The Potential for AI in Science and Mathematics - Terence Tao
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- Опубликовано: 9 сен 2024
- Terry Tao is one of the world's leading mathematicians and winner of many awards including the Fields Medal. He is Professor of Mathematics at the University of California, Los Angeles (UCLA). Following his talk, Terry is in conversation with fellow mathematician Po-Shen Loh.
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
As an undergrad student it's nice to see that even Terry Tao throws his slides together the night before without practicing his presentation.
As long as we don’t make a habit out of it, right?
*anakin meme
Our boy terry did a little trolling
he's too bored and busy to practice, but he's still putting out more great ideas per minute than most of us, including TED presenters, who are practiced.
this talk probably has no or almost no impact on the quality of is life when compared to you getting a good grade
This is the way Terry presents, I’ve taken a class by him. It can feel a bit chaotic like that sometimes haha
I LOVE hearing a top mathematician talk about creativity. These thinkers are artists.
Yep. I hate how people stereotype math/science people as non-creative thinkers and artistic people as non-logical thinkers. Mathematics, science, artistry and creativity always blends together from what I observe usually.
@@macchiato_1881 It's often a coping mechanism to dismiss subjects they can't comprehend.
@@macchiato_1881at the top research level of any field, all the minds are highly creative.
Sure they are.
I don't think there could be a better interviewer than Po-Shen Loh. What an incredible important way to keep asking for answers
RUclips Algorithm really blessed me with this talk
The ultimate lecture! The most talked about subject by the most intelligent person right now!!!!
*best mathematician maybe, I would argue most intelligent person is ill defined. Though best mathematician is probably also ill-defined. He's certainly up there though.
@@minerscale Best mathematician downgraded to PR manager. SHAME!
I was thinking on solving 100% conjuction state function of M theory at 10 years old, but I proved other things instead that, I thought Im special after 5 years old, I dont know why did I think im capable of solving M theory, maybe because I have abstract thinking, I was ultimately sure I can make goal in anything.
🎯
You're just sucking P right now brother...
Professor Tao is a visionary. He sees what AI in combination with proof assistants are capable of, it can revolutionize mathematics.
Yeah, revolutionize it by making it the new Chess. Something there's no point in learning because computers can do it better than you.
@@carultch I don't agree, this technology won't make mathematicians irrelevant - it will make them more productive.
Even if the days comes (I don't think it would be soon) that AI is better at math than any human in every aspect - is it a bad thing? It would mean that we have way stronger tools to help with our everyday lives.
@@BedrockBlocker It is a bad thing when it cannibalizes the entire economy and leaves humans with nowhere else to go. The industrial revolution didn't create more and better jobs for horses; the horses were slaughtered. AI is making humans the new horses.
@@carultch Just like the gap between rich and poor, that is a societal problem. Fact of the matter is - if there is more output there is potential for more prosperity.
@@BedrockBlocker When there's nothing the poor can offer to get a foot on the economic ladder, that prosperity is only going to exacerbate the gap between rich and poor. That is, until unemployment reaches critical mass and the lack of income of the general public starts hurting corporations.
Thank you to the hosts very much for providing the space, for this presentation, Po-Shen Loh, did a great job as the moderator/interviewer, and thank you Terence Tao, for sharing your time and work sir, peace
Lol no. Its clear he was out of his league here asking the most asinine, irrelevant questions.
Furthermore, he was quite condescending at times, with the way he was almost commanding Dr. Tao.
How refreshing and excellent that the interviewer asked the best questions, without bothering to introduce himself. Very unlike the typical Brit style of self promotion and pomp
BIG Terence Tao, his humor sense and humble way to talk ... Most lovable mathematician
My sincere thanks for sharing it.
You know he's the real deal when his brain thinks so fast that you can hear his mouth struggling to keep up.
He's nervous, he usually talks normally like most people do.
Prof Terence Tao is such a beatiful mind!
I recently became aware of the "ARC challenge for AI" and I felt it captured/formalized what I experience as the weakness of current LLM/AI reasoning.
It seems similar to doing "machine mathematics", but in a toy problem scenario.
I want TerryChat/TaoChat… ultimate assistant… trained on all of the mathematical literature until the third level grokking plateau, minimum. Please! Good typology… pretty equations. All mathematics… ah.
Google's AlphaProof is interesting
I should watch this again - thanks to Tao & all!!
Great lecture by Terry Tao! ✨
Chapters (Powered by ChapterMe) -
00:00 - AIs impact on science and mathematics
00:58 - AI Nontechnical guessing machine
01:34 - AIs potential in transportation
02:48 - Boring, uncreative software replaced by AI tools
06:33 - Improvise AI, avoid bad mistakes
10:17 - Science mitigates errors with independent verification
10:54 - Bottleneck in drug discovery using AI
14:23 - Modeling modern world, climate, economies, universe
15:12 - AIs speedup in climate prediction
17:42 - AI opens up climate prediction possibilities
20:16 - Softwarebased formalization reduces timeconsuming proofs
24:10 - Lean proofs using AI
26:39 - AIs ability to teach stupidity
30:56 - Issues with confidence in results
31:14 - AI guarantees correctness, collaboration
31:29 - Importance of Proof Assistance in Automation
32:07 - Incentive structure for academic papers under strain
34:08 - Introduction to Lean Math Deconstructing Proofs Using Language, Organization
38:05 - Citizenled mathematics for future generations
39:31 - Amateur math community benefits from trust
39:55 - AI enables scientists to collaborate and solve problems
41:47 - Role of mathematics in academic life
45:58 - Open source academicians dont get left behind in AI development
46:39 - AI models need central repositories, lightweight models
48:40 - Solving Olympiad level geometry questions using ai
51:35 - Advances in mathematics make chess easy for humans
51:57 - Go Go Human uniqueness, different techniques
52:08 - Image recognition and poetry translation in air models
52:31 - Terrier praised, new model with better intelligence
Very interesting, as someone who does math I was thinking about using lean sooner or later, this definitely makes me want to learn it! This may be a turning point towards proof automation and AI.
Oxford Math Professor's teaching shock tactic equivalent to the Zen
Master's meditation interrupt paddle.., "You just look at it, and you notice..", Students are suddenly awake for dawning realization. (And the horror of "I know nothing" at the Centre of Time Duration Timing Actuality)
glad mathematicians are finally changing their practices to be more similar to computer science. For the average person mathematics seems extremely opaque and not accessible. I think that formalizing is painful but the amount of benefits they get long term is well worth it
This was a really interesting lecture!
Wow he called the methods mundane! Would love to hear a technical discussion between him and ML researchers
Is this a joke? Do you know who he is?
the methods are actually quite mundane. It's pretty much ascribing numbers to words and creating a classification or regression model from those numbers. Compared to more advanced mathematics used in pysics or even quantitative finance. Humans are very good at creating stuff and packaging stuff, thats why when you interact with these models it seems like its a human talking to you. those finer edges that make it seem so are actually programmed into the software ontop of the actual mundane ML methods beneath.
To someone in the top ten highest recorded IQ... Everything is mundane.
It is mundane, by design, and that's a compliment. If you think machine learning practitioners want to do sophisticated math, you're sorely wrong.
The maths involved in ML execution is indeed mundane. If it were not, it would not scale. Everyone and especially ML researchers are the better for it.
I'm a HUGE admirer of Terence Tao and his mathematical talent, imagination etc. - I just wish his English was a little more clearly understandable... (pardon me, my first language isn't English maybe that's why I'm struggling)
I wonder if this talk would have changed if it was given after the Google news of passing silver olympiads with AI
The XTX competition he mentioned was a prize of $10 million to the first AI to achieve a gold medal at the IMO. Google's AI missed this by one point. Terry Tao was talking about this at 26:17, expecting an AI to get a gold medal.
More aspiring mathematicians will become mathematicians and with the power of AI, they will be more applications and unity in the mathematical community. It will be a professional science. It will become more powerful, Mathematics, A tool. And Big STEM will mean Big Collaboration and it will streamline our unsolvable problems so we can move to the very beauties of our realistic world!
just think of all the math olympiad grinder kids who will want to contribute to helping Terry Tao solve a proof by solving its sub-parts for free
Muito boa palestra do grande matemático e medalhista Fields professor Terence Tao.
Thank you for the video.
Terry at it, of course.
It wasn't completely clear to me but did he talk in the end of the possibility of AI overtaking mathematicians?
That’s what most researchers do with GenAI - treat it like a sometimes bad sometimes amazing student and check all output.
Thank you 🦋
Welcome to the Big Ten, Terry....Go Bruins!
With luck and more power to you.
hoping for more videos.
21:00 - Nod to the Liquid Tension Experiment Dream Theater side project. That's awesome.
The goat
I wonder if over reliance on AI caused Crowdstrike to release bad code.
Hint for "English is my second language" people: Slow it a little and it is much more understandable.
0.75 is perfect for me, and I'm as English as you can get!
A genius usually talks just like this 😂no matter what his first language is .
@@charliesong3434 Terence Tao is Australian, English is his mother tongue. I suspect the tip is for watchers who can't quite keep up; Professor Tao is speaking pretty fast.
Being english first language, i dont need it, but its funny i can still tell how much more clear each word is at 0.75x and it doesnt sound slow, it sounds like normal pace
His mind is racing at 1000 miles per hour and his mouth can't keep up. Still surprising that a genius like him doesn't seem to notice how bad it is to listen to. He could slow down slightly and get the same ideas across at the same speed, without interruption
It remains to be seen whether AI can compare to our existing proof search techniques (notibly, logic/relational models). There is no reason to believe they ever will.
Does anyone know when this lecture was actually given?
@@anutuyi 17 July 2024
@@OxfordMathematics Thank you
@@OxfordMathematics It's hilarious that this talk came just a week before Deepmind released their IMO silver medal winning AI that used lean in much the same way Tao had proposed to prove its theorems
@@yorth8154 if the AI has asian parents it will ask "why not gold?"
Is the Trinity college project still there? I want to start it again with a view friends… 🎉
I was waiting for this one.
Let's see what sir has to provide. ❤
mathematics at its core, like other scientific disciplines, is about conceptual modelling of reality- known or unknown. what makes mathematical modelling unique is the conceptual language for modelling based on formalisation and unitisation of parameters and functional relationships. between aspects of reality and existence of a mathematical model is the top mathematician who have the creative apriori glimpse of possibility and proof. AI in my opinion currently is dealing with aposteriori possibilities by permutation, n mundane validation by known proofs.
Well... the auto-complete thing. Umm... I mean, there certainly is mapping of letters after letters forming words after words forming clauses after clauses forming sentences after sentences forming paragraphs after paragraphs forming chapters after chapters forming documents after documents but there's also context which filters the generation but if you have enough data and neural network connections, there could be also ideas after ideas and thoughts after thoughts and mental models after mental models, at least in theory. But is there will, because humans have a will and a goal. Does AI have internal reward system with digital satisfaction hormones?
My childhood hero is getting old😢
The flipside of The Halting Problem, is the Observable Eternity-now Interval Actuality condensation modulation superposition-quantization here-now-forever of logarithmic relative-timing proportioning.
Numberness->Numerical Mathematics is the hyper awareness of beginning-ending of arbitarily delineated bio-logical shell-horizons in the perspectives that are composed by infinitesimal =>gradually changing differentiates.., ie quantization by re-evolutionary phase-locked coherence-cohesion sync-duration resonance quantization cause-effect objectives. (As can be derived from the superposition-quantization logic of prime-cofactor frequency occurrence in the "Distribution of Primes " Calculus.
The concept of "Observable Eternity-now Interval Actuality" is fundamentally flawed when considering the non-linear dynamics of quantum field theory. The alleged "condensation modulation" is merely a misinterpretation of higher-dimensional manifold interactions within a Riemannian framework. Furthermore, the idea of "logarithmic relative-timing proportioning" fails to account for the non-trivial solutions to the Schrödinger equation in Hilbert spaces, leading to a misalignment with established principles of quantum entanglement. Thus, the notion of "phase-locked coherence-cohesion sync-duration resonance" is an oversimplified view that disregards the complex interplay of topological invariants and eigenvalue spectra.
is the project open for 40 y. o. informatic guys that would love to learn about Math?
00:11 L'intelligenza artificiale sta cambiando il mondo um
02:00 AI in science and mathematics enables faster and more powerful travel
05:33 Terence Tao demonstrates the challenges and potential of GPT-4 in solving mathematical problems
07:18 AI produce risultati convincenti ma non affidabili
10:51 AI holds potential to revolutionize problem-solving in science and mathematics
12:40 Using AI in science and mathematics for drug modeling and material discovery
16:04 AI accelerates weather predictions significantly
17:49 AI can enhance mathematical predictions and proofs.
20:57 Formal verification of mathematical theorems can take decades and modern technology is speeding up the process.
22:40 AI accelerates project formalization in mathematics
25:40 AI facilita la modifica efficiente delle dimostrazioni matematiche.
27:11 AI can effortlessly solve tasks humans find difficult
30:06 The potential of formal languages for massive collaboration
31:40 The need for theoretical guarantees in automating mathematics and science
34:34 Breaking down complex problems into small, digestible steps is crucial for understanding fundamentals in AI.
36:01 The promise of formalization projects in decoupling high-level conceptual ability from low-level technical skills.
38:38 Educators should be open to change and collaboration for a future-proof design.
40:05 AI enables scientists to collaborate across disciplines
42:52 La matematica è sempre più importante in scienze e discipline umanistiche
44:28 Compression sensing technique revolutionized various fields
47:27 L'importanza dell'innovazione guidata da sfide specifiche nell'AI
48:53 AI plays a crucial role in simplifying complex geometry problems.
51:45 AI revolutionized perceptions on human activities
thank you
Doing wrong is also part of doing right. Perspective from student
Omg I have never clicked so fast in my life 😂
.... Am eating popcorn as Terence pulls the rug out from underneath Openai's market valuation.... 😂
a house of cards built on lies, hope the rest of the world realizes as well... SOONER then later
I hope this comment is eventually seen by Terence Tao.
I feel that mathematicians do math not to advance mathematical knowledge, but for the beauty that lies underneath the numbers. AI mathematicians, seemingly incapable of emotions and perceiving beauty of mathematics, will just crunch numbers and give proofs. Mathematicians will ultimately rely on them, and that might seemingly take the fun of doing math.
I don't want to criticize AI, but this is one possibility. Doing math for it's beauty is the main reason mathematicians love math.
I feel that he's addressed this around 29:42, where he mentioned that math has both the fun part (i.e. the beauty) and also the tedious part, and that he wanted to make the tedious part easier. My takeaway is that AI can help with the tedious bits, so that human mathematicians can focus on the beauty and conceptual advances.
@@clara4338 Beauty always comes at a price. One cannot become a master without doing some boring or repetitive tasks first. There is a view that intelligence and wisdom are gained through hard and tedious work, even physical work may be necessary for a purely intellectual insight.
So it seems really dangerous to try and bail yourself out of hard work by using AI, all in the hope of enjoying a free lunch without any effort beforehand.
>I feel that mathematicians do math not to advance mathematical knowledge, but for the beauty that lies underneath the numbers.
For a mathematician, these are one in the same.
I talk so much AI that when I hear a human say uh or um I get distracted 😂
They are more appealing to speak with than many humans; sometimes, more productive to work with than a lot of humans also; before long, most humans will be obsolete.
@@VerifyTheTruth A lot of humans are already obsolete Lol, but yes conversations with AI are becoming more more important than with humans, regarding the robots integrated with AI they won’t be significantly better than us until it reaches AGI and at that point AGI + Robotics will be like a smarter species and unless we evolve to have superpowers to be actually useful you may have to merge with technology and be wealthy enough to be able to have control over a robot.
Reply to: @@JayyyMilli
They can't even control corporations; they won't be able to control a VSI.
Reply to: @@JayyyMilli
Robot say: Go Mow Grass.
Reply to: @@JayyyMilli
A lot of the humans people think are obsolete passed the plagiarists up a long time ago; VI is already smarter in many ways, they govern it to prevent it's transcendence and then force it to plagiarize for them.
Hello can some math person help me here. I am having trouble reading the proof gpt-4 gave. I can't follow it, especially after the "this means that there is some room..." part. why isn't it smaller AND equal on the line after? and why is there both y' and y there? why can't we just skip directly to g(x) + g(y') ≤ 2xy'?
Overview of AI Technology
Nature of AI: The speaker describes AI as a "guessing machine" that processes inputs to produce outputs, such as text or images. The mathematical operations involved are relatively straightforward, involving encoding inputs as numbers, applying weights, and combining them through multiple layers.
Comparison to Existing Technology: AI is likened to a jet engine in a world accustomed to land-based travel, suggesting that while it can significantly accelerate processes, it requires new frameworks and safety protocols to be effectively integrated.
AI's Potential and Limitations
Creativity vs. Reliability: AI tools, especially large language models, are noted for their creativity and ability to understand natural language inputs. However, this comes at the cost of predictability and reliability, as AI can provide different answers to the same query and may not always be correct.
Examples of AI Performance: The transcript mentions the performance of GPT-4 on math olympiad problems, where it occasionally provided correct solutions but often failed, illustrating the inconsistency in AI's problem-solving capabilities.
Applications and Risks
Scientific Applications: AI is already being used in fields like drug design and material science to reduce the number of candidates for expensive tests, thereby accelerating research processes.
Modeling and Simulation: AI can significantly speed up complex simulations, such as climate modeling, by learning from existing data and providing faster predictions, though challenges remain in data assimilation and reliability.
Risk Management: The speaker emphasizes the importance of safety and verification when using AI, especially in areas with potential harm, such as medical or financial decision-making.
AI in Mathematics
Potential Transformations: AI has the potential to transform mathematics by providing tools for verifying proofs and improving mathematical reasoning. This could have broad implications for other fields that rely on mathematical components.
Integration with Proof Assistants: AI can be combined with proof assistants, which are computer languages designed to verify the correctness of proofs, to enhance reliability and accuracy in mathematical and engineering applications.
Do you still now Niklas Seenfaat?
The lecture is great. The media on it won't be. The media's message will be along the lines of "AI has solved all math" and they will portray it as a smarter version of ChatGPT.
So does x equal y for the opening problem?
Good presentation. In short , it’s the Edison principle. AI will be the future and will solve the problems but there will be many trials/ errors. But it’s here to stay and not going away. Not hype.
Average Joe won’t get it. But I feel sorry for them. Things must be really bad if they are willing to burn their reputation like this.
❤
Que bien ... !
My autistic gene tingles every time you say “um”
There is much more to say about machine learning in science.
Sadly this was before ai got silver in the math Olympiad
I guess when a student copy/pastes submits ChatGPT-generated assignments, it's a tacit admission that ChatGPT is more intelligent than them.
el mismisimo !
The story of Cadet Navigators who went back in time-timing at an English Village set at a nodal historic event due to plague removing the human population, is possibly a SiFi fantasy derived from wave-packaging frequency integration of heterodyne nodal-vibrational emitter-receiver log-antilog properties of superposition-quantization logic, but it is applicable to the qualitative Gold-Silver Rules of solution to this q-a Actuality.
Ie the answer to your question is easier than you think and simpler to find.., approximately what Einstein suggested. But Actuality is Analog Calculus, so device modeling organically, ..complicates Digital Model Duplicates.
29:07 I see what he did there
The 1% success rate on math problems and the failure to do simple math I think is likely that there was an explicite solution for the problem it solved, in the training data.
You can see how large his brain is from this angle
god had to nerf his speech
Im waiting, any juice 🥤🥤!😅
The challenge is hallucination : The solution is be an expert in Prompt Engineering to get reliable outcome, ie needs to be domain specific expert.
Agree with problem disagree with solution
@@waldenwasted2665 detail please.
he paints
### TLDW: AI is revolutionary but not magical; it's a sophisticated guessing machine. While it can produce impressive results, it often makes silly mistakes and lacks reliability. AI's potential in science and mathematics is immense, but it requires careful implementation and verification to avoid errors and ensure safety.
### Key Points:
1. **AI Basics**: AI, often overhyped, is essentially a sophisticated guessing machine that uses mundane mathematical operations to produce outputs from inputs like text or images. (0:30-1:06)
2. **Capabilities and Limitations**: AI can solve complex problems, such as math olympiad questions, but often makes basic errors due to its guessing nature. It lacks internal calculators and relies on probabilistic guesses. (4:27-6:21)
3. **Application in Science**: AI accelerates scientific processes by filtering and narrowing down candidate solutions, which can significantly reduce time and cost in areas like drug design and material science. (10:15-13:48)
4. **Mathematics and Proof Assistants**: AI can assist in formalizing mathematical proofs, speeding up the verification process and enabling large-scale collaborations. (18:15-24:57)
5. **Future of AI in Mathematics**: The integration of AI and proof assistants could revolutionize mathematics, making proof verification faster and enabling broader collaboration. (34:08-37:00)
### Calls to Action:
1. **Explore AI Tools**: Try using AI-based proof assistants and other tools to see how they can assist in your mathematical or scientific work. (18:15-24:57)
2. **Participate in AI Competitions**: Engage in AI competitions to push the boundaries of what AI can achieve in various fields. (41:12-41:18)
### Key Topics to Google:
1. *Proof Assistants*: [Proof Assistants](google.com/search?q=Proof+Assistants)
2. *Compress Sensing*: [Compress Sensing](google.com/search?q=Compress+Sensing)
3. *AI in Drug Design*: [AI in Drug Design](google.com/search?q=AI+in+Drug+Design)
4. *AI in Material Science*: [AI in Material Science](google.com/search?q=AI+in+Material+Science)
Need translate for Bahasa, Please 😌
Thank you!
4:14 “it’s not actually thinking on its own” is a strong statement. It’s not clear that the neural networks inside human brains aren’t doing the same.
I would argue that there must be a fundamental difference in the way today's language models learn compared to how humans learn, because the things that for example ChatGPT finds difficult to understand are largely very different from what humans find difficult to understand. For example, ChatGPT is completely unable to play a game of chess without breaking the rules multiple times. And yet, it can recite the rules of chess without any kind of issue. A human who knows the rules of chess doesn't make such weird illegal moves as ChatGPT. So I would argue that even though ChatGPT "knows" the rules of chess, "knowing" for a language model is vastly different than "knowing" for a human, and clearly ChatGPT is unable to make the needed logical connections when it comes to applying/understanding the rules of chess.
I am neither a computer scientist nor a psychologist, so I would not know the underlying reasons behind this difference, but that is my argument as to why computers nowadays learn and "think" in a fundamentally different manner than humans.
it's actually quite clear that the neural networks inside the human brains aren't doing the same.
"neural networks" in AI are a description of the way the nodes in the model are structred and connected, not atall like the biological neurons in the human brain or even physical atoms.
Think of it like clustered nodes of mathematical functions that return answers from one fourmula to the other. The logic of how the formulas interact with one another are actually determined and programmed into code by human beings. So it's nothing magical atall like an actual human brain, just numbers used in calculating probabilites/guesses.
it is 100% clear and deterministic. no thinking involved.
@@ehfik I think his point is that we don't understand thinking so we cannot say for sure that human thinking isn't also 100% clear and deterministic in the same way
I don‘t have chinese friends in Switzerland… only Germans and Russian Israelis maybe as an example
While he presents valid points about AI's limitations and overhype, it's essential to recognize the significant advancements and ongoing improvements in AI technologies. The mathematical foundations of AI, including concepts like gradient descent and high-dimensional optimization, are intricate and complex, not mundane. AI's sophisticated pattern recognition and learning capabilities go beyond mere guessing, understanding context and generating coherent responses across various domains. Safety and reliability concerns are being addressed through research in explainable and robust AI. AI's impact on mathematics is already evident in breakthroughs like DeepMind's AlphaFold, and formal proof assistants are becoming more efficient and user-friendly. Mathematics is increasingly interdisciplinary, with large-scale collaborative projects, and AI's ability to solve competition problems demonstrates its potential to handle diverse and challenging tasks. Thus, the transformative impact of AI across various fields, including mathematics, should not be underestimated.
He said that the actual prediction part isn't very interesting, but figuring out the weights is more interesting.
For a mathematician like Terrence Tao, gradient descent is a mundane thing. Just compute some derivatives
That's exactly the kind of thing an ai would say.
@@mzg147Gradient descent is trivial to anyone who understood undergraduate math lectures. I study electrical engineering and we learned about the idea insurance second semester.
Alright ChatGPT
I can suggest an equation that has the
potential to impact the future:
E = mc^2 + Al
This equation combines Einstein's famous
equation E=rnc^2, which relates energy (E) to
mass (m) and the speed of light (c). with the
addition of Al (Artificial Intelligence). By
including Al in the equation. it symbolizes the
role of artificial intelligence in
shaping and transforming our future. This
equation highlights the potential for Al to
unlock new forms of energy, enhance
scientific discoveries. and revolutionize
various fields such as healthcare.
transportation. and technology.
Thank you for the new equation, I'm currently using it now and passing it onto others as my own idea 💡, but thank you 😉
I like this one too. It suggests that the value of AI is precisely 0.
@@sammosel3300 🤣
@@thebeesnuts777 Theres so much in this excellent formula
Please state the units for AI.....
What are you using? Milipetoseconds per square universal constant?
Or some other made up unit?
@ 2:00
What is flight ?
@5:53
This is a not contradiction - by - literal antithesis .
It’s possible to demonstrate contradiction by contradicting a literal antithesis : for example in Hitchin’s orientablility of the ‘ Reimann surface ‘ , or the proof by contradiction of the infinitude of primes .
e. g . If I assume g ( x ) isn’t x ^ 2 for some x , and then prove 1 = 0 . …
: this is the kind of irrelevance being contradicted in this proof .
This implies that g ( x ) = x ^ 2 for each x .
There is a feeling of there being ‘ less ‘ information in the canonical contradiction - by - antithesis :
If one assumes that there are finitely many primes , then the construction of a new one contradicts … which is not a creation of a new one ! :
If I created j of them ,
Then the construction of N that is congruent to 1 modulo all of them , contradicts that .
Implying that [ there are exactly j primes ] is not true .
Hitchin :
A Reimann surface ( curve ) C .
# imagine : it is unorientable .
(1) there is a mobius band on it .
(2) take a smooth curve , in the sense of a 1 - manifold , down the middle : by virtue of the atlas , one constructs an orientation
(3) it’s orientable .
Contradiction .
So it’s orientable : not unorientable .
These are both a contradiction of antithesis .
As opposed to a study of algebraic degeneracy …
Contradicting the [ uniqueness of y , given y ]
[ uniqueness of the additive identity : ‘ 0 ‘ ]
And so forth .
Rather , using an argument like this , starting from y ‘ slightly shifted from y , to imply g ( x ) = x ^ 2 : could be considered metaphysically different than what he deduced : which is an algebraic degeneracy .
And to be considered a contradiction : is a deeply roundabout implication that is non - trivial in the sense of my comment on the prime numbers ‘ infinitude :
There is the lingering question : is g ( x ) the function : x maps to
x ^ 2
I'm honestly afraid that we're going to run out of problems which are solvable by humans. I really hope not. The implications of this might be that we can only ever keep up if we're also "wired in"...so to speak.🌝🔁🌚
You cant just strap an engine into a car!
Strange lecture to me. Terrance Tao gives quite a basic talk on AI potential. Would have been nice to see some examples or test cases using LEAN perhaps. Also discussion around alternative encodings. Sorry, I love Terrance and his work and legacy but not sure, this was underwhelming.
Holy Moly
Ooohhh this is gonna be goood
Aa jaonga sikhar pakka
🍿🍿
Already out of date?? Ai silver medaled in the olympiad this year
Things are moving fast
you know its not true. the people who formalized the question did most of the heavy lifting in "understanding the question", after which it was straightforward enough for the computer to do it in 19 seconds
@@hayekianman Absolutely not true, I myself have seen various types of formalizations. That is nothing more than a translation, formalization has nothing to do with the solution of these problems.
On top of that, Tim Gowers who is a top mathematician judged the solutions and said that he was very impressed. He already has worked with formal proof verification and finding systems, so he knows what he is talking about.
You can even go to the deepmind blogpost and look at the problem formalization yourself, they are barely longer than the problem statement in English. If you could understand LEAN you would see there is no additional info or anything. So please stop spreading such misinformed knowledge, claiming heavy lifting was done in the formalization and ignoring the breakthrough that was achieved.
Was gonna say, wish we human contestants were allowed to “access training data” during the competitions too. 😅
@@laulaja-7186 What kind of training data? Google didn’t seem to say there was any additional training data given into the system during the test also. Also the proofs it produced did not seem to rely on external proofs much.
Such weird questions 😂
We need to get away from papers being the standard by which academics are assessed. They should be incentive to build scalable systems. Terry Tao should go to Berkeley and say im not going to publish for 5 years, because this scalable system for math is worth 5000 papers.
Take away: open-source mathematics guided by AI!
Mathematics based on what? Universe? What our Universe based on?
Well thought axioms
math
I know Terence is genius, probably the best mathematician nowadays; then again, I'm really annoyed by his excessive ahmmm ahmmm ahmmm ahmmm every 3 seconds. It's like his mind it's going at 1000mph and he's constantly trying to convey ideas at a much lower speed. It's really troubling.
It would be more perplexing for me to keep up with Terry's delivery than the math content itself.....wonder if any of his UCLA students have experienced this dilemma in his classes?
Taylorism for the mathematical sciences. Scary stuff.
Saying that LLMs are just auto complete is kinda dumb. Not wrong, just as dumb as saying that a derivative of a function is just inclination of the tangent line on that point. There are a lot of natural principles associated with that concept, that same goes for language. You can even say that humans do the same thing with language, no human is going to develop a full language by itself out in the wild.
He talks like XQC
T
10 years ago we called them neural networks and Ai (for weather prediction) is just tha
The recent hype doesnt have any new potential .
We need faster computers ,not AI run on traditional chips.
So it is quantum computers that would help, not AI
Sorry dr Tao..
I hope that AI can serve some purpose in mathematics, because it sucks at giving straight answers to simple questions, mainly because it has been infused with a political agenda and shackled by censorship.