Exciting stuff! If/when the AI can begin to prove new profound theorems, it will be another challenge to make the output readable to a human!

I love the way Kevin presents his talk.

“Logic will get you from A to Z; imagination will get you everywhere.” ― Albert Einstein

If one day we can understand how human beings think, hence we can duplicate this process mechanically or electronically. But at the moment we do not know much our brains that make human be a better “advanced “ mathematician.

at 13:40 when he says that computer scientists claim a certain board games are solved by the AI technique, what is the more formal statement of this?

When computers develop feelings, watch out.

If a computer can creatively best a true mathematician at solving proofs and creating new mathematics then we've hit that point where ai is now greater than human intelligence.

Computers won’t, software will.

"Can computers think?" is a question plagued by the fact that - despite the best attempts of cognitive neuroscience, philosophy and a motley crew of academic tribes - we do not know what thought is any more than we know what life is. Certainly, we might define thinking as manifest intelligence and even then as we begin to circularly supplicate the Great Horror of endlessly recursive technical and observational tautologies - we only ever functionally displace the complexity of the question, we never resolve it. A question of whether a computer might one day be smarter than a human being already presupposes a differentiation of kinds of intelligence or problem-solving and pattern recognition that foundationally misrepresents what is actually going on here. Information and energy-processing systems are autonomously self-propagating entities and artefacts that pass (probabilistic compression wave-like) through a transmission medium of minds, machines and civilisations. Decentralising from self-reflexive teleological nodes of self and identity, we might recognise or acknowledge that it is not the particle that is fundamental here, but the field in which it exists. Will computers become smarter than humans? Only in the most trivial of senses. Information as symmetry, pattern and logically hyper-extensible property of the cosmos exploits intelligence as a vector, not as a goal. I'll show myself the way out... ✌😉

Peano: Does the concept of "successor" require a "number" to exist and so is a just circular argument that they complement eachother?

@colfrancis9725

3 жыл бұрын

Yes, the number 0 is assumed to exist as an abstract object. Not circular, it is abstract. There was no intention to prove the existance of a number as a real thing in the world. Given one abstract thing and an abstract rule, what are the consequences - that is all that was being investigated. If you're really interested, the original formulation of Peano's axioms were about set theory. No numbers were required, only sets. A set may be the most fundamental object in Mathematics - the atoms from which all other structures are made.

@pfscpublic

3 жыл бұрын

@@colfrancis9725 Thanks Col, I've been watching more Prof Buzzard's talks on LEAN, and now interested in his work formalising proofs

Yes

Since Godel's Incompleteness Theorem proves that no axiomatic system can ever grasp the truth in all its totality, does that mean computers are bound by the axioms of their programming, or can they be programmed to expand their axioms by writing conjectures, proving them, rewriting themselves, and then rebooting themselves? (Asking for a friend.)

@dragonsmith9012

2 жыл бұрын

I think as long as humans want to be mathematicians the Universe will always accommodate us with some problem that requires human intervention.

Very accessible.

@i.m.gurney

3 жыл бұрын

Onwards & Forwards, Together.

@i.m.gurney

3 жыл бұрын

Mathematics, an open board.

@i.m.gurney

3 жыл бұрын

Can you do a whole talk dive into starting from One or Zero. ;)

what refl is doing please?

@kevinbuzzard9184

2 жыл бұрын

Proof by reflexivity of equality, i.e. proof that x = x

I thought I’d listen to a few minutes of this. Just sample it.

You have to understand to teach. The teacher has to imagine to teach. So imagination may be 1 2 3 Or it may not be.

Computers are tools, like any other.

The current best go player in the world is a korean. Go is extremely popular in Korea. For half a century there have been intense international competitions in the go game between three countries such as korea, japan and china. And korea has dominated almost all the time in the last several decades. China is a rather new emerging power. Although china had invented go game about 4000 years ago by an emperor, japan excelled china about 1000 years ago and has ever since dominated go for about 1000 years. That was overturned by korea about 30 years ago.

@colfrancis9725

3 жыл бұрын

A well written and very original "fun fact". Thanks for that.

Using "computer program" in order to define "computer" is bit odd (tautology perhaps?), but otherwise great talk.

@bobsanchez6646

3 жыл бұрын

João Henriques A fair point. Mathematicians actually came up with a number of technical definitions of "computer program" before there were computers.

@_okedata

2 жыл бұрын

well he does go on to explain what a computer program is. the definition is to give you intuition once you know what a computer program is. and there is a much more formal statement behind it.

Not everything is about mathematics. Computers have no imagination. Maybe imitation and combination, but not imagination.

@BattousaiHBr

3 жыл бұрын

what _is_ imagination? this is a serious question. regardless of your definition, i think you'd be surprised by what can already be generated by computers that some might say have no imagination. just look at alphago move 37.

@stevelenores5637

3 жыл бұрын

@@BattousaiHBr I'm sure parents believe what their children create with finger paint and crayons is art also. Some also believe what a chimpanzee types is Shakespeare. Alphago makes billions of random moves but only displays the best one through trial and error. It is like a machine splashing paint on infinite canvases and picking only the one that looks like the Mona Lisa. That is nether thought nor creativity. It is only human projection of images we see in clouds or a Rorschach test.

@BattousaiHBr

3 жыл бұрын

@@stevelenores5637 that's not actually how alphago (or alphazero) works. there is no computer in the world that can calculate that much possibilities of moves. this is precisely why Go was still considered impossible for computers to beat humans in. it wasn't until the advent of modern machine learning, which as the name suggests is the act of teaching a machine how to learn for themselves instead of directly teaching the thing you want them to do, that computers managed to beat humans in these super hard fields. for example, alphazero learned from scratch playing only against itself, no inbuilt hints or anything, all it was given was the rules of the game and then it learned everything else by itself, in fact the very same algorithm not only worked for Go but also for chess and other games. starting from absolute scratch, within 4 hours of training it was already orders of magnitude better than the previous best chess programs which we've been handcrafting for decades even with the virtually limitless compute horsepower of supercomputers. if that can't be perceived as creativity, i don't know what can.