alt Hacker NewsSuppose you are a maths researcher and you come across a problem, ... most likely, you will feed it to an AI. There are two possibilities: either the AI solves the problem or it does not.
If it solves the problem, you can ask the AI to explain it you. But if it does not solve it, will you really wager 30 years of your life on the possibility that you might be smarter than the AI?
I keep hearing about people spending their entire career on a single problem. And I think that time has ended. I think in Mathematics will be like chess.
Replies
> I think in Mathematics will be like chess.
What do you mean?
Do you think more people than ever will start doing math, with millions of people solving daily math puzzles on their phone on math.com[1] while commuting ?
I don't think Mathematics will be like Chess.
[1]: (or its open-source variant limath.org)
I dont get this. What is the difference if you replace "AI" by "Tao"? And people still were doing math.
I get HN is a Software site. But all math posts are invaded by people that think Math=Software. Probably based on the way they were taught maths when they were young.
Why would a theoretical physicist spend 30 years developing a theory that could be made false by a new experiment with a new technology? Was Newton gravitation worth if einstein was going to come later?
We are heading directly into a world where people forget about what values, philosophy, poetry, math, physics, or any other "non economically valuable" things are. And we all know what happened any other times in history when that happened.
> If it solves the problem, you can ask the AI to explain it you.
Will I get an understandable and verifiable explanation? And, if the system cannot solve the problem, will I get an understandable and verifiable explanation of that? As a researcher I'd think that shared understanding is the point.
Math research isn't all or nothing on a single problem. Rather, the problem would serve as inspiration to explore achievable subproblems, weaker problems, related topics, etc. These would be interesting papers by themselves, but if lucky may also lead to progress on the main problem. So this leaves lots of room for using AI as an assistant.
> I keep hearing about people spending their entire career on a single problem. And I think that time has ended. I think in Mathematics will be like chess.
Is the Langlands Program a single problem? Much of it is still ill-defined. How will AI win at newfangled chess when they haven’t got the rules yet?
>But if it does not solve it, will you really wager 30 years of your life on the possibility that you might be smarter than the AI?
Sure. Just because current technology can't prove or disprove something, doesn't mean it can't ever be proven or disproven.
> But if it does not solve it, will you really wager 30 years of your life on the possibility that you might be smarter than the AI?
The "AI" is trained on centuries of human theoretical frameworks and innovations. The "AI" can also work on problems full-time without teaching, admin, or mentoring duties. OpenAI spent millions to race human researchers on Navier Stokes, and that doesn't account for any training costs. How many person-years would that pay for? Since the key ideas were developed by humans just a few years prior, it's not unreasonable to surmise that a comparable level of total effort by humans would also have decent chances of breakthrough, with the additional benefit that the insights uncovered along the way would be immediately digestible and easy to communicate to other mathematicians.