> back in 1988, when we first introduced Mathematica, there was also some of the same kind of talk about math being taken over, and made pointless. Of course that’s not how it worked out at all.
Makes sense.
> For me, its greatest use in mathematical pursuits has been its ability in effect to thematically mine the knowledgebase of human mathematics. ... Modern AI is, first and foremost, a way of leveraging the existing corpus of human knowledge.
AI is more a database of knowledge (stolen knowledge but let's leave that discussion asside) than a thinking machine. You can query a compressed version of millions of books.
That is very useful. (Are we already StarTrek-communists?
> generating useful mathematics is a much more exacting activity than generating language.
This is something that most people forget. Generative AI is mostly LLMs, and they are chatbots not mathbots.
> It’s a frustrating feature of modern times that someone like me gets sent many AI-generated documents every day that have the “statistical texture” of math papers, but that one at least expects have a very low probability of being meaningfully correct
And here is the trick. A million monkeys with a million typewriters may write a Shakespeare masterpiece. But they would not be able to differentiate it from garbage text.
> So, yes, there’s every reason to expect a bright future—now with some additional help from AI—for that most rarefied of human pursuits: research in pure mathematics.
I think the big question is whether these recent gains continue. It’s entirely plausible that the ai firms are going to run out of human trainers capable of further refining the model. It’s also possible we are on the cusp of real superintelligence.
Much more rejections due to more submissions, and AI will probably not help you (unless you solve a major open problem).
Even frontier models still struggle at proving small conjecturers despite all the hype about major breakthroughs. It really depends a lot on the prompt, the type of problem, among other factors. But AI does not suddenly make publishing in a journal easier, although it does make it easier to produce papers.
The desperately needed TL;DR is that perhaps the actual mathematics itself (i.e. proofs, calculations, etc.) can be done by AI, but why we do it and deciding which problems to solve can only be done by AI. Therefore mathematician do maths.
I'm not a mathematician, but this seems like a weak and slightly bizarre argument.
I'm wondering how we are going to maintain a critical mass of people who understand frontier mathematics if in another five or ten years the only "mathematicians" truly working at the frontier anymore are AIs. Or maybe "understanding" at depth will become a thing of the past, superseded by broad-strokes grasp of results plus machine verification.
If training data are purely historical, then how does the AI look forward?
And if human mathematicians are drummed out of producing future training data, then can AI end up proving itself so much "eating the seed corn", only at scale?
If training data are purely historical, then how does the human look forward?
Seems to me not impossible that given current knowledge, AI generate one nugget more of knowledge (eg a proof of Navier Stokes), and given current knowledge + the nugget, generate yet some more new knowledge.
> back in 1988, when we first introduced Mathematica, there was also some of the same kind of talk about math being taken over, and made pointless. Of course that’s not how it worked out at all.
Makes sense.
> For me, its greatest use in mathematical pursuits has been its ability in effect to thematically mine the knowledgebase of human mathematics. ... Modern AI is, first and foremost, a way of leveraging the existing corpus of human knowledge.
AI is more a database of knowledge (stolen knowledge but let's leave that discussion asside) than a thinking machine. You can query a compressed version of millions of books.
That is very useful. (Are we already StarTrek-communists?
> generating useful mathematics is a much more exacting activity than generating language.
This is something that most people forget. Generative AI is mostly LLMs, and they are chatbots not mathbots.
> It’s a frustrating feature of modern times that someone like me gets sent many AI-generated documents every day that have the “statistical texture” of math papers, but that one at least expects have a very low probability of being meaningfully correct
And here is the trick. A million monkeys with a million typewriters may write a Shakespeare masterpiece. But they would not be able to differentiate it from garbage text.
> So, yes, there’s every reason to expect a bright future—now with some additional help from AI—for that most rarefied of human pursuits: research in pure mathematics.
Happy to hear that.
What is a good exit strategy?
We live not to have a good time, but to make the times good.
Interstellar diaspora.
Read by the author https://www.youtube.com/live/gPrWX8i1htM (with multiple mentions of the Wolfram language and such)
Some arguments are based on "past experience..."
However, such experiences are not absolute truths and cannot be equated with the current situation.
I think the big question is whether these recent gains continue. It’s entirely plausible that the ai firms are going to run out of human trainers capable of further refining the model. It’s also possible we are on the cusp of real superintelligence.
Much more rejections due to more submissions, and AI will probably not help you (unless you solve a major open problem).
Even frontier models still struggle at proving small conjecturers despite all the hype about major breakthroughs. It really depends a lot on the prompt, the type of problem, among other factors. But AI does not suddenly make publishing in a journal easier, although it does make it easier to produce papers.
The desperately needed TL;DR is that perhaps the actual mathematics itself (i.e. proofs, calculations, etc.) can be done by AI, but why we do it and deciding which problems to solve can only be done by AI. Therefore mathematician do maths.
I'm not a mathematician, but this seems like a weak and slightly bizarre argument.
> but why we do it and deciding which problems to solve can only be done by AI
Sorry, was there a typo here? Both sides of the comparison are AI, and in the affirmative?
I'm wondering how we are going to maintain a critical mass of people who understand frontier mathematics if in another five or ten years the only "mathematicians" truly working at the frontier anymore are AIs. Or maybe "understanding" at depth will become a thing of the past, superseded by broad-strokes grasp of results plus machine verification.
If training data are purely historical, then how does the AI look forward?
And if human mathematicians are drummed out of producing future training data, then can AI end up proving itself so much "eating the seed corn", only at scale?
This applies to all professions, not just mathematicians.
The most common answer I’ve heard so far is “well, AI will train on its own output… maybe”.
I don’t think that’s even possible.
If training data are purely historical, then how does the human look forward?
Seems to me not impossible that given current knowledge, AI generate one nugget more of knowledge (eg a proof of Navier Stokes), and given current knowledge + the nugget, generate yet some more new knowledge.
Not a given, but not obviously impossible either.