Is AI Replacing Mathematicians? Discussing Google’s AlphaGeometry

Is AI going to replace mathematicians? Should we be worried? Discussing Google's latest artificial intelligence system - AlphaGeometry!

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[kdog]

Yeah but an AI doesn't get a buzz from smashing a tough maths problem.

[benjaminbirdsey]

It seems almost impossible to me that AI could replace mathematicians or research scientists.

First, the AI is trained only on things that are known, so it will be much better at interpolating datasets than extrapolating. Second, the space of possible mathematics and possible knowledge is so incredibly huge* that the algorithm will not be able to determine which novel "discoveries" are interesting to humans (e.g. because if it is truly novel then nobody could possibly know whether it is interesting).

Further, real-world mathematics is often so complicated that it is often said that nobody understands General Relativity, even though we can mostly calculate it. How much less do we understand string theory or quantum chromodynamics, which might just exist on the NC part of the C/NC conjecture.

* This brings to mind Douglas Adams's quote about how incredibly big space is, but like how big that is to that same power.

[ambrish]

Please can you make videos on research initiatives working on other mathematics areas like continuum and topology and what r the current bottle necks

[Morpheus-zwpx]

nah chat gpt 3.5 cant even consistently give me the roots of a 3rd order polynomial

[Ben_D.]

It's going to be amazing. Cant wait.

[musashi]

Iteration at the speed of light may be novel but not brilliant. It's akin to primates inadvertently writing the Iliad given trillions of attempts.

[LuisBrudna]

Every single year artificial intelligence will get better and better

[peterseissler]

Hey, I used Macsyma, a MIT based algebra system, in the late 1970s (I was an undergrad at Hopkins and then grad at MIT). I used that for complex PDEs. It was not based in neural net but symbolic manipulation. It was grant from ARPA and three Professors developed, Joel Moses, Carl Engelman and William Martin, all at MIT.

[saturdaysequalsyouth]

Not sure how this ended up on my feed but good video. No hype or hysteria just straight info.

[mrkrud]

For someone like me with limited math vocabulary and some math is one of many necessary skills, watching the steps is a gold mine. Thank you for that concise and insightful introduction.

[Andrew-rcvh]

Surely the Wolfram system is the bulk of the work? The AI is giving it a user-friendly front end to it. Regarding lack of training data, the Wolfram system got a lot of stuff uploaded by hand. This is because you don't want it to learn mistakes.

Another good AI I saw the other day designed a CPU chip from scratch. They built it up and got it running and it was about as powerful as a 486.

[veganath]

Wasn't a new faster matrix dot product algorithm discovered by AI?

[derekgreenacre]

Very interesting, if the Ai is to be extended into other areas of maths I can foresee a couple of snags 1) Could it be that proof becomes so long and tedious that it would be impossible for a human to check it, and if we could not check it how would we know if the machine is lying? 2) Mathematics is essentially a creative process and humans are great at thinking outside the box. For example take the invention of complex numbers using the letter "i" to stand for a number that does not exist is an idea that appears to have no purpose but we know how useful it is when it's possibilities are explored. The idea of exploring such barren areas is a human trait and difficult to mimic in machines.

[dietwald]

Intuition and inspiration are what separates intelligence from algorithms.

[davidmurphy]

An AI solving maths is just another case of maths solving maths. It's like using pythogoras to get the magnitude of a vector. You're using linear algebra and calculus to solve a geometric problem.

[RAZTubin]

Hold on. AI solved problems with known solutions. If it was trained, it basically copied human solutions.
Give it a problem with an unknown solution from the Millennium Prize Problem.
If it can be solved then, I'll be impressed.

[carljones]

Since you're also a mathematics grad, I won't go easy on the jargon. Your description of how we solve problems mathematically is a bit incomplete. And kind of in a sad way, because it doesn't leave any room for creative problem solving, although you touch on that concept just a bit.

Incompleteness and Tarski's undefineability tell us that all machines (a process which computationally solves a problem) are strictly stuck in productive sets; i.e. AI is not able to be a creative task (unless someone has invented a problem-solver that doesn't rely on computation and hasn't let the rest of us know). Those same previously mentioned theorems also tell us that the collection of solvable problems can be partitioned into those which can be solved productively and those which can only be solved creatively. And, we already know that the collection of undecideable problems (i.e. those which cannot be solved productively) is even larger than the collection of decideable problems.

I say all of that to say this: AI will certainly, within our lifetime, become capable of solving every problem which is computationally decideable. However, until someone figures out how to make a problem-solver that doesn't rely on computation, the problems which will be left to us human mathematicians to solve remain uncountably numerous with unknowable potential for importance, elegance, and fun among them. The most exciting part of AI is that it will help us to discover problems even faster than we (or it) can formulate them, let alone solve them. All of us have very bright futures, including the lowly applied mathematicians like me.

[paulgaddis]

The thing to consider is that this is just two models working in concert together. Imagine what happens when they start training a model for each specific math domain. Then you mixture of experts them. With a really really creative (playing with the attention values) LMM as the head model over seeing the agent work flow. You can already do this with coding agents to get them to build software on a local machine. I'd be very curious to see what a MOEMM (mixture of experts maths model) would be capable of solving if it had the knowledge domains of geometry, calculus, trig, and probably more.

[mickistevens]

You know, there should be a way to get to the gist or answer of the title in a Youtube title for those who are aware of the issues but that would deny Youtube all the viewing time.

[DarwinianUniversal]

I have a concept relating to anomalous galaxy rotation velocity. I can work the concept as a geometric consideration, and Claude was able to conceptualize my work and develop the mathematical formulation. What a gift