Suppose 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.
> 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.
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 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?
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've long been a fan of the way 3b1b illustrates and explains math.
I wonder if something like OpenAI's recent IntelligentUI feature couldn't also be used to creature beautiful, intuitive walkthroughs of otherwise opaque areas of math?
Suppose 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.
> 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.
> 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 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?
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.
>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 what if Fable 6 solves it next year?
The goal of mathematics is to solve problems the same way the goal of a marathon is to do a 42km travel.
Why are people running in the first place when they could just take their car?!
Wrong analogy. Solving a problem that is already solved is different from running a distance that is already traveled.
I've long been a fan of the way 3b1b illustrates and explains math.
I wonder if something like OpenAI's recent IntelligentUI feature couldn't also be used to creature beautiful, intuitive walkthroughs of otherwise opaque areas of math?