Terence Tao on Prime Numbers
ฝัง
- เผยแพร่เมื่อ 22 พ.ย. 2024
- The following clip is a highlight. To view the full talk visit www.abc.net.au/...
Former child prodigy Terence Tao has grown up to be one of the world's greatest living mathematicians. At 24 he became the youngest ever person appointed full professor at UCLA, and at the tender age of 31 he was awarded the maths world's highest honour, the Fields medal. Back in his childhood home of Australia, he visited the ANU to deliver this fascinating talk about one of his favourite subjects, prime numbers.
A great mathematician can be gauged by his inability to make eye contact. This guy is a boss.
Is more better or less?
follow up question, how can you tell how much/little eye contact he makes from this video?
Wth lol
Lol
Many geniuses are on the spectrum.. hence the lack of direct eye contact.
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...
When this guy was 7 years old he could do math stuff at the level of a 24 year old
"I don't even know everything going on" - fear strikes the crowd
Feeeeaaaarrrrr
Could listen to him explain math all day.
gris186
Shits boring and common sense
@@bustownbc2787 This is a terrible attitude for exploring math
@@MixMastaCopyCat
After some Math they're gonna say Shits boring and explodes head
Yup I could listen all day and still not understand math haha.
Mr tao is my inspiration and indeed my fav mathematician,I listen to him very much
Terence Tao is a top mathematician; the mathematics of 21st century will be remembered with his name. I've read his PhD thesis. Normally, a PhD thesis must be about 170 pages but his was roughly 40 pages and accepted. He's a genius harmonic analyst, which let him prove, along with Ben Green, that any residue class of any modulus has infinitely many primes. Also, he's a chief editor of one of the journals of the AMS. Oh, by the way, his annual worth is 463 000 $.
If this is true, that's crazy!
@Anderson Jeffrey He's not paid for writing on blackboard dude, he's paid for advancing the knowledge for humanity. He's well underpaid comparing the celebrities, athletes and politicians.
@Anderson Jeffrey That club of high rollers have gatekeeping mechanisms (*cough* income taxes *cough) that prevent individuals even with the fattest paychecks from getting in or sustaining their position there. It's a different pecking order entirely.
@Anderson Jeffrey as @Zero says, this guy is quite underpaid compared to his advances and all he is given to human knowledge. Is not just writing on a blackboard.
You could say stupid things like that about sports for example.
@Anderson Jeffrey totally agree that there are people out there doing great stuff, for example, a lot of scientists with pretty mediocre salaries due to bad politics. Tao's work is great and I think he deserves that, as I also think there are a lot of people just getting to much
3:55 I didn't know that Euclid was attending Terence's lecture.
@Anderson Jeffrey I was joking
@Anderson Jeffrey The guy on the right looks like Euclid. That's what he meant.
@Anderson Jeffrey Bruh.. is this your first day on the internet? the guy means there is a person in the audience that looks like Euclid...
@Anderson Jeffrey r/whoooosh
@Anderson JeffreyPretty sure everyone got the joke (beside you ofc)
"prove something is true by proving that it is not false"
So obvious, yet so useful
Yeah, Could listen him all day! His comprehensive expression of mathematics is very beautiful plus useful.
Surprisingly insightful. I could follow him quite easily and I'm not a mathematician.
So, you're a good listener... LOL
@@stickyrice2141 shh
I have no idea what he is talking about, but I continue to watch anyway.
its an honor to even be learning from him on youtube
I am wondering, 11 years later, if you would reply to this comment, how crazy would that be
it'd be even crazier if you replied to this one
More crazier if you reply to this one
siuuuuuu
I have no idea how I got here, but this is my third video in a row of him I've watched; and I'm beyond intrigued! What a beautiful mind.
This man is from another planet. Plain and simple.
This is the only video of him where I understood his lecture just because he talked about basic of real numbers also in a beautiful way
Learned about this guy doing research for my math history project (I’m a math major) literally yesterday. This guy is awesome
TH-cam or Google collected your data
"It takes a while to get used to this type of argument." -- says the guy who understood it at the age of 4.
3:04 the most excellent reasoning.
Euclid was a real genius.
Yes he really was a towering genius
I don't mind him being my maths teacher.. he's just so passionate
oh you 'don't mind' him... wow what an honour it would be for him to not be minded by you to teach
@@shucklesors Why must you be an ass? Obviously Adrianus meant, I "WOULDN'T" mind him being my math teacher.
@@shucklesors lol
@@petehenry7878 you do realize how entitled it sounds?, to be the one to "not mind" have a renowned mathematician as your tutor?
@@eurko111 BTW sweetheart, Tao is a professor, a professor is a teacher. Either way he teaches more than one student at a time. Where as a tutor is a private teacher, so if anyone is making any kind of entitled comment, it's you.
It's fascinating to hear that Euclid was "rejecting the null hypothesis" so long ago. This is a fundamental tool in science even today.
I wouldn't exactly think of it this way. Rejecting the null hypothesis just tells us the null hypothesis doesn't fit the data as well as the alternative hypothesis (with high confidence), whereas a contradiction proof says we can't even assume the contrary without arriving at a paradox. One is incompatible with the data we happened to sample, while the other is incompatible with logic itself.
@@JM-us3fr It's fundamentally the same process. We bisect a distribution of possibilities, we demonstrate that one of the possibilities can't be true, so the other must be true.
@@niemand262 you are clearly not a pure math major. That’s ok. But they are NOT “fundamentally the same concept”…🤦🏻♂️
5:04 when you thought Terence will talk about something too complex and advanced(y I hesitated playing this vid) yet end up listening about basic number theory.
he speaks so fast like his brain also thinks like that fast.. Cool!
I have seen so many dumbs speaking very fast
Fool... You clearly are a hypocrite just of what you said. I suggest that you exercise your flawed logic.
Considering tao has one of the highest IQs in human history he should have a hard time putting all of that in words
He speaks too fast.
Terence Tao is the greatest living Mathematician.
ever heard of gregory perelman?
@@jenniferlawrence944 no
@@TravelWorld1 how can you not know who grigory perelmen is. He proved Poincare conjecture. And don't swallow everything Numberphile says.
Perelman is great, but I think Terence Tao is more versatile like Gauss and more collaborative like Erdös.
@@jenniferlawrence944 yeah the guy who turned down 1million and lives in his mums basement?
Had to read that over a couple of times
I'm actually currently learning this in class. I love it !!
He's like roger federer of math
lol
ndk4 they both computers
You mean Federer is the Terence Tao of tennis
Actually the current Nobel Prize mathematician is Arthur Ávila.
more Nadal :-)
He is Bruce Lee of math
He is too great to be compared to some dancing boi
tao of math.
@@maxwellsequation4887 😴
Wonderful!
This feels like a primer to primes for elementary schoolers not college students and professors.
One of my academic heros
Me too. I love Prof. Tao
Great man he can solve each and every sum and problems just because of his mind and memory.
the "memory" is not a thing, it is a matter of how you are
Awesome set induction of how an element or compound is composed of atoms by using concept of prime or fundamental theorem of arithmetic.
"This is abc fora" hits me like a sleep twitch.
I did lol irl
Lol
1059 vieuws ? this guy is a legend ! guys spread this and have it as favorite ! so we promote it ! and give it a 5 star
5:20 what an interesting way of coming to a conclusion. I find that so creative!
Will Crawford thats basically how most math problems get solved: by stating the opposite and proving that this isnt possible after
True, but there are many forms of proofs. There are direct proofs and induction is effective when dealing with sums.
Millennium problems such as reimann hypothesis which is claimed to be proven uses proof by contradiction
There are lots of other theorms which are proved this way, cause in mathematics you have infinitely large number to prove such thing lots of mathematics use this
@@nuc1eu52 Riemann Hypotheshis wasn't proved lol
prime numbers pure elements
How about optimus prime that came to invade our world
Optimus Prime didn't come to invade our world moron, he was trying to save it.
yo surely are a moron
What a cool guy!
Whoa, I get Euclid's proof now! That remainder of 1 is the key!
so much head happening in these comments... must be a rock star+
I saw 2 things in Paris. ET and Rodin Museum. This was very interesting.
I read Simon Singh's "The Simpsons and Their Mathematical Secrets" which mentioned this exact proof, but I find it odd that he didn't mention one thing.
There are two parts of Euclid's discovery. The first is what Tao mentioned which is that if you multiplied all the primes and add 1 it could result in another prime that wasn't part of the original set. You know it wasn't part of the original set because it is much bigger than all of the numbers in the set (for example 31 is much larger than 2, 3, and 5 since you're multiplying them to produce a new number). LONG STORY SHORT: Tao mentioned the first part of the theorem.
What he missed was also amazing. Euclid said that if the number produced by multiplying all the numbers in the set and add one to produce a COMPOSITE number (i.e. not a prime number), then you can come up with even more primes. Let's say you have the set 2, 3, 5, 7, 11, and 13. If you multiply them and add 1, you get 30031. That is a composite number meaning it has factors besides 1 and itself. It turns out its other factors are 59 and 509, which are 2 new primes that were not included in the set.
Why does this always produce new prime numbers?
If you try to divide 30031 by any of the numbers in our set 2, 3, 5, 7, 11 and 13, then the remainder will always be 1 (which makes sense). Therefore, if a composite number is formed by multiplying all the primes and adding 1, it will always produce at least 2 new primes.
I see that a lot of the comments are either saying that Tao's fast talking/stuttering is due to his fast mind or that they didn't understand anything, so I don't think this comment really belongs here. Respect the man's content.
that is an addendum if anything, since the "first part" already proves the theorem by LEM.
oh I see what you mean, you werent talking about expliciting them.
the thing is this proof is generally given in such a way that the second step is considered obvious when I agree it should not be.
I'm glad youtube offers the option to slow down 0.75x
Adelar Scheidt loool
😂
😂😂😂😂
He does sound so much better, and understandable.
You're a "practical" genius
Uploaded on my birthday
I wonder if Terence is able to calculate as fast if not faster than Ramanujam.. coz both of them are masters in number theory
This guy and Dr James Maynard intonate the same when they say the word "Prime" .
I love this man
But (2 x 3 x 5 x 7 x 11 x 13 x 17) + 1 is not prime because You can divide it by 19
Im sure he said em.. a prime number of times
He’s simply the best mathematician
Perelman
Terence Tao is one of the most smartest people in the world and yet still gets nervous talking to the audience.
I'm clearly missing and important piece of information. It seems like we can generate new largest primes by just multiplying all of the prime numbers up to the largest then adding one. Or is that outside of current computational abilities?
If we had a list of all the prime numbers up to a certain point, then yes we could do that. The issue is that you can't be missing any primes up to the largest one you know about.
Suppose you knew 2 and 7 are prime, but didn't know that 3 or 5 are prime. Then multiplying all the primes you know about (2 and 7), then adding one you would get 2*7+1=14+1=15, but 15 is not prime.
The largest prime number known currently is 2^74207281 − 1, which is 22,338,618 digits long. We could find a larger prime if we knew all of the primes smaller than this one, but it would take more effort to find all the missing primes than trying to compute a bigger one by other methods.
Martin Derige the number that you get from multiplying all the primes is not guaranteed to be a prime number, just to have a previously unknown prime factor.
There are a coupe of problems. One is, that primes tend to be more or less randomly distributed. Using this method on its own may leave gaps. The second is, as you mentioned, computation. Integer multiplication is a very fast operation, however, any machine would choke up for months trying to multiply 10^25 numbers for example. It's a good way to start, but it's not feasible in the long term.
@@thiantromp6607 :: Right. It means that none of the known primes is a factor of that product-plus-one number, so it is either a prime, or has a prime factor larger than the largest known prime (and of course, smaller than that product-plus-one number.)
Terence Tao defenitely needs a beard
Bro looks like he gonna live till 120
Answer to Riemann
The answer to the Riemann Hypothesis is Infinity.
Infinity times infinity equals infinity to the power of infinity.
Infinity squared equals infinity to the power of infinity.
If 2 is a prime then so is infinity.
You are all welcome.
All numbers are comprised of Primes but not all numbers are comprised of non-Primes. Primes make up the building blocks of infinity. They are telling the other numbers what to do. People are looking at numbers and infinity incorrectly. Infinity is Prime so case closed on the Hypothesis.
He wouldn't mind saving me from IP class and doing my homework would he?
thankssss you
The argument is very subtle. If you take all the primes until some number N, the construct P again as the product of all those +1, then this number is *not* always a prime. (I believed that for too long)
of course the number of primes until N has to be an uneven number, since each prime is uneven, and even numbers cannot be prime (beside 2)
GREATEST OF MATH TAO
The moment I noticed his habit of constantly touching his chin unconsciously I knew this man is a Genius.
Full talk somewhere? Link in description doesn't work.
Beautifull ❤️ just beautiful
wow, it must be amazing :)
i live in Zvolen, Slovakia
Che ammirazione!! Super!
im ur 1000th subscriber
Rất thông minh. 🦄😚😑😑😐🎏🎏🙂🦄☺️😚☺️😐😚☺️😍😑🎁😍😑🎁🤗🤗🐯
He and each time he touches his chin; shows his quest to explain more and more what he knows. But non superpositionary vocal conversation has some limits..
Sir factors of 1 are( cost + i sint ) and ( cos t-- i sint ) . Where i^2 = --1
Interesting guy
What I wonder is why do we consider natural numbers as the product of primes instead of the sum of 1s? For example, instead of considering 8 as 2 x 2 x 2, why don't we consider it as 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 instead? By doing it this way, there would be no need for prime numbers, a sum of 1s is all we would need. Just a thought btw, because to me it seems that the rule "only divisible by 1 and itself and not equal to 1" is arbitrary.
Mahikan Nakiham
The two most important structures on natural numbers are addition and multiplication.
While 1 might be the additive building block for all natural numbers, the prime numbers are the multiplicative building blocks for all natural numbers.
This fact is used all over number theory and even other fields of mathematics.
For instance, finding the greatest common divisor of two numbers is equivalent to finding their common multiplicative building blocks.
In English: you can find the greatest common divisor of two numbers by looking at their prime factorizations and finding their common factors.
Note that this is not the fastest way to determine the greatest common divisor, it is just an example of the usage of prime numbers
Thanks for the explanation. I understand that primes are the multiplicative building blocks but isn't multiplication just a series of additions? For exemple, 2 x 2 is just 2 added 2 times. So to me, multiplication just seems like a concept we invented to facilitate calculations but doesn't seem to be part of the real world.
the natural numbers are in fact mainly constructed by successors
I only watched the prime number parts of the video starting at 0:02
From the description: "To view the full talk visit [broken link]" Any chance this will be fixed?
i was lost from 0:05 to 5:29 .. the rest i understood
haha what is left lol
Un brasileño reveló el secreto de los números primos, con mi respeto a todos los aquí presentes, ¿qué impacto tendría decir que algunos números no son primos? y los primos gemelos no existen? con dos fórmulas estándar dentro de una progresión aritmética (PA).
dos; 19; 41; 59; 61; 79; 101; 139; 179; 181; 199; 239; 241; 281; 359; 401; 419; 421; 439; 461; 479; 499; 521; 541; 599; 601; 619; 641; 659; 661; 701; 719; 739; 761; 821; 839; 859; 881; 919; 941; 1019; 1021; 1039; 1061; 1181; 1201; 1259; 1279; 1301; 1319; 1321; 1361; 1381; 1399; 1439; 1459; 1481; 1499; 1559; 1579; 1601; 1619; 1621; 1699; 1721; 1741; 1759; 1801; 1861; 1879; 1901; 1979;
En mi concepto, un número para ser primo tiene que ser factorizado sólo con el número primo en sí, de menor a mayor, y de mayor a menor, por lo que será considerado un número primo... como sancioné una ley que siempre debe ser respetado... .por lo que solo habrá un divisor para cada número primo factorizado... por lo tanto solo será divisible por el número primo mismo... sin comprometer la seguridad de un número cifrado, pero será seguridad sin fronteras, quiero decir: un escudo que nunca se romperá en la era actual...Sr. Sidney Silva, autor de algunas tesis científicas en el campo de las Matemáticas...un descubrimiento único y majestuoso...un descubrimiento impactante e intrigante. .. √2; √3; √4; √5; √6; √7; √8; √9; √10; √11,√12, √877, √350734139, ¿es igual al enigmático número de Pi, con 02 fórmulas increíbles?
THIS IS ABC FORA
Wish Ramanujan's work got recognised similarly.
Aditya N Ramanujan's work is very well recognized. The novelty of his story has actually eclipsed the work of more prolific mathematicians of the same era.
More people (specifically mathematicians) know and revere Ramanujan than Terence Tao.
I don't think I know the name of more than 20-30 mathematicians. I know who Ramanujan was
The one who knew ''infinity'.
you indian nationalists are everywhere. everybody already knows about ramanujan
the disposition of the prime quarantined double but only in half will get you £=¥ giving you the smallest gap of 264
Kent Pellerin I smoked a prime # of bong hits and ate 3.14
not to insult AT ALL - meaning quite the opposite…I say: he speaks as if his voice is being replayed back at 2X speed! amazing man, and prodigy/genius as a young child and into his adulthood…just fascinating!
‘i wonder how his chess game is?!’ lololol
he is agenius with iq 230 it is totally normal for him to speak like that
Perfect! :) How are you old?
if Terence Tao is a rapper, Eminem would be the pizza delivery dude while Nicki Minaj would be working in McDonald's
He speaks too damn cast.
Fun drinking game, take a shot every time he says "umm"...
Page 2 material in almost any article on primes - there must have been more interesting stuff later on.
Mathematics is hard to put into easy words
Why does he like prime numbers so much 🤔
5:02 i literally screamed out "FUCK YOU!!" to all the people yawning. I'm sorry
2:48 my man Verdi!
Dude is overclocked
5:01 Woman on the upper left with the FAAAT yawn. LOL. Awesome video though, Terence Tao is an amazing mathematician
Beautiful presentation but would that proof be necessary as if there’s an infinite number f numbers then there has to be an infinite number of primes no matter how low the chance is of one showing up?
this argument does not work. you have to show why specifically the property of being a prime number cannot be limited to a finite set of numbers, which is what the proof here shows. it's not enough to have a hunch like this.
@@DrakePitts ah yeah my bad I was sleepy when I wrote the comment thanks for correcting me
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.
nice.^ and where are you from?
I'm 17.
video after terence tao teaching something: *this is abc fora*
me: *nobody cares*
Time is prime, because "in-form-ation", the timed measurement of motion with motion (vectors) mechanism, is the principle of connection at specific ratios, causing a tangential difference of "ratio-n-al-ity", "everything all at once" instantaneous alignment in the:- zero to infinity, now in eternity, divided interval of relative ratios of fluid change.
It gives the appearance of identity in space, "something in nothing", materializeation spectrum of relative time-timing duration history.
Ie it's the Quantum Mechanism Universe, in plain language.
Dude, wtf do you smoke?
You're delusional if you think any of this is even slightly true, get help
You literally made 0 sense here, bud
Terence Tao is the best living mathematician in the world.
His Brain at 3000 Hz, Mouth at 60 Hz, A Genius ,,.............
Actually his brain is 3000hz, his mouth is 240hz, our brains are 15hz. That the challenge
Where is the rest??
Light takes a huge bend over universes. Relevant primes. Smaller primes are closer. Light is million prime over million and there are primes beyond. Million over million is just a spec.
Where can i find this complete video
I don't get the proof. The fundamental theorem of arithmetic doesn't state that in the factorisation every prime can appear at most 1 time - they can appear more often. So why is the sum of all known primes + 1 not dividable by any other combination of primes?
Lets say we know 1000 primes and the sum of all + 1 is dividable by 1000*p2 + 54*p3 + p99.
1000*p2 + 54*p3 + p99 is not a product of primes (what this is would be called a 'linear combination').
Basically, any number x = p_1^(i_1)p_2^(i_2)...p_n^(i_n)
Where i_1...i_n can be 0, or a positive integer.
So for the proof: P = p_1...p_n + 1. If this isn't prime, it should be representable as a product of primes from p_1 to p_n (repeats allowed). This means some p_i is a factor of P. So, P/p_i should be an integer.
But P/p_i = p_1...p_(i-1)p_(i+1)...p_n + 1/p_i
p_1...p_(i-1)p_(i+1)...p_n is an integer. But 1/p_i is not, because the smallest prime is 2, so 1/p_i is either 1/2 or smaller. So P/p_i is not an integer.
Spherica I failed with the linear combination :D
But thank you for the further proof.
He is not taking the sum of all known primes, but the product of all known primes
Proof. Suppose there’re finite number of primes,
Multiply them all plus 1=p.
Clearly, none of those primes divides p since none divides 1.
Now, we have an p that’s not a product of any prime and bigger than 1, by definition itself must be a prime, yet p is not within that total prime list we assumed.
Hence, it’s a contradiction, and the original statement “there’s only this finite number of primes” must be wrong, and primes must be infinite.