@@christopherblanchard2099 A fact can never be trite, (you can do something with a fact & zero with an ideal) do your own maths and take responsibility. Take care!
This comment has to come from somebody without a PhD. LOL Let me tell you something, a PhD doesn't mean much and most of the time, it (using s/he is too much trouble and offends the 36th sex) only knows some very basic concept of other field, but lots of specialized knowledge in its tiny and narrow field. These panel members are a rare collection and I see some of these in my own field once in a blue moon (I happen to be a hybrid and ran a few conferences in the past so I know a bit broader than most average scientists).
I am fully willing to respect Jugimon S and Leonardo Mito, that there are people on this world who are more intelligent than myself. I know a lot of information but it is superficial rather than being able to solve anything or be creative or truly intelligent myself.
I love how Taos mind works. All these fellows are brilliant, but because Tao is so young and his first language is English, he has thought a lot about these fundamental questions and can explain himself better. What a great event
They are so real. Very childlike. It's fascinating but why are they like that? 'Normal ' human interaction involves people having layers upon layers but these guys are so genuine . Why I wonder.
It’s because they don’t spend time on backbiting or planning wrong things.They just work and explore beautiful ideas which results in a calm,peaceful and positive brain.
Their brilliance spare them . They dont need manipulation , ego amplification and emotionnal deffences to market themselves and get their way through life . The inherent value transcends the need to fit in .
I really loved Jacob's answer to the 1st question , it was indeed ingenious of him to think like that, he certainly impressed me among all the people..
That answer given by Jacob to the first question is not original. Many philosophers, especially, kant, put forth those ideas centuries before. Jacob is rehashing those ideas of kant. Read Kant's 'Critique of Pure Reason,' and you will understand what I stated.
Mathematics is a way to bound the simulation of possible conclusions to those derivable via some set of axioms. Though those conclusions are implied by our axioms, the axioms are phrasings of things we have reason to believe implicitly, a priori.
***** It is the generation of a set of principles, as per a set of principles, such as to generalize the observed behavior of system, whether that system is "real" or imagined.
Shy reticent panel - not your usual flamboyant egocentric popularisers - quite a refreshing change. Take home points: Mathematics is discovered - We live in a Matrix computer simulation.
If want to solve Fermat need attention to are integer x.y.z conditions carefully Define Sx=1+2^2+3^2+4^2+....+x^2.=x(x+1)(2x+1)/6=(2x^3+3x^2+x)/6 Sy=1+2^2+3^2+4^2+....+y^2=y(y+1)(2y+1)/6=(2y^3+3y^2+y)/6 Sz=1+2^2+3^2+4^2+....+z^2=z(z+1)(2z+1)/6=(2z^3+3z^2+z)/6 So 2x^3=6Sx-3x^2-x 2y^3=6Sy-3y^2-y 2z^3=6Sz-3z^2-z So x^3=3Sx-3/2x^2-x/2 y^3=3Sy-3/2y^2 - y/2 z^3=3Sz -3/2z^2-z/2 Suppose x^3+y^3=z^3 3Sx-3/2x^2-x/2+3Sy-3/2y^2 - y/2 - (3Sz -3/2z^2-z/2)=0 Or 2Sx-x^2-x/3+2Sy-y^2 - y/3 - (2Sz -z^2-z/3)=0 Or 2Sx+2Sy-2Sz-(x^2+y^2-z^2) =(x/3+y/3-z/3) Because 2Sx+2Sy-2Sz-(x^2+y^2-z^2) is integer So (x/3+y/3-z/3) is also integer or x=3k y=3h and z=3g K,h,g are integers So 27k^3+27h^3=27g^3. Or k^3+h^3=g^3 had had conditions x ^ 3 + y ^ 3 = z ^ 3 Cannot satisfy two conditions in the same time except x=k,y=h and z=g But x=3k and k=x So x=3x this is impossible! Conclusive x^3+y^3=/z^3 General Z^n=/x^n+y^n Using formular 1^a+2^a+3^a+4^a+....+n^a
Questioner asked about prospects of Univalent Foundations which is a foundational program in Mathematics still under development under which a newly developed theory that goes by the name Homotopy Type Theory will replace the current foundations of Mathematics i.e Zermelo Frankel Set Theory with Axiom of Choice.
There's infact a whole heated discussion in the comment section of a Blog post specifically on Lurie's " No Comment ! " reaction. mathematicswithoutapologies.wordpress.com/2015/05/13/univalent-foundations-no-comment/ Lurie himself is part of this discussion.
@ 37:11 "Can you imagine a massive group making a significant break through (in mathematics)?" The proof of the classification of finite simple groups. Yes, that took place before the Polymath Project, but it displays a similar approach to the project. Break a big problem into lots of little parts, then individuals go to work on the various parts. What the Polymath project brings is nearly instantaneous communication via technology.
John Conway is the mind behind the classification. All the other helped but the ideas were all Conway’s. In fact he probably had it in mind all along, what remained was for the others to convince themselves. Not really a massive group after all...
12:04 - This is incorrect. At its fundamental level, biology also adheres to physical laws. Even Richard Dawkins mentioned on his channel that Darwinian natural selection would be the primary mechanism by which organisms form and evolve. This suggests that extraterrestrial life could potentially resemble us.
13:26 Great insight on the topic of whether mathematics are to be discovered or invented. The notion of "real numbers" is an excellent example of something that makes perfect sense in the human mind -since it agrees with our intuition for "movement"- but does not necessarily reflect how the universe works (especially if we assume that space-time is quantized). It's our way to understand reality.
Paul laurie, brilliant but the jerky head movements are peculiar. I found that his answers were deep , specific, and well-constructed, and Terry Tao is just brilliant. Taylor is well-spoken. Maxim and Donald - ackward. Marhematicians do bring "ackward' to higher dimensions, but they are beautifully creative.
The ultimate computational language (not a programming language; the distinction being an easy interface for humans to think computationally (rather than translating thoughts into a programming language for the computer to do the calcuation)) is Wolfram Langauge.
+FichDichInDemArsch I've watched all of these people speak except for Hirata, and these guys are as good at speaking as a any of them. In fact, I'd say Wiles and Perelman are worse speakers than everyone there. Witten is a better speaker than Kontsevich in English, but Kontsevich is a much better speaker in russian or french than he is in english.
@ 25:30 "We have a small number of axioms from which we can build all the mathematics that is known today", what does that mean? So is all of mathematics is axiomatizable? I thought that question was settled. Godel's incompleteness theorem anyone?
+SalEd LirO'c What are you talking about? It's not a question. All of mathematics we do is axiomatized (people don't actually think about axioms when they work all the time, ebcaue it isn't important). But all mathematics known today can be built up from propositional and predicate logic. It's not a question that Godels theorems prove or disprove.
Grothendick Thanks for reply. I was thinking more along the following lines. "Principia Mathematica was an attempt to describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could in principle be proven. As such, this ambitious project is of great importance in the history of mathematics and philosophy, being one of the foremost products of the belief that such an undertaking may be achievable. However, in 1931, Gödel's incompleteness theorem proved definitively that PM, and in fact any other attempt, could never achieve this lofty goal; that is, for any set of axioms and inference rules proposed to encapsulate mathematics, either the system must be inconsistent, or there must in fact be some truths of mathematics which could not be deduced from them." Quotation taken from: en.wikipedia.org/wiki/Principia_Mathematica Best wishes.
One thing is to have a formal system in which to express all mathematics, and other (proved to be impossible in the case of Arithmetic by Gödel) thing is to ask for that system to be complete (so that all meaningful statements in that language are decidable in a finite number of steps).
Maxim comments that he can't believe that nature resembles a vector space, and that it should instead be a manifold. What exactly does he mean by that?
+Kexin Zhang: It's a running joke in mathematics: Q: _"Who was the greatest father/son team in mathematical history?"_ A: _"Gauss and his father."_ Sometimes the answer is: _"Gauss and whoever his father was."_
+Kexin Zhang: Right! Gauss' father wasn't even a mathematician, he was I think a mason, but Gauss' talent was such that it was enough for both of them to outmatch any father/son mathematical team.
At 19:00 , Maxim Kontsevitch comments about the so-called Simulation Hypothesis and states that he believes it possible. There is evidence in support of the Simulation Hypothesis. Said evidence may support a proof. If proven, what then do we do about it? How might that change our view of society and reality?
11:36 Now, it surprised me to hear this from a mathematician: Assumption 1: Aliens (if they're civilised) need to count Assumption 2: Counting can't be any different anywhere in the universe Assumption 3: Anywhere in the Universe you'd have to measure time and measure space Conclusion: Probably they'd have the same sort of mathematics
How math of aliens may be different? This question has not been deeply explored. I think, they would have different choices of axioms for logic and set theory to model the same phenomena. They could have different axiomatization of probability, and so on. They could be finitists, discovering finite difference equations, rather than differential equations. They could be more abstract, not limiting mathematics to mathematical operations between objects, but exploring properties of objects under arbitrary sets of operations, and so on. However, mathematical philosophy aside, their math would be applicable to solve physical and practical problems. So, imagine what other algorithms could solve the same physical problems that we have, and you can discover what alternative mathematics aliens may have.
Milner (8:47) starts out looking so tense and nervous that he's going to faint. Then throughout the rest of the discussion he's as laid back as a pot smoker.
David Wild Give him credit he started this, I hope he encourages others in the bay, and throughout the world that California and the USA appreciate math, as much as China, India or France, Germany or Russia.
Are you condescending Jacob? It seems like he has Aspergers; he reminds me a lot of the protagonist from The Good Doctor who has near-exact mannerisms as Jacob
@@Divine_R Me condescending to Jacob? What a notion! I have not seen the movie; but Jacob reminds me of a lot of super brainy coves who are awkward socially. Not saying he has Aspergers, but those who have it tend to be good at numbers. One of my nephews is on the more serious side. He did not respond socially and went to special schools for ages. But he managed to become a chartered accountant and is gainfully employed, and married with children.
wcottee Depends on the size of the ditch, more people doesn't always equal faster work, for example if the ditch is is just big enough for two people to work in, ceterus paribus, adding more people won't increase the speed to dig the ditch
Depends on the relation between people and time it takes for a ditch to be made. Two data points is not enough to have a good idea about the relationship between the two variables.
Intelligence spreads in a multidude of ways and while mathematicians have a deep understanding of a narrow part of their sub field and a lot of creativity, they would clearly recognize their ignorance in most other areas of knowledge... Your statement more than not funny is I think degradant.
It's true that the collective intelligence (g-factor) on that panel is not probably but definitely higher than the average of a handful of some countries altogether. No one said anything about knowledge, it's about intelligence. Intelligence ≠ knowledge.
It would be easy to agree with all of them and praise them. I feel that ultimately we developed mathematics to serve the demands of our physical world and it’s physics as we understood it. In another world where another totally different physical world exists, Taos and Lauries of that world probably developed mathematics totally differently. Just my 2 cents.
Tao and Taylor seem to have a balanced view of Strong-AI, while Kontsevich is one of the paranoid simple-minded thinkers who think AGI is just around the corner. Those AGI proponents or scaremongers are a bit loony IMHO. We have no idea how the human mind really works, at least if we take subjective consciousness seriously (and yes, I've read the books Chalmers, Pinker, Dennett, Minsky, et al., they all have no idea how consciousness arises, or deny that consciousness is real). Folks like Kontsevich and the Singularity Institute crowd are off on big intellectual wanks thinking they can reproduce consciousness in a computer. The bottom line is that there is simply no proof, not even close, that the human mind is basically a machine. Richard Taylor's point is quite deep: all the fast problem solving computers we have are acting almost the opposite of how brains think, brute force AI is completely the wrong direction if you want any hope of creating consciousness in computers, because the only examples of consciousness we have are ourselves, and DeepBlue and BlueGene etc., are operating algorithmically in almost the complete opposite style of how human minds/brains appear to operate (not that there is a thing here I can define as "opposite style" but you know what I mean). You can say the brain is something like a machine, but until we understand fundamental physics and causality there is no proof, given quantum processes are non-deterministic we might even find causality is not a well-defined concept, which means all hopes of constructing AGI+consciousness from causal software is a bit naive. But what these folks overlook, which is even more worrisome, is that supposing AGI gets created, then to be scared of these beings is just another form of xenophobia, and human history, if it teaches us anything, is that xenophobia and fear based on other people's differences never ends well. If we get to create Strong AGI then they should be welcomed as part of the human race. "Human" does not need to be genetically defined as homosapiens. "Human" is a culture, not a genotype category. If we start thinking of ourselves as beyond our genes and body types then we stand a chance of making great progress and benefiting from AI and AGI, and will have nothing to fear. So I suspect human discoveries in mathematics will be an art & science we can look forward to enjoying a lot more of as human civilisation advances. Why? Because I don't think you can do mathematics, not truly, unless you are conscious and have mental access to the world of ideals. I know that sounds even more loony perhaps than the Singularity hypothesis, but, at least for me, I have direct knowledge of the platonic realm of ideas, I use it to do all my mathematics and science, and if you can reproduce that inside a machine, well then good luck, you ill have an entirely new class of humans to Human culture. SmartMachines won't cut it in my view, they'd be the theorem checking or suggesting helpers Terry Tao refers to, but genuine mathematical discovery will, IMHO, require access to conscious ideas. Having said all that, if a deterministic computer system does turn out to be capable of genuine discovery and human-like introspection, I would be amazed but also welcome this as one of our greatest ever scientific achievements, it should not be something we regard as unethical or fearful. It would tell us that maybe, after all, we are jsut sophisticate machines.
Mathematics, also, cannot be completed. If you disagree with validity of the total generality of some principle, for every possible reality, you will amend it and from those amendments will follow consequences that you will either totally agree with or not. As well, if there are things you can prove that your system cannot, you may just want to embed that ability into the consequences of the grammar you decide to use. What functions are the minimal abilities of a logical system? Can't you just say that, "yea, the world i'm thinking of doesn't have that axiom, so that doesn't happen".
I had a dream that we were all in a video game at 6, a method of control and disillusion. My parents were politicians, and later I became fascinated with math, but it may be just a comment on nature or humans.
Tao is a true math expositor. His manner and openness to the others' ideas are admirable.
He's inspiring
It is wonderful and fantastic that we have people like these who push the boundaries of our collective knowledge further into the unknown.
What you are really saying sir is, it's wonderful we have these people to do the work while we sit on our ass. When you are going to think and change?
@@garryfitzgerald6233 I think your comment is a little trite
@@christopherblanchard2099 A fact can never be trite, (you can do something with a fact & zero with an ideal) do your own maths and take responsibility. Take care!
@Castlier I'm here!
@Castlier What something is depends on when it is.
Hearing leading mathematicians discuss or answer questions which are largely philosophical in nature is a beautiful thing
Up at 4 am binge watching these videos. I love seeing how mathematicians think. These guys are so inspiring!
I think even the cleaning lady has a PhD in that room.
loll
Xd
This comment has to come from somebody without a PhD. LOL Let me tell you something, a PhD doesn't mean much and most of the time, it (using s/he is too much trouble and offends the 36th sex) only knows some very basic concept of other field, but lots of specialized knowledge in its tiny and narrow field. These panel members are a rare collection and I see some of these in my own field once in a blue moon (I happen to be a hybrid and ran a few conferences in the past so I know a bit broader than most average scientists).
@@willh.2155 I think you proved your point. You have a PhD and still the joke flew right above your head making a swooosh :P
Probably even the fly in that room got one.
Tao is very coherent and makes things easier to understand . That's definately a sign of his great intelligence
Legend says: if you are stuck in a problem for years, almost giving up on that, your only hope is to interest Terence Tao on it.
Are these 2014 Breakthrough Prize Winning Mathematicians really cleverer than me?!
I am Very Factual and Quite Clever!
I am fully willing to respect Jugimon S and Leonardo Mito, that there are people on this world who are more intelligent than myself.
I know a lot of information but it is superficial rather than being able to solve anything or be creative or truly intelligent myself.
I would like to be a Dr of History or Philosophy but I am not clever enough.
I feel his mouth cant catch up with his brain/thoughts
Towards the end they mentioned Grothendieck was alive. That would be true for another three days.
No he died on 13th November
🤣🤣🤣a true inventor of mathematics, Grothendieck
@@smangalisomhlongo5707 I know that your comment is old, but that's not the crying emoji, that's crying while laughing emoji.
@@amritkaur9007 you're replying to a 5 year old comment Amrit.
@@muhammadputera6593 and u r replying to a 1 year old comment lol
This must the the highest concentration of brain power in the entire universe!
th-cam.com/video/v-bpGe3f4VQ/w-d-xo.html
cedric vilani,andrew wiles,michael attiah,mikhail gromov just to name a few.
ever heard of the Solvay conference?
It's really wonderful to see and hear these great great mathematicians of the century.
I love how Taos mind works.
All these fellows are brilliant, but because Tao is so young and his first language is English, he has thought a lot about these fundamental questions and can explain himself better.
What a great event
tao is legit thinking about how to solve the twin prime conjecture while doing this...
Tao, Tao, Tao, you're just too brilliant and humble. Very beautiful human being.
They look so young for their age.Tao about 39 at the time. Jacob 36.
Watching this in 2021 and all I can think is: they are sitting so close together!
They are so real. Very childlike. It's fascinating but why are they like that? 'Normal ' human interaction involves people having layers upon layers but these guys are so genuine . Why I wonder.
their laughter made me think the same, great question
It’s because they don’t spend time on backbiting or planning wrong things.They just work and explore beautiful ideas which results in a calm,peaceful and positive brain.
Their brilliance spare them . They dont need manipulation , ego amplification and emotionnal deffences to market themselves and get their way through life . The inherent value transcends the need to fit in .
@@youssraelkhoulali8147 This is about the best answer I've seen. Thank you sir
@@youssraelkhoulali8147 Very well put👍🏻
Taylor is like agent Smith here, just making sure nobody says anything about the matrix.
I really loved Jacob's answer to the 1st question , it was indeed ingenious of him to think like that, he certainly impressed me among all the people..
That answer given by Jacob to the first question is not original. Many philosophers, especially, kant, put forth those ideas centuries before. Jacob is rehashing those ideas of kant. Read Kant's 'Critique of Pure Reason,' and you will understand what I stated.
Mathematicians are really strange people ! But I love them :)
That is because other people are too common.
Facts
There incredible strengths are not normally in there social capabilities but deeply rooted in there problem solving.
I am a math teacher . After listening to these great people, I feel that I know nothing about math...555
Hey I teach math on TH-cam too
Jump to about 10 min to get started, post accolades. Amazing video, panel, lovely answers.
A unique moment with the best mathematicians and physicists currently
Mathematics is a way to bound the simulation of possible conclusions to those derivable via some set of axioms. Though those conclusions are implied by our axioms, the axioms are phrasings of things we have reason to believe implicitly, a priori.
***** It is the generation of a set of principles, as per a set of principles, such as to generalize the observed behavior of system, whether that system is "real" or imagined.
Terence Tao is such a lovely guy. A true genius but with such a nice manner and way of expressing his ideas.
It’s exciting to watch these great mathematicians giving their ideas...
the amount of brain power concentrated in such a small room is warping spacetime critically to form a black hole
They seem to be really enjoying themselves
Did not understand what they were talking about, but it sounds so interesting 🤔
Awesome panel.
Ikr
Shy reticent panel - not your usual flamboyant egocentric popularisers - quite a refreshing change. Take home points: Mathematics is discovered - We live in a Matrix computer simulation.
+Hythloday71 found neo yet?
no, but it is my destiny to, the oracle told me ;o)
If want to solve Fermat need attention to are integer x.y.z conditions carefully
Define
Sx=1+2^2+3^2+4^2+....+x^2.=x(x+1)(2x+1)/6=(2x^3+3x^2+x)/6
Sy=1+2^2+3^2+4^2+....+y^2=y(y+1)(2y+1)/6=(2y^3+3y^2+y)/6
Sz=1+2^2+3^2+4^2+....+z^2=z(z+1)(2z+1)/6=(2z^3+3z^2+z)/6
So
2x^3=6Sx-3x^2-x
2y^3=6Sy-3y^2-y
2z^3=6Sz-3z^2-z
So
x^3=3Sx-3/2x^2-x/2
y^3=3Sy-3/2y^2 - y/2
z^3=3Sz -3/2z^2-z/2
Suppose
x^3+y^3=z^3
3Sx-3/2x^2-x/2+3Sy-3/2y^2 - y/2 - (3Sz -3/2z^2-z/2)=0
Or
2Sx-x^2-x/3+2Sy-y^2 - y/3 - (2Sz -z^2-z/3)=0
Or
2Sx+2Sy-2Sz-(x^2+y^2-z^2) =(x/3+y/3-z/3)
Because
2Sx+2Sy-2Sz-(x^2+y^2-z^2) is integer
So
(x/3+y/3-z/3) is also integer
or
x=3k
y=3h and
z=3g
K,h,g are integers
So
27k^3+27h^3=27g^3.
Or
k^3+h^3=g^3
had had conditions x ^ 3 + y ^ 3 = z ^ 3
Cannot satisfy two conditions in the same time
except
x=k,y=h and z=g
But
x=3k
and
k=x
So
x=3x
this is impossible!
Conclusive
x^3+y^3=/z^3
General
Z^n=/x^n+y^n
Using formular
1^a+2^a+3^a+4^a+....+n^a
pretty sure you can't conclude from x+y-z=3*integer that both x,y and z have to be divisible by 3. take for instance x=1,y=4,z=2.
MrDpsc read french philosophy.
can someone tell me which is the question at 55:00 which is remained unanswered? I do not get to understand
Questioner asked about prospects of Univalent Foundations which is a foundational program in Mathematics still under development under which a newly developed theory that goes by the name Homotopy Type Theory will replace the current foundations of Mathematics i.e Zermelo Frankel Set Theory with Axiom of Choice.
There's infact a whole heated discussion in the comment section of a Blog post specifically on Lurie's " No Comment ! " reaction.
mathematicswithoutapologies.wordpress.com/2015/05/13/univalent-foundations-no-comment/
Lurie himself is part of this discussion.
@@pursuingstacks I can understand very little of the discussion, but thanks for your answer!
@ 37:11 "Can you imagine a massive group making a significant break through (in mathematics)?"
The proof of the classification of finite simple groups. Yes, that took place before the Polymath Project, but it displays a similar approach to the project. Break a big problem into lots of little parts, then individuals go to work on the various parts. What the Polymath project brings is nearly instantaneous communication via technology.
John Conway is the mind behind the classification. All the other helped but the ideas were all Conway’s. In fact he probably had it in mind all along, what remained was for the others to convince themselves. Not really a massive group after all...
Math block chain lmao
Terence Tao predicting Chat GPT at 40 minutes, 8 years ago.
Andrei Linde speaks at 53:12 I think (not shown in video). Correct?
All are un comparable and my favourite in yet another way....
Math is the only field where collaborate effort makes a lot of sense, almost any other field involves looseness in system or subjectivity in decisions
I feel so stupid when I watch things like this
🤔... what I would do to have the opportunity to work/learn with any one of them.
Prof. Terrance Tao teaches at UCLA, so u could learn from him if u attended
12:04 - This is incorrect. At its fundamental level, biology also adheres to physical laws. Even Richard Dawkins mentioned on his channel that Darwinian natural selection would be the primary mechanism by which organisms form and evolve. This suggests that extraterrestrial life could potentially resemble us.
13:26 Great insight on the topic of whether mathematics are to be discovered or invented. The notion of "real numbers" is an excellent example of something that makes perfect sense in the human mind -since it agrees with our intuition for "movement"- but does not necessarily reflect how the universe works (especially if we assume that space-time is quantized). It's our way to understand reality.
Paul laurie, brilliant but the jerky head movements are peculiar.
I found that his answers were deep , specific, and well-constructed, and Terry Tao is just brilliant. Taylor is well-spoken. Maxim and Donald - ackward.
Marhematicians do bring "ackward' to higher dimensions, but they are beautifully creative.
I didn't know if it was summer or winter.
I wonder if their check books are balanced?
43:48 can anyone clarify what he was talking about the proper names for it all
Jacob Lurie had an excellent answer to the first question. Cheers.
he is one who is born in a century.Just terribly genius of highest(est) order!
The ultimate computational language (not a programming language; the distinction being an easy interface for humans to think computationally (rather than translating thoughts into a programming language for the computer to do the calcuation)) is Wolfram Langauge.
Imaginen que entre todos ellos también expresara sus ideas Grigori Perelmán, creo que no hay ningún video donde él exprese su forma de pensar.
Edward Witten, Andrew Wiles, Grigori Perelman, and Chris Hirata anyone?
FichDichInDemArsch It's not your fault.
+FichDichInDemArsch I've watched all of these people speak except for Hirata, and these guys are as good at speaking as a any of them. In fact, I'd say Wiles and Perelman are worse speakers than everyone there. Witten is a better speaker than Kontsevich in English, but Kontsevich is a much better speaker in russian or french than he is in english.
I think I'll stick with the Mr Men books and ABBA.
@FichDichInDemArsch I guess u just can't live normally.
Sir Roger Penrose
Who is being referred as gauss's father?@53:00
his father
@@Simon-xi8tb Oh so a nonsensical joke...
@@Viakskwhat’s nonsensical about it?
@ 25:30
"We have a small number of axioms from which we can build all the mathematics that is known today", what does that mean?
So is all of mathematics is axiomatizable? I thought that question was settled. Godel's incompleteness theorem anyone?
+SalEd LirO'c What are you talking about? It's not a question. All of mathematics we do is axiomatized (people don't actually think about axioms when they work all the time, ebcaue it isn't important). But all mathematics known today can be built up from propositional and predicate logic. It's not a question that Godels theorems prove or disprove.
Grothendick Thanks for reply. I was thinking more along the following lines.
"Principia Mathematica was an attempt to describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could in principle be proven. As such, this ambitious project is of great importance in the history of mathematics and philosophy, being one of the foremost products of the belief that such an undertaking may be achievable. However, in 1931, Gödel's incompleteness theorem proved definitively that PM, and in fact any other attempt, could never achieve this lofty goal; that is, for any set of axioms and inference rules proposed to encapsulate mathematics, either the system must be inconsistent, or there must in fact be some truths of mathematics which could not be deduced from them."
Quotation taken from:
en.wikipedia.org/wiki/Principia_Mathematica
Best wishes.
One thing is to have a formal system in which to express all mathematics, and other (proved to be impossible in the case of Arithmetic by Gödel) thing is to ask for that system to be complete (so that all meaningful statements in that language are decidable in a finite number of steps).
52:22 Grothendieck passes away three days later.
The GOAT
Awesome discussion
the questions are so low
when Tao said that was 2 % of the job done i stopped the video and recalculated 200/10000 ...proof check completed..okthxbye
come in contact with aliens and the first thing Tao thinks about is let me see your text books. WOW
Maxim comments that he can't believe that nature resembles a vector space, and that it should instead be a manifold. What exactly does he mean by that?
Why they speak "discretely"? what did the math do with them?
I feel smart just by watching this video.
Can anyone pls. tell me what Tao said in 52:57？ I only catched 'Gauss is his father'……
+Kexin Zhang: It's a running joke in mathematics:
Q: _"Who was the greatest father/son team in mathematical history?"_
A: _"Gauss and his father."_
Sometimes the answer is: _"Gauss and whoever his father was."_
+Sandor M thanks: ) Is it simply saying that Gauss is mathematician nonpareil?
+Kexin Zhang: Right! Gauss' father wasn't even a mathematician, he was I think a mason, but Gauss' talent was such that it was enough for both of them to outmatch any father/son mathematical team.
+Sandor M hahaha quite true...There're a vast number of Gauss Facts, this one should be added! Mathematicians love him.
At 25:50 Terrence looks like he knows somethings up
Do light waves deteriorate over time ?
I myself received a passing grade in business math while still in high school.
At 19:00 , Maxim Kontsevitch comments about the so-called Simulation Hypothesis and states that he believes it possible. There is evidence in support of the Simulation Hypothesis. Said evidence may support a proof. If proven, what then do we do about it? How might that change our view of society and reality?
11:36 Now, it surprised me to hear this from a mathematician:
Assumption 1: Aliens (if they're civilised) need to count
Assumption 2: Counting can't be any different anywhere in the universe
Assumption 3: Anywhere in the Universe you'd have to measure time and measure space
Conclusion: Probably they'd have the same sort of mathematics
Terence is really a master mind of mathematics
Thank you really interesting!!!
Why the moderator seldom ask question to Donaldson ?
He's a moron.
Just like you
Really interesting to hear super brainy people talk!
this was actually rlly fun to watch. very informative and interesting
43:30 !This is when the professor knew he really fucked up
Can you subtract from infinity
How math of aliens may be different? This question has not been deeply explored. I think, they would have different choices of axioms for logic and set theory to model the same phenomena. They could have different axiomatization of probability, and so on. They could be finitists, discovering finite difference equations, rather than differential equations. They could be more abstract, not limiting mathematics to mathematical operations between objects, but exploring properties of objects under arbitrary sets of operations, and so on. However, mathematical philosophy aside, their math would be applicable to solve physical and practical problems. So, imagine what other algorithms could solve the same physical problems that we have, and you can discover what alternative mathematics aliens may have.
Terence tao!
I'm keep waiting for the to bring Hirata, Tao, Ung and Pereleman together.
@Sirin Kalapatuksice But DAAAAMN! DAAAAAMN! I want them to live together, They would make human civilization fly
Genius insight at 13:27 (on the role of experience, defined by our physiology, in shaping the mathematics of human beings).
Terence Tao is the greatest living Mathematician.
Mein Freund not even close
Pookz then who is?
Matias Cornet Perelman wiles
ошибаешься, теренс не самый великий математик, способный, но не гений.
I guess maybe Shing-Tung Yau is the right one??
Why can't we measure time itself ?
53:03
Milner (8:47) starts out looking so tense and nervous that he's going to faint. Then throughout the rest of the discussion he's as laid back as a pot smoker.
why is donaldson ignored
que piensan ? como mover una cuerda dentro de un circulo sin nada ?? de forma ilimitada ?????? :D
The line of questioning is so strong!
So guys I hope you'll have invented time machine
@40:00, What he said.
24:24 every time he speaks he makes me think of Ben Kingsley, lol...
waw ,great panel!!..nice discussion
The chair here was dreadful.
David Wild Give him credit he started this, I hope he encourages others in the bay, and throughout the world that California and the USA appreciate math, as much as China, India or France, Germany or Russia.
Does anyone study shadows ? Can a shadow be infinite?
Terence Tao is the most outgoing. Also Richard Taylor. Jacob is really conforming to the nerdy, awkward type.
Are you condescending Jacob? It seems like he has Aspergers; he reminds me a lot of the protagonist from The Good Doctor who has near-exact mannerisms as Jacob
@@Divine_R Me condescending to Jacob? What a notion! I have not seen the movie; but Jacob reminds me of a lot of super brainy coves who are awkward socially. Not saying he has Aspergers, but those who have it tend to be good at numbers. One of my nephews is on the more serious side. He did not respond socially and went to special schools for ages. But he managed to become a chartered accountant and is gainfully employed, and married with children.
If 3 people can dig a ditch in 2 hours, how long will it take for 6 people to dig a ditch?????
wcottee Depends on the size of the ditch, more people doesn't always equal faster work, for example if the ditch is is just big enough for two people to work in, ceterus paribus, adding more people won't increase the speed to dig the ditch
Depends on the relation between people and time it takes for a ditch to be made. Two data points is not enough to have a good idea about the relationship between the two variables.
ssc mein fail ho jaayoge saare bhai tum log
Do the six all have arms?
4 hours for 6 people to dig the ditch and 4 years for 1 person to give you a simple fucking answer that someone else could have given you.
This is very inspiring.
The collective intelligence in this room is probably higher than that of a few countries 😂🤣
Intelligence spreads in a multidude of ways and while mathematicians have a deep understanding of a narrow part of their sub field and a lot of creativity, they would clearly recognize their ignorance in most other areas of knowledge... Your statement more than not funny is I think degradant.
@@liammarin4450 I bet you must be fun at parties.
It's true that the collective intelligence (g-factor) on that panel is not probably but definitely higher than the average of a handful of some countries altogether.
No one said anything about knowledge, it's about intelligence. Intelligence ≠ knowledge.
数学により宇宙の外側は、観測できますか？
数学により脳を解明できますか？
My answer to greatest mathematician ever is S.RAMANUJAN, EULER AND JACOBI
Tao looks more like a grad student.
You don't notice camera work until someone does it badly.
My OCD was screaming all though this video
It would be easy to agree with all of them and praise them. I feel that ultimately we developed mathematics to serve the demands of our physical world and it’s physics as we understood it. In another world where another totally different physical world exists, Taos and Lauries of that world probably developed mathematics totally differently. Just my 2 cents.
Tao and Taylor seem to have a balanced view of Strong-AI, while Kontsevich is one of the paranoid simple-minded thinkers who think AGI is just around the corner. Those AGI proponents or scaremongers are a bit loony IMHO. We have no idea how the human mind really works, at least if we take subjective consciousness seriously (and yes, I've read the books Chalmers, Pinker, Dennett, Minsky, et al., they all have no idea how consciousness arises, or deny that consciousness is real). Folks like Kontsevich and the Singularity Institute crowd are off on big intellectual wanks thinking they can reproduce consciousness in a computer. The bottom line is that there is simply no proof, not even close, that the human mind is basically a machine. Richard Taylor's point is quite deep: all the fast problem solving computers we have are acting almost the opposite of how brains think, brute force AI is completely the wrong direction if you want any hope of creating consciousness in computers, because the only examples of consciousness we have are ourselves, and DeepBlue and BlueGene etc., are operating algorithmically in almost the complete opposite style of how human minds/brains appear to operate (not that there is a thing here I can define as "opposite style" but you know what I mean). You can say the brain is something like a machine, but until we understand fundamental physics and causality there is no proof, given quantum processes are non-deterministic we might even find causality is not a well-defined concept, which means all hopes of constructing AGI+consciousness from causal software is a bit naive. But what these folks overlook, which is even more worrisome, is that supposing AGI gets created, then to be scared of these beings is just another form of xenophobia, and human history, if it teaches us anything, is that xenophobia and fear based on other people's differences never ends well. If we get to create Strong AGI then they should be welcomed as part of the human race. "Human" does not need to be genetically defined as homosapiens. "Human" is a culture, not a genotype category. If we start thinking of ourselves as beyond our genes and body types then we stand a chance of making great progress and benefiting from AI and AGI, and will have nothing to fear.
So I suspect human discoveries in mathematics will be an art & science we can look forward to enjoying a lot more of as human civilisation advances. Why? Because I don't think you can do mathematics, not truly, unless you are conscious and have mental access to the world of ideals. I know that sounds even more loony perhaps than the Singularity hypothesis, but, at least for me, I have direct knowledge of the platonic realm of ideas, I use it to do all my mathematics and science, and if you can reproduce that inside a machine, well then good luck, you ill have an entirely new class of humans to Human culture. SmartMachines won't cut it in my view, they'd be the theorem checking or suggesting helpers Terry Tao refers to, but genuine mathematical discovery will, IMHO, require access to conscious ideas. Having said all that, if a deterministic computer system does turn out to be capable of genuine discovery and human-like introspection, I would be amazed but also welcome this as one of our greatest ever scientific achievements, it should not be something we regard as unethical or fearful. It would tell us that maybe, after all, we are jsut sophisticate machines.
It was very interesting to read your comment 👍👍
Mathematics, also, cannot be completed. If you disagree with validity of the total generality of some principle, for every possible reality, you will amend it and from those amendments will follow consequences that you will either totally agree with or not. As well, if there are things you can prove that your system cannot, you may just want to embed that ability into the consequences of the grammar you decide to use. What functions are the minimal abilities of a logical system? Can't you just say that, "yea, the world i'm thinking of doesn't have that axiom, so that doesn't happen".
Also QUINE is great because NF set theory is hella dope.
I had a dream that we were all in a video game at 6, a method of control and disillusion. My parents were politicians, and later I became fascinated with math, but it may be just a comment on nature or humans.