@@ryanh1013 Could you please define what "adjacent" means?
2 is not adjacent to 6 because it cannot be described as 6n+1 or 6n-1, where n is a positive integer. This is the pattern I deduced from Matthew's statement.
In that case, 3 cannot be either, which is why I wrote my comment.
5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, etc are can be expressed in the form of 6n+1 or 6n-1.
Why is 3 adjacent to 6 but 2 isn't?
@@wanlitan7406 6n-1=3 it’s obviously adjacent
He stutters and says “um” a lot but still managed to give a concise, interesting, and clearly understandable presentation. So called “public speaking skills” only matter when you really don’t have anything of substance to say.
The reason he stutters is because he is trying to talk fast without stuttering but fails to ,if he instead just speaks slowly with pronouncing each word clearly he won't stutter. I mean if he practices it a bit then boom no stuttering but i guess he has better things to do. That is why he doesn't put efforts not to stutter.
@@ritvikreddy3959he stutters cause his brain is processing things faster than he can speak, elon musk is another example... Its not something you can just 'fix'.
@@MTran0708 Not really processing is one thing and conveying is different. I have had a problem of stuttering while i was having brain fog. I didn't pay attention to what i was and was talking at a faster pace. What helped me was keeping a calm mind and saying words slowly. You can definitely fix it.
I don't know anything about maths; but I find this strangely therapeutic. It reminds me of how stupid and insignificant my life is, and it is very humbling.
I'm supposed to know 'something' about maths, since it's by farrr the main thing I do in life and I'm doing a degree in maths at a top university.
But Terence Tao as a mathematician reminds me how stupid and insignificant my life is too. In fact, any genuinely good mathematician makes me realise how stupid and worthless my piece of sh*t brain is. Oh well. I have nothing else anyway lol.
good point, lectures like this should compulsory for politicians and other "leaders", at least once a month
I dont pretend to understand more than a small percentage of what he says here... but, dont you find he has a wonderfully clear and simple way of explaining such high-end stuff? is that just me? I find him very easy to listen to and attempt to learn from somehow? to me, its just further proof of his truly towering genius!
It's like counting sheep.
Yes, but can he change the oil in his car?
He's such a great explainer for both technical and non-technical audiences. A mathematician not afraid to use metaphors and analogies in explanation? Yes please. So humble, so brilliant. Love Professor Tao.
As someone who has been a Math guy, I love the great ones such as Terence who are so humorous. We love this subject and it brings joy that cannot be described. Number theory is deceptively simple in the sense of making statements, but notoriously difficult to prove. The proof of Fermat's last theorem is a canonical example. Taniyama, Shimura (also Weil) conjecture... What the hell have Modular forms have to do with a seemingly simple statement about some integer power sums. They do! Another example is from my thesis adviser's thesis adviser (Feit) ... Groups of Odd Order are Solvable (Feit - Thompson). This is beautiful. Once the commutator descends, one can apply induction and prove all kinds of things. This why the whole subject is so spiritual. Love it!
This presentation really opened my eyes and mind to prime numbers. I now wish I had taken a life path in mathematics. There is SO much in the pattern of primes that I wish I knew how to express mathematically.
"How does one disprove a conspiracy?" The question with the greatest resonance in 2020!
Maybe his best comment!
Thanks for putting into simple wording the method of double-lock information transfer
"You want problems that are compelling but also have some chance to be solved"
(True Intellect begets humility)
Did he just unload about 80% of Number Theory in this lecture? ...
No
Nope, not at all
School level?yes
Advance number theory? Nope. Not even scratched the surface
Indeed, we can only speculate! :)
There were some parts in the video where he would find something funny but no one else would, it seems most people were laughing at things which relate to normal life, whereas he found mathematical formulas funny. A difference in humour, and humour is all about unsaid truths.
U can feel his mind going too fast his speech having a hard time keeping up
Given the subject point out here my research, in Italian, in which I show that a law for prime numbers does not exist, even in an algebraic version. I have also proofed the non primality of number 1. For now there is in English the algebraic version of my demonstration with an informal introduction : tesisuinumeriprimi.blogspot.it/
To understand ALGEBRA in itself to the core, this is the real matter.
a symptom of a savant. His brother is one of them.
thats such bs lol. i stutter like crazy but im anything bus a genius.
s0ngf0rx You mistake the statement and the converse.
Very thankful to have found a recording of this lecture. Deeply gracious, UCLA.
I used to help this guy with his homework
You guys used my room to work..
Like English poetry homework? I can surely buy that.
Yes, when he was 2 years old.
@@bestnocture r/thathappened
lol bs this nigga PG
There is actually a much more satisfying reason for not including 1 as a prime. If you define a prime as being a number with exactly four unique divisors, 1 and itself and minus 1 and minus itself, then the number 1 does not fill that bill. As far as I know no one uses this definition, but it seems to me that it would eliminate a common student confusion about the role of 1, and the role of 2 for that matter.
Nice.
if you're going to bring negative numbers into it, why not include imaginary numbers and have 8 divisors?
Honestly just by looking at this dude he seems like a super genius.
Just 220 IQ :D
A memorable lecture that shows the "lumpyness" of the Number Line via the concept of Prime occurring in the unit cycle of "counting", which is a particular identification of ePi connection multiples..
And if you stare at the blank page or black board, the context in which we visualize Numberness condensed from Mathematical Imagination and Intuition, the omnidirectional-dimensional Origin of Superspin preceeds all function cause-effect of form, In-form-ation formulae.
So the reference to the logarithmic relationships with Prime Number, the fact of the inherent-implied processes of Differentiation and Integration "Interfere" as numberness in potential possibility, of time-duration = calculation manifestation, substantiates the Mathematical holistic conditions of Polar-Cartesian Coordination and Geometry in Spacetime, by which observation in Methodology self-defining difference in Principle produce these Proof/Disproof circumstances.
This lecture also promoted the idea of pseudo random fields of Uncertainty in otherwise specific resonance interference positioning Image condensation and certain vertices in vortices of e-Pi-i interference positioning resonance of resonances.., ie "simple", and messy, complexity.
Mathematicians may prefer Spinfoam Totality of Superspin, a Modulation conception, to "resonances"? Terminology is the real problem of further Education, in my worthless opinion.
The antilog "Chord of Superspin" Modulation Totality, (could be an opening to a "Music of Prime", Eternity-now Interval of Vector, Temporal Opera?).
There's another well defined concept, pseudo random conglomerations of primes and cofactors, either in a lump of Granite conglomerate, or box of unsifted Sand, the idea is reducible to mathematical expressions. Same applies to "fluid" fields of Uncertainty in otherwise specific resonance interference positioning that becomes turbulence and the Navier-Stokes Equations..
The intuitive reason for the properties of numbers is the temporal vectors of time duration timing modulation, by the naturally occurring superimposed probability, in potential possibilities conception, of whole number base logarithms, in the Superspin-calculations=> antilog-> self-definition numberness context of e-Pi-i continuous creation connection QM-TIMESPACE Principle.
Time is ONE at zero-infinity, and Timing is the hyperfluid state of zero-infinity sum-of-all-histories wave-package probability ONE, from which all phenomena self-define. (P=nP doesn't seem to define itself from the logarithmic fluid state, intuitively)
Put simply, the time duration timing modulation functional probability of Primes and multiples of Primes=> cofactors, are the cause-effect embodiment of the QM-TIMESPACE Principle Universe.., this Mathematical Eternity-now Interval/format.
The Kieth Newman book, "God is a Mathematician", is consequently a degree of fact, because "Mathematics has Substance" in Actuality.
It's somehow so hard to imagine him being a mathematical prodigy (in addition, also actually, a child prodigy, if more precise). He is one and it has been proven that he is a genius. But he looks so normal. Like a normal Asian young adult, just like any one of us (except for the fact that not all of us are Asian, lol). What makes him what he is? His physical appearance is also very pleasing and he seems like a sympathetic, honest and a polite person. I really do find him likeable.
I watched this lecture some days ago already so I just thought I'd drop by and say what I just said. If I had to say something about this particular lecture, I do not have any strong opinions in one way or another. It was a nice basic presentation without any technical detail.
I also stumbled upon Terry's personal blog and saw his mathematical powers in action. I'm a mathematical noob and would like to learn A LOT but, hah, I might never reach the level to even understand any of Terry's mathematical stuff.
25:09 about how to send secret info over a public line, very cool. i never understood public key before.
and keep note he said we do not grant the number 1 the property of primality, as the primes as a group use the number 1 in axiomizing them as a subset of the integers, thus using the number 1 is a self reference hence circular arguement, ie treating 1 as a prime is equally useful as saying 1/1 = 1, which is the required property of an identity element under the operation of division!
Thank you so much Dr. Tao and the organizers. This was an excellent talk.
I feel wonderful to hear this great Mathematician explain math...
I guarantee this man could fix the budget and point our country in the right direction. He is the type of man that would tackle any problem with cold calculating logic, and be smart enough to recruit any assistance he needs to fix any problems he encounters.
No, intellegence in one domain does not lead to intellegence in other domains.
Opera It's within the realm of problem solving, which he's obviously incredible at.
Joshua Bruce Taylor Tao is good at technical problem solving. "Pointing our country in the right direction" is far more difficult and demanding than solving technical problems. Human emotions are very much involved in the job of a powerful leader.
Joshua Bruce Taylor I think not. Many good mathematicians were bad finance ministers, economists, etc.
Joshua Bruce Taylor Hell, those are easy problems. Even I have already solved the damn budget "problem". It's the leadership that counts.
Constance Reid (sister of the brilliant Mathematician who died so tragically young and author of (among other books on popular maths) "Mathematical People") wrote: People have spent more time think-ing about prime numbers than war.
A really cool talk.
Also, there is an *excellent* popular maths book on the Poincaré conjecture. The part that Professor Tau (great name) left out, was that so many people were try-ing to claim the prize (for make-ing what were (it seems) minor corrections to his 3-part proof) that he refused to have anything to do with the money and returned to teaching and research. This is parallel to Richard Feynman's comment about the Nobel Prize he shared that the reward was to work on the problems and make some headway to *understanding* the universe.
thanks, for the post -r.
His name is Tao, which is totally unrelated to the Greek letter tau. It is Chinese (陶) and means pottery.
I spent years searching for the essence of truth through poetry and fiction. Became a lawyer but was miserable every minute I practiced. As I continued searching for that essence, I was led to study mathematics. I feel that math has provided all the solace I had been searching for. If you're reading this and have wondered if mathematics is worth your time and effort, trust me it is. Math is an inexhaustible well of discovery and enlightenment. You will never regret it.
What a charming great scientist. It's amazing that one can reach him on his blog, for advice or to read his thoughts.
+Giorgos Argyropoulos A link to his blog is hereby requested.
+Ole Kristian E terrytao.wordpress.com/
+KeepYouRight It has been removed?
Yi Jiun The link still works.
+ΣΚΡΟΥΤΖ ΜΑΚ ΝΤΑΚ That is called service to the enlightenment of man.
Even though the topic is very deep and difficult to grasp but he simplified it for a large audience. Amazing lecture easy to understand.
Brilliant, Terry has the guts to say "we don't know", very unusual. A brilliant lecture from a young genius
One of the most beautiful lectures. Love it.
19:05 all primes (except numbers 2& 5) contain a last digit of 1, 3, 7 or 9 or to put it in a different way: is n*10 + {-3, -1, +1, +3} !!!
Apart from 2, all primes are odd, which assumes they end in either 1,3,5,7 and 9.
I am not mithered by the fact that there are people in the world more brilliant than me! It doesn't bother me! Nope! Nope! I am quite content! I may try and read a chapter from the book The Identity of Man by J Bronowski, tonight. I find reading difficult!
I failed GCE English with a D Grade from college in 1999 at the age of 24.
Surely the only prime ending in a 5 is 5 itself.
Because we use decimal system, as 10 is divisible by 5. If we use another basis, it would be different.
the encryption analogy kind of blew my mind
Thank you, UCLA, for posting this video. Terrence Tao and his work has further inspired me to pursue mathematics, I someday wish to come to UCLA to take courses or go to lectures under Mr. Tao.
How have u been?
Jesus loves you
I listen to this to help me fall asleep every night
Yeah mod functions can change things a lot. It's a simple concept though, which is used a lot in maths but not taught in schools. All you do for mod P is divide by P and keep the remainder. For example, our clocks use mod 12, so if 25 hours have passed, we divide by 12 and keep only the remainder. Thus, the time shows 1 hour later.
An elegant explanation of private and public keys in computer encryption :)
Such a nice guy and a good lecturer!
The only problem is he isn't too confident
+Santiago Arce Of course not, confidence is highly correlated with low intelligence. The more intelligent a person is the more anxiety they will generally have as they realize how many things in the world can go wrong while most people are completely oblivious. Also, most geniuses think they are stupid as unlike most people they are aware of their own ignorance.
that is true
I meant the tone it created isn't really stable
Very good
7:00 this was so cool “a chess player may offer you his rook or bishop to win the game but a mathematician offers the game itself and still wins”
I love this stuff. Pure genius. The great ones are very humble. I was fortunate to meet some of them as a young child (Weil, Borel, Atiyah, Bombieri, Godel … all at IAS (Princeton) ) where my dad spent some years.
Omg you met Godel I’m so jealous...haha but seriously that’s awesome
At age 7 he wrote a Basic programme about Fibonacci numbers in which he first got players to guess the year of birth of Fibonacci and if they were much to late the programme responded _"Fibonacci has gone to heaven."_ In this presentation he talks about _"God does not play dice..."_ I wonder if he has considered the following:
Mathematics reveals many patterns in the numbers, why? Answer, patterns mean what we are seeing is a non-random field or fields of concepts which are related to our reality in some way. Non randomness in thermodynamics means *order* and it is possible to show that all order comes from information and all information comes from a mind, (Ref Max Planck).
So is this a mathematical proof of Gods existence?
Please watch this Prime Numbers in Holy Quran and Nature --- th-cam.com/video/qAWpApzxa_I/w-d-xo.html
There is a verse in Holy Quran Chapter 59 verse 23 with most number of God's names (Attributes) i.e. 8 names.
He is Allah, other than whom there is no deity, the Sovereign,1 the Pure,2 the Perfection,3 the Grantor of Security,4 the Overseer,5 the Exalted in Might,6 the Compeller,7 the Superior.8 Exalted is Allah above whatever they associate with Him.
Few prime number facts:
1) 59 is a prime number
2) 23 is a prime number
3) This verse has 19 words in Arabic 19 is another prime number.
4) 8th prime number is 19
5) Concatenate 59, 23 we get 5923 a prime number
6) Sum of the digits 5+9+2+3 = 19 a prime number
7) Add 8 to 23 we get 31 a prime number.
8) Add 8 to 59 we get 67 another prime number.
9) Concatenate 8 with 23 we get 823 a prime number.
10) Concatenate 8 with 59 we get 859 a prime number.
11) Add 59, 23 and 19 we get 101 another prime number.
12) Add 58, 23, 19 and 8 we get 109 another prime number.
This shows that as a number grows faster the density of prime gets lesser?.what one can infer or what about the significance is ,one
can draw from this statement
Thank you for this very much for this video. The video shows that pi is approximately 22 / 7. This value is approximately 3.14. Using the properties of this value we can compute prime numbers in sequence, which is based on the existing computing capability. The formula was an algorithm, that was developed by a well known mathematician. Using his formula and the method that I discovered, I can compute prime numbers in sequence using 22 / 7 .
can you explain this method?
19:27 aw come on man, why you gotta creepy zoom
Terrence, a brilliant mathematician.
7:51, Euclid proved (by contradiction) that 2, 3, 5 were not the only prime by multiplying then adding or subtracting one (2x3x5+1 or -1) thus creating 31 and 29 which are two prime numbers since if 31 and 29 WERE NOT PRIME, then by the fundamental theorem of arithmetic which states that every positive integer can be expressed as a product of at least one prime then 31 and 29 should have been, but they could not.
That is, if 31 and 29 were not prime then they could be expressed as a product using 2 or 3 or 5 or DIVISIBLE BY 2,3, OR 5. Since they can't then the fundamental theorem of arithmetic would have been violated. Therefore 2, 3, and 5 were not the only prime.
Terence Tao is the greatest living Mathematician.
and?
Colombo Man one of, not ‘the’
@@kenirving5240 THE. 😳
One of them. I respect him a great deal. Would love to meet him.
I think I was channeling a little Douglas Adams with that thought. But I'm not even exaggerating: math is beyond comprehension in it's beauty and complexity. There's symmetry, fractals, recurring themes and hidden spaces everywhere. It's like an infinite cathedral built at the height of the late medieval. My apologies if you already know this; I'm taking some classes on modular forms and I'm just beginning to wrap my head around the symmetries and relationships.
He's such a great teacher in a way that, despite his problems with the idiom (also he speaks too fast) and his obvious shyness, he can make very difficult math problems sound easier than they really are, also he makes you want to know more...
I HUMBLY LOVE YOU PROFESSOR TAO. INFACT YOU SAVED MY LIFE.
26:43 A neat trick and analogy! This should be listed in every schoolchild's book of puzzlers like the "get the people across the river" game.
Because I am also a programmer, I wrote 2 applications to demonstrate how Diffie-Hellman works and how RSA works. I wrote my own large integer math library in C to aid with the effort. I also used a large prime generator based on a Rabin Miller test. It can handle 100 digits easily.
[-well-known result-] p.s. what does it sound like when you play the "music of the primes"... play a sample for us...
Actually, 10, ten, is very special in number theory-there are constructions that work only for radixes 2 and 5 whence 10, e.g. dragon curves by 90°, (radix 3 works at 60°),... (P.S. I tested radixes 2 and 5 but not radices 2 and 5 together..., and radix 4 closed up...)
God delivered this extraordinary human being. It is not just his outstanding talent, but because of his impressive character!
Pedro Fernandez you are too stupid to appreciate a genius such as his. Please stop breathing the precious oxygen that should be saved for those who aren't grossly immoral narcissistic schizophrenic ignoramuses
God does not exist
jordan rasmussen
my comment's better
lol tru
+bob smith Pretty tough behind a keyboard aren't you.
Thanks TH-cam for the recommendation. I'm now part of Mathematician family.
42:30 k^k Would be the inefficient bound given large k, as lim (trash^k)/(k^k) as k->∞ is 0. The trash^k is still interesting despite being terrible for small values of k.
In fact progressions of seven seems to be very easy... It's in fact already shown as progression of 6 at the end like 7, 157, 307, 457, 607, 757 however just attach 907 to it and [7, 157, 307, 457, 607, 757, 907] you have prg. 7
Tao comes in at 2:40
The prime sequence is based off of a sieve from the first 2 primes (2&3) : 2-4-2-4-2....with the only exception being a prime multiplied by a prime. Ex: 5,7,11,13,17,19,23, (25 = 5*5), 29,31,(35 = 5*7),37,41,43,47,(49=7*7),53,(55=5*11).You can use the arctangent of the reciprocal of the prime number to define the azimuth for these exceptions.
You are literally genius
There is no way You read my comment after 11Long years
But sir that literally crazy
id really like to study under this guy he is part Australian so I followed his career really inspirational
I read somewhere that he could be working on proving or disproving the Riemann Hypothesis. Hopefully, I am still around when he eventually accomplished a feat several generations of the most brilliant mathematicians has attempted to do.
he should write a book. "The Tao of Mathematics" :D HAHAHHAHAHAHA!
He is faster than Bruce Lee in some way.
Collatz conjecture that oscillate between even number divided by half becoming a odd number follow 3x+1 that follow a reduction towards number 1 skewing seems to be very interesting analogy starting from any infinite number following time stepping can be compared with Kuprekar constant stability at 1694 as even number blocking once for all in between maxima and minima finally reduced to 1694 but not a prime number.Any chemical bonding oscillating along frequency of natural vibration will destruct itself the the very nature of chemical bonding as applicable in cancer therapy.Any chemical bonding oscillating along multiple harmonics of natural bring forth a destructive property.
Sankaravelayudhan Nandakumar
Sankaravelayudhan Nandakumar
FORMULA OF PRIME NUMBERS
Positive integers which are not members of arithmetic progressions:
Q(ik)=a(i)+b(i)*k a(i)=6*i^2-1; b(i)=6*i-1
R(ik)=a(i)+c(i)*k c(i)=6*i+1
Are indexes P of all prime numbers in the sequence S1(P)=6*P+5; i=1, 2, 3,…; P=0, 1, 2,…, k=0, 1,2,…
Positive integers which are not members of arithmetic progressions:
T(ik)=d(i)+b(i)*k d(i)=a(i)-2*i;
U(ik)=f(i)+c(i)*k f(i)=a(i)+2*i;
Are indexes P of all prime numbers in the sequence S2(P)=6*P+7; i=1, 2, 3,…; P=0, 1, 2,…, k=0, 1,2,…
OMG, this guy is a fields medal winner. He deserved it.
Terry Tao is the real real Will Hunting.
+lgbtTV5 I have heard of Ramanujan. I was referencing the similarity regarding their math intrests. Also, if you have Netflix you can watch it. ps: please check out my TH-cam channel I do math and science on it
+Tyler Dipietro And there math genius
Basically it was William James Sidis 😂😂
Sidis was.
True dat. I was only kidding.
In your wisdom may you find a path of light for us all to follow my friend.
Distribution of primes is explicitly defined (without randomness of any kind) by the following statement (MATRIX DEFINITION OF PRIME NUMBERS):
There are two 2-dimensional arrays:
|5 10 15 20 ..|
6i^2-1+(6i-1)(j-1)= |23 34 45 56...|
|53 70 87 104...|
|95 118 141 164...|
|149 178 207 236...|
|... ... ... ... |
| 5 12 19 26 ..|
6i^2-1+(6i+1)(j-1)= |23 36 49 62...|
|53 72 91 110...|
|95 120 145 170...|
|149 180 211 242...|
|... ... ... ... |
Positive integers not contained in these arrays are indexes p of all prime numbers in the sequence S1(p)=6p+5,
i.e. p=0, 1, 2, 3, 4, , 6, 7, 8, 9, , 11, , 13, 14, , 16, 17, 18, , , 21, 22, , 24, , , 27, 28, 29, ...
and primes are: 5, 11, 17. 23, 29, , 41, 47, 53, 59, , 71, , 83, 89, , 101, 107, 113, , , 131, 137, , 149, , , 167, 173, 179, ....
There are two 2-dimensional arrays:
|3 8 13 18 ..|
6i^2-1-2i+(6i-1)(j-1)= |19 30 41 52...|
|47 64 81 98...|
|87 110 133 156...|
|139 168 197 226...|
|... ... ... ... |
| 7 14 21 28 ..|
6i^2-1+2i+(6i+1)(j-1)= |27 40 53 66...|
|59 78 97 116..|
|103 128 153 178...|
|159 190 221 252...|
| ... ... ... ... |
Positive integers not contained in these arrays are indexes p of all prime numbers in the sequence S2(p)=6p+7,
i.e. p=0, 1, 2, , 4, 5, 6, , , 9, 10, 11, 12, , , 15 , 16, 17, , , 20, , 22, , 24, 25 , 26, , , 29, ...
and primes are: 7, 13, 19. , 31, 37, 43, , , 61, 67, 73, 79, , , 97, 103,109, , , 127, , 139, , 151, 157, 163, , , 181 ....
So, in order to find primes we need not to perform any calculations, we simply have to find positive integers which do not appear in these four arrays.
See:
ijmcr.in/index.php/current-issue/86-title-matrix-sieve-new-algorithm-for-finding-prime-numbers
www.planet-source-code.com/vb/scripts/ShowCode.asp?txtCodeId=13752&lngWId=3
Well, that's a sieve. The problem is that calculating, storing and scanning those arrays is of the order of n^2*log(n). Which is much worse than O(n + n*log(log((n))) that the classical Erasthotenes sieve requires, never mind more efficient sieving methods.
It also provides no information whatever on the large-scale _distribution_ (as opposed to computation) of primes.
BTW - your link to IJMCR does not work.
hi thanks
He is full of awe at his own presence
Why right ear!
This is a "core Mathematical substance" illumination of basic QM manifestation. A confluence-collider of concepts in the general Conception of Time. This distinguishes the "sides" of wave-particle duality that has no absolute sides, the mutual synch-alignment of amplitude and frequency Primes in a superimposed line-of-sight superposition of the concept of material Number, and the empirical timing-synch of precedents, in metastable sustainability.., a coexistence parallel resonance that's mutual simultaneous alignment, and re-evaluation, corresponding active connection existence.
So there's also a "physical manifestation" reason not to use 1 as a Prime, which is because of exponential time function active connection, and natural logarithmic condensation wave-particle uncertainty, "designed" by the surrounding wave-field projection+/-, of superimposed Primes. Ie it's the cause-effect of Temporal Superposition Synchronisation shape shifting positioning.., around the instantaneous .dt infinitesimal potential possibilities of the e-Pi-i pivotal Planck Dimension, and zero-infinity Singularity Vanishing Point Perspective Positioning, a structured time duration position differentiation by potentially mathematically pure.., relative timing motion integration functions.
Therefore the Minimum Time, motionless in Time trajectory that is the Omni directional and dimensional Origin @.dt, is self-defining infinitely distributed vanishing point positioning, singularity function, probability of constant primary combinations of synchronisation. WYSIWYG Physics of pulsed time duration, Quantitative Mechanism.
The rationale and reasoning of the lecture shows that because Primes are calculated from the POV of Mathematical calculations of Idealized Real Numbers, that the existence of the infinite objective, Prime, line of sight analog of ONE P, is the definition of an impossible positioning from outside of the Universe. Ie, the hypothetical Big Bang Singularity. (Which is a "legitimate belief" according to empirical evidence, and an arbitary Mathematical "Accounting" choice within the e-Pi-i format)
This mans IQ is so high, he isn't considered smart, proficient, genius, or even extreme genius. He is in a category all his known named unmeasurable genius (around 230).
not true but he is a genius
what about Grigori Perelman?
I started a project where I'm took the base video and started cutting out ums, uhs, and repeated words. Already got it down to 42:25. Fascinating talk, though.
And I thought I was smart...
I got 80 in an iq test. Apparently I'm "Borderline retarded".
A few people are missing the point here
We consider a "largest" prime, p. Then we examine N, the product of ALL the primes up to and including p, plus 1.
N = (2 x 3 x 5 x 7 x ... x p) + 1.
If N is prime, it is a prime greater than p and so p is not the largest prime after all. If N is not prime, then it has prime factors. And its prime factors are greater than p, because p and all the smaller primes leave a remainder of 1 when they divide N. So, the prime factors of N are greater than p. QED.
of course there are only finite amount of primes, just watch revenge of the fallen :p
It isn’t always the math material itself which merely makes the subject so fucking scary to people, it’s living breathing talking titans like tao who make his level of expertise incomprehensibly unachievable, but we’re still glad people like him exist to conquer such a universal beast
conquer what
Pn is approx nLog(n)
Entropy = kLog(n)
Interesting.....
You will find ergodic theory interesting then, since it is the mathematical way of dealing with 'random large systems', such as thermodynamics.
EinSofQuester Is this a joke? Those two equations couldn't be any less related. The Boltzmann constant k is just a proportionality constant, whereas n obviously varies. Those two quantities are not even proportional.
Reposting and slight editing of recent mathematical ideas into one post:
Split-complex numbers relate to the diagonality (like how it's expressed on Anakin's lightsaber) of ring/cylindrical singularities and to why the 6 corner/cusp singularities in dark matter must alternate.
The so-called triplex numbers deal with how energy is transferred between particles and bodies and how an increase in energy also increases the apparent mass.
Dual numbers relate to Euler's Identity, where the thin mass is cancelling most of the attractive and repulsive forces. The imaginary number is mass in stable particles of any conformation. In Big Bounce physics, dual numbers relate to how the attractive and repulsive forces work together to turn the matter that we normally think of into dark matter.
Complex numbers = vertical asymptote. Split-complex numbers = vertical tangent. Dual numbers = vertical line. These algebras can be simply thought of as tensors. Delanges sectrices can be thought of as opposites of vertical asymptotes. Ceva sectrices as opposites of vertical tangents, and Maclaurin sectrices as opposites of vertical lines.
The natural logarithm of the imaginary number is pi divided by 2 radians times i. This means that, at whatever point of stable matter other than at a singularity, the attractive or repulsive force being emitted is perpendicular to the "plane" of mass.
In Big Bounce physics, this corresponds to how particles "crystalize" into stacks where a central particle is greatly pressured to degenerate by another particle that is in front, another behind, another to the left, another to the right, another on top, and another below. Dark matter is formed quickly afterwards.
Ramanujan Infinite Sum (of the natural numbers): during a Big Crunch, the smaller, central black holes, not the dominating black holes, are about a twelfth of the total mass involved. Dark matter has its singularities pressed into existence, while baryonic matter is formed by its singularities. This also relates to 12 stacked surrounding universes that are similar to our own "observable universe" - an infinite number of stacked universes that bleed into each other and maintain an equilibrium of Big Bounce events.
i to the i power: the "Big Bang mass", somewhat reminiscent of Swiss cheese, has dark matter flaking off, exerting a spin that mostly cancels out, leaving potential energy, and necessarily in a tangential fashion. This is closely related to what the natural logarithm of the imaginary number represents.
Mediants are important to understanding the Big Crunch side of a Big Bounce event. Black holes have locked up, with these "particles" surrounding and pressuring each other. Black holes get flattened into unstable conformations that can be considered fractions, to form the dark matter known from our Inflationary Epoch. Sectrices are inversely related, as they deal with dark matter being broken up, not added like the implosive, flattened "black hole shrapnel" of mediants.
Ford circles relate to mediants. Tangential circles, tethered to a line.
Sectrices: the families of curves deal with black holes and dark matter. (The Fibonacci spiral deals with how dark matter is degenerated/broken up, with supernovae, and forming black holes. The Golden spiral deals with black holes being flattened into dark matter during a Big Bounce event.) The Archimedean spiral deals with black holes and their spins before and after a reshuffling from cubic to the most dense arrangement, during a Big Crunch. The Dinostratus quadratrix deals with the dark matter being broken up by ripples of energy imparted by outer (of the central mass) black holes, allowing the dark matter to unstack, and the laminar flow of dark matter (the Inflationary Epoch) and dark matter itself being broken up by lingering black holes.
Delanges sectrices (family of curves): dark matter has its "bubbles" force a rapid flaking off - the main driving force of the Big Bang.
Ceva sectrices (family of curves): spun up dark matter breaks into primordial black holes and smaller, galactic-sized dark matter and other, typically thought of matter.
Maclaurin sectrices (family of curves): dark matter gets slowed down, unstable, and broken up by black holes.
Jimi Hendrix's "Little Wing". Little wing = Maclaurin sectrix. Butterflies = Ceva sectrix. Zebras = Dinostratus quadratrix. Moonbeams = Delanges sectrix. Jimi was experienced and "tricky".
Jimi was commenting on dark matter. How it could be destabilized by being slowed down, spun up, broken up by lingering black holes, or flaked off. (The Delanges trisectrix also corresponds to stable atomic nuclei.)
Dark matter, on the stellar scale, are broken up by supernovae. Our solar system was seeded with the heavier elements from a supernova.
I'm happily surprised to figure out sectrices. Trisectrices are another thing. More complex (algebras) and I don't know if I have all the curves available to use in analyzing them. I have made some progress, but have more to discern. I can see Fibonacci spirals relating to the trisectrices.
The Clausen function of order 2: black holes and rarified singularities are becoming more and more commonplace.
Doyle's constant for the potential energy of a Big Bounce event: 21.892876
Also known as e to the (e + 1/e) power.
At the eth root of e, the black holes are stacked as densely as possible. I suspect Ramanujan's Infinite Sum connects a reshuffling from the solution to the Basel problem and a transfer of mass to centralized black holes. Other than the relatively small amount of kinetic energy of black holes being flattened into dark matter, the only energy is potential energy, then: 1 (squared)/(e to the e power), dark matter singularities have formed and thus with the help of Ramanujan, again, create "bubbles", leading to the Big Bang part of the Big Bounce event.
My constant is the chronological ratio of these events. This ratio applies to potential energy over kinetic energy just before a Big Bang event.
Methods of arbitrary angle trisection: Neusis construction relates to how dark matter has its corner/cusp singularities create "bubbles", driving a Big Bang event. Repetitious bisection relates to dark matter spinning so violently that it breaks, leaving smaller dark matter, primordial black holes, and other more familiar matter, and to how black holes can orbit other black holes and then merge. It also relates to how dark matter can be slowed down. Belows method (similar to Sylvester's Link Fan) relates to black holes being locked up in a cubic arrangement just before a positional jostling fitting with Ramanujan's Infinite Sum.
General relativity: 8 shapes, as dictated by the equation? 4 general shapes, but with a variation of membranous or a filament? Dark matter mostly flat, with its 6 alternating corner/cusp edge singularities. Neutrons like if a balloon had two ends, for blowing it up. Protons with aligned singularities, and electrons with just a lone cylindrical singularity?
Prime numbers in polar coordinates: note the missing arms and the missing radials. Matter spiraling in, degenerating? Matter radiating out - the laminar flow of dark matter in an Inflationary Epoch? Corner/cusp and ring/cylinder types of singularities. Connection to Big Bounce theory?
"Operation -- Annihilate!", from the first season of the original Star Trek: was that all about dark matter and the cosmic microwave background radiation? Anakin Skywalker connection?
I like the conspiracy analogy.
To say that there is randomness in the primes sounds so strange and yet it's so wonderful to know.
Either prime numbers being unpredictable is proof that randomness is an inherent characteristic of the universe, or it is yet another example of a problem with our invented numerical system that is not an intrinsic part of nature.
I have though long and hard about that question myself and I think that is our numerical system should not exist in nature. The theory of relativity suggests this
+Ethan Cemer relativity describes > spacetime follows > dimension > there are lots of them
+Jose Diola numerical system describes > spacetime OR numerical system describes > dimension
+Jose Diola dimension > there are lots of them > are all nature > exists because you pondered > you pondered because you are outside looking in > which a glimpse of omnipotence > that is GOD..
+Monochromicornicopia I don't think you could have a generally usable number system that allowed for simple, efficient arithmetic (the way digital numbers do) in which prime numbers were orderly and easy to generate. You could imagine a number system where each number is expressed as the product of its prime factors (Ex. p(1)^2 * p(2)^7 * p(4) = 2^2 * 3^7 * 7). Representing primes would become a breeze, but addition and subtraction would become a nightmare.
Math is knowledge and knowledge is power, this is the “will to power.”
I smoked some pot and as always meditated upon reality. I could actually grasp the pattern of all the prime numbers but I can not remember nor explain; but at the time it was clear and very easy to understand how and why all prime numbers seems to appear randonmly and how they form everything there is in the material world up to some levels above where it is yet not spiritual but is mid way, for example the part and level of the universe where dreams occur.. I am positive that the insight I had about prime numbers is the final answer to mathematics, but I unfortunately cant recall the main ideas.. I can recall something that was fundamental for this understanding and it has to do with the real nature of numbers itself. I remember realizing the existance of only 3 fundamentals for creating all numbers, something like binary systems where the idea of 1 (one) is to the masculine principle and the idea of 0 (zero) the negative or feminine. the intercourse of both creates the plurality of all existing numbers.. And I also remember I could understand how and in what degree each of this 2 (1 and 0 ) would relate to each other and create "pockets" where each of this "pockets" would be enclosed by a positive prime in the beggining and a negative prime in the end enclosing this pocket.. for example in between the 2 and the 3 is one individual pocket the 3 and the 5 is another pocket and so on for eternity revealing all primes.. I can recall the theoretical part of all but I cant grasp the insight that made me recite primes for almost one hour amazed becouse I didnt know primes.. I actually could tell primes forever without calculating anything, thus I know it was not a pot trip, it was real ... It was really scary and I remember felling shivers all over my spine that felt like jolts of real electricit and my body was somehow numb.. It really felt like an extraordinary degree of inteligence where in the realms of numbers I could understand absolutly everything yet it was something really simple and fundamental.. I wish I could think of this again.. But the more I try when I get high the harder it gets to recall .. I guess it something sponteneous;; But if anyone into mathematics, try to think of the numbers as only 2 "beings" inteligent and living beings habitating higher dimentions of our personal universe. Try to imagine them "having sex" yeas its funny but I remember imagining numbers having sex and really "having a swing party" thats how I can describe my thoughts at the moment, than it was unfolding into understanding and seem where each prime would "give birth " to the created numbers.. It was in other words like looking into a lineage of numbers where the first ones to conceive would first conceive primes and the primes would conceive "lesser beings" . I know it sounds crazy, but at the moment I was really concerned about my sanity upon this thoughts..
Dude I know what you mean, I feel like if more people burned up and did math or science or art or w.e as opposed to just sit there then alot more things will be discovered. Paul Erdos said that when he took amphetamines he will look at a piece of paper and have many ideas. I'm studying Math at University of Toronto and when I took M and went to the club, for some reason my interest and the way the perspectives I saw math opened up, it was weird, but I know what you're sort of saying.
i think u smoked lot of pot not "some" :)
Fernando Penas get help. U r psycho
Next stop: LSD
I understand what you're talking about, I was on LSD at the time. It's very difficult to communicate your experience from a different dimension; it's like it's the golden rule (you can feel the truth but not allowed to share it. People have to discover the truth for themselves.) 0 and 1 is the key. The universe is about dualities. When I was in this alternate dimension under the influence of psychedelics I was free from all forces of the physical world. You feel as one with all and everything is clear. I've felt all spectrums of good and bad / high and low whilst under and they go together. At my highest euphoria I discovered the secret and became number 1. One key tip I've learn't that I can share with all is that be 100% with any decision you make in life; whether that decision takes an instant or a lifetime.
26.43: Why doesn't Alice simply subsequently mail the key and save a step?
Reductio ad absurdum, not absurdam. But it's ok, Latin isn't a prerequisite these days for being a genius in maths.
+Daniel Pavlovsky Dear Daniel, I didn't have the luck to study Latin in my school years (or on my own), so I'm not sure on which grammatical rule the phrase "reduction ad absurdum" obeys. I just keep it in mind along with a dosen more which are used in science and mathematics (and actually I usually google it to make sure I get it right). A very stupid comment anyways, under such an illuminating video.
Get a life this not English
You can find interesting facts and puzzles about Prime Numbers and Magic Squares, Smith Numbers, and Arithmetic and Palindromic Primes on Glenn Westmore's blog.
He is good, but definitely not better than me.
That's true! We now have so many people in the world, that there will be enough people to do all the important and interesting things in life.
The audio on this is not correctly recorded -- damn it! Come on, you have this amazing man and you can't bother to get the sound right! Inexcusable!
What is prime in terms of matter content is the distribution of matter types. Matter can take any one of the prime forms only and others are molecules or mixture. Usually primes occur as cluster like gold and silver and iron but the low primes are carbon and oxygen.
Twin primes are isotopes.
Randomness in primes are because of sequences are always waves and waves can get to a higher order if a trough meets a trough or amplitudes are in sync. Or frequencies.
A beautiful man with a beautiful mind. All my consideration!
Very interesting presentation - I liked so much.
Im pretty sure there isn't a finite formula that can describe primes, but i think they can generate a formula F(x) which can determine how another formula G(x) changes, G(x) being the formula for the nth prime.
..Yes, he can. If he lock the box and send it back to Alis before reaching Bob, he read or alternate the message then put his lock and send it to Bob..
This is probably dumb, but could you see the first number as G to the A call it (#1). Then see the number Bob sends back which is G to the AB call it (#2). Then ask to what power do you have to raise #1 to get to #2. This will find B. Then when Alice sends it back (it'll be sent back as G to the B). All you have to do is take the B root, which you know, and you'll get G. Maybe this Mod P, stuff prevents that.
1:n^2
2 :n
3: n+(n+1)=2n+1
4:n^2+2n+1=(n+1)^2
Riemann's-Euclid's zeta function ζ(s) = Σ(1/nˢ) has curious parallel in a disproof of 0.999... = 1.000... because Σ(9/(10-ε)ⁿ) (ε→0) eventually rounds up a carry though in its limit looks okay like the difference between pointwise and uniform convergence...