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Can AI do maths yet? Thoughts from a mathematician

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Re: Can AI do maths yet? Thoughts from a mathematician

#141

Post by Hizonner »

jebarker wrote: post #118

> I am dreading the inevitable onslaught in a year or two of language model “proofs” of the Riemann hypothesis which will just contain claims which are vague or inaccurate in the middle of 10 pages of correct mathematics which the human will have to wade through to find the line which doesn’t hold up. I wonder what the response of working mathematicians will be to this. If the proofs look credible it might be too tem…

Don't waste time on looking at it unless a formal proof checker can verify it.

Re: Can AI do maths yet? Thoughts from a mathematician

#142

Post by deepsun »

busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

By the way, don't trust Nobel laureates or even winners. E.g. Linus Pauling was talking absolute garbage, harmful and evil, after winning the Nobel.

Re: Can AI do maths yet? Thoughts from a mathematician

#143

Post by exprofmaddy »

tananan wrote: post #89
voidhorse wrote: post #63

Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans. Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the…

> Unless you believe in determinism and an overseeing god Or perhaps, determinism and mechanistic materialism - which in STEM-adjacent circles has a relatively prevalent adherence. Worldviews which strip a human being of agency in the sense you invoke crop up quite a lot today in such spaces. If you start of adopting a view like this, you have a deflationary sword which can cut down most any notion that's not mechani…

Agreed. If someone believes the world is purely mechanistic, then it follows that a sufficiently large computing machine can model the world---like Leibniz's Ratiocinator. The intoxication may stem from the potential for predictability and control.

The irony is: why would someone want control if they don't have true choice? Unfortunately, such a question rarely pierces the intoxicated mind when this mind is preoccupied with pass the class, get an A, get a job, buy a house, raise funds, sell the product, win clients, gain status, eat right, exercise, check insta, watch the game, binge the show, post on Reddit, etc.

Re: Can AI do maths yet? Thoughts from a mathematician

#144

Post by exprofmaddy »

red75prime wrote: post #85
voidhorse wrote: post #63

Eventually we may produce a collection of problems exhaustive enough that these tools can solve almost any problem that isn't novel in practice, but I doubt that they will ever become general problem solvers capable of what we consider to be reasoning in humans. Historically, the claim that neural nets were actual models of the human brain and human thinking was always epistemically dubious. It still is. Even as the…

> there is no reason to believe a connection between the mechanical model and what happens in organisms has been established The universal approximation theorem. And that's basically it. The rest is empirical. No matter which physical processes happen inside the human brain, a sufficiently large neural network can approximate them. Barring unknowns like super-Turing computational processes in the brain.

The universal approximation theorem is set in a precise mathematical context; I encourage you to limit its applicability to that context despite the marketing label "universal" (which it isn't). Consider your concession about empiricism. There's no empirical way to prove (i.e. there's no experiment that can demonstrate beyond doubt) that all brain or other organic processes are deterministic and can be represented completely as functions.

Re: Can AI do maths yet? Thoughts from a mathematician

#145

Post by pfisherman »

busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

I used to do bench top work too; and was blessed with “the golden hands” in that I could almost always get protocols working. To me this always felt more like intuition than deductive reasoning. And it made me a terrible TA. My advice to students in lab was always something along the lines of “just mess around with it, and see how it works.” Not very helpful for the stressed and struggling student -_-

Digression aside, my point is that I don’t think we know exactly what makes or defines “the golden hands”. And if that is the case, can we optimize for it?

Another point is that scalable fine tuning only works for verifiable stuff. Think a priori knowledge. To me that seems to be at the opposite end of the spectrum from “mess with it and see what happens”.

Re: Can AI do maths yet? Thoughts from a mathematician

#146

Post by vouaobrasil »

busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

I was just thinking about this. I already posted a comment here, but I will say that as a mathematician (PhD in number theory), that for me, AI signficantly takes away the beauty of doing mathematics within a realm in which AI is used.

The best part of math (again, just for me) is that it was a journey that was done by hand with only the human intellect that computers didn't understand. The beauty of the subject was precisely that it was a journey of human intellect.

As I said elsewhere, my friends used to ask me why something was true and it was fun to explain it to them, or ask them and have them explain it to me. Now most will just use some AI.

Soulless, in my opinion. Pure mathematics should be about the art of the thing, not producing results on an assembly line like it will be with AI. Of course, the best mathematicians are going into this because it helps their current careers, not because it helps the future of the subject. Math done with AI will be a lot like Olympic running done with performance-enhancing drugs.

Yes, we will get a few more results, faster. But the results will be entirely boring.

Re: Can AI do maths yet? Thoughts from a mathematician

#147

Post by joshuaissac »

bondarchuk wrote: post #104
newpavlov wrote: post #101

Earlier quoted context omitted.

It's a property of the "semi-artificial" problem chosen by Google. If anything, it means that we should heavily discount this claim of "quantum advantage", especially in the light of inherent probabilistic nature of quantum computations. Note that the OP wrote "you MUST compute something that is impossible to do with a traditional computer". I demonstrated a simple counter-example to this statement: you CAN demonstra…

Apparently they can't, right now, as you admit. Anyway this is turning into a stupid semantic argument, have a nice day.

If they can't, then is it really quantum supremacy?

They claimed it last time in 2019 with Sycamore, which could perform in 200 seconds a calculation that Google claimed would take a classical supercomputer 10,000 years.

That was debunked when a team of scientists replicated the same thing on an ordinary computer in 15 hours with a large number of GPUs. Scott Aaronson said that on a supercomputer, the same technique would have solved the problem in seconds.[1]

So if they now come up with another problem which they say cannot even be verified by a classical computer and uses it to claim quantum advantage, then it is right to be suspicious of that claim.

1. https://www.science.org/content/article/ordinary-computers-c...

Re: Can AI do maths yet? Thoughts from a mathematician

#148

Post by red75prime »

exprofmaddy wrote: post #144
red75prime wrote: post #85

Earlier quoted context omitted.

> there is no reason to believe a connection between the mechanical model and what happens in organisms has been established The universal approximation theorem. And that's basically it. The rest is empirical. No matter which physical processes happen inside the human brain, a sufficiently large neural network can approximate them. Barring unknowns like super-Turing computational processes in the brain.

The universal approximation theorem is set in a precise mathematical context; I encourage you to limit its applicability to that context despite the marketing label "universal" (which it isn't). Consider your concession about empiricism. There's no empirical way to prove (i.e. there's no experiment that can demonstrate beyond doubt) that all brain or other organic processes are deterministic and can be represented co…

Function is the most general way of describing relations. Non-deterministic processes can be represented as functions with a probability distribution codomain. Physics seems to require only continuous functions.

Sorry, but there's not much evidence that can support human exceptionalism.

Re: Can AI do maths yet? Thoughts from a mathematician

#149

Post by noqc »

bondarchuk wrote: post #84
newpavlov wrote: post #38

Earlier quoted context omitted.

>in the quantum research to demonstrate any valuable forward progress you must compute something that is impossible to do with a traditional computer This is factually wrong. The most interesting problems motivating the quantum computing research are hard to solve, but easy to verify on classical computers. The factorization problem is the most classical example. The problem is that existing quantum computers are not…

No, it is factually right, at least if Scott Aaronson is to be believed: > Having said that, the biggest caveat to the “10^25 years” result is one to which I fear Google drew insufficient attention. Namely, for the exact same reason why (as far as anyone knows) this quantum computation would take ~10^25 years for a classical computer to simulate, it would also take ~10^25 years for a classical computer to directly ve…

the unverifiable regime is a great way to extract funding.

Re: Can AI do maths yet? Thoughts from a mathematician

#150

Post by Radim »

deepsun wrote: post #142
busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

By the way, don't trust Nobel laureates or even winners. E.g. Linus Pauling was talking absolute garbage, harmful and evil, after winning the Nobel.

> don't trust Nobel laureates or even winners

Nobel laureate and winner are the same thing.

> Linus Pauling was talking absolute garbage, harmful and evil, after winning the Nobel.

Can you be more specific, what garbage? And which Nobel prize do you mean – Pauling got two, one for chemistry and one for peace.

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