alt Hacker News> 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.
Replies
>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.
Outdated view. Reasoning models do a lot of "thinking", and can solve novel problems - even quite difficult problems.
The whole reason we're even having this conversation is because AI solved a millennium prize problem that no human knew an answer to.
AIs have representations of the training data, but they also do search. Search creates new knowledge. For example, a chess program doesn't have a representation of all chess games, but can search and in doing so create new games. This isn't (just) random generation, but generation constrained by an evaluation function.
> AI is more a database of knowledge than a thinking machine. You can query a compressed version of millions of books.
No…? Isn’t the entire reason we are having this discussion because LLMs are coming up with results that are not already represented in the training data?