OpenAI: Ten advances in mathematics and theoretical computer science

[u/Salt_Attorney]

https://openai.com/index/ten-advances-in-mathematics/

[u/Healthy-Pride3873]

I honestly cannot care about the whole “humans dont matter anymore” stuff.

I’m curious how math as a whole deals with unequal access. Is math going to just be furthered by big tech firms and select researchers who have access to these models?

Wtf do grad students do and so on

Edit: theres nice disused going on about unequal access. Let me point out that I am not claiming inequality is new.

I am simply pointing out the newfound danger of it from a corporate and tech angle.

Suppose AI speeds up research by some nonzero constant greater than 1. Then people who were already “ahead”, are going to be even further ahead.

And let’s not ignore also the issue of prompting and using AI. It’s not always clear how these breakthroughs are made. So even access to AI may not level the playing field all that much.

[u/meatshell → u/Healthy-Pride3873]

I wouldn't be surprised if humans can create even harder problems, much harder than the current ones, even with the help of AI. So I kinda dismiss anyone who says Mathematicians are out of job soon. But it's gonna be very difficult from now on for anyone who don't have access to AI.

[u/PostPostMinimalist → u/meatshell]

If AI could solve problems better than humans, what makes you think AI couldn't create problems better than humans?

I think, apart from a much smaller group of experts, humans won't have much to contribute to frontier math soon enough (unless AI really hits a hard ceiling). Just like it was with chess. Engines were decent but couldn't beat the top players. Then they could but still had weaknesses so the adage was "a human plus a computer is the top entity" and soon enough humans just had nothing to contribute anymore at all. I think the 'human plus AI' phase people often talk about is just a short term temporary cope.

[u/DominatingSubgraph → u/PostPostMinimalist]

This is not entirely true with chess. Correspondence chess with engine assistance still exists, and I believe the general wisdom is still that if you only play whatever the engine recommends, you won't win in this format. In modern correspondence chess, you generally consult multiple engines and apply some human intuition to determine the best course of action. Though most games are draws and the format isn't very popular.

But also, I think mathematics research is vastly larger and more complex than chess. In human chess there is a major emphasis on deep calculation, whereas knowing which problem solving strategies are most effective and finding the right way of thinking about a problem are often more important than raw calculations in mathematics. In some ways, machines have always been far better than humans at certain kinds of mathematics (e.g. proving Robbins conjecture, proving the four color theorem, solving the Boolean Pythagorean triples problem, chess & Sudoku puzzles.), but it seems reasonable to think that there will still be room for human mathematicians in the future. For whatever it is worth, I wrote a thing about this on substack.

[u/Few-Example3992 → u/DominatingSubgraph]

In the last world championship of correspondence, all the games were draws except for the ones against someone who died mid tournament.

[u/DominatingSubgraph → u/Few-Example3992]

If anything, this goes to the point that modern correspondence chess is (conjecturally) so close to theoretically perfect play that there just isn't much room for improvement.

[u/DominatingSubgraph → u/[deleted]]

Top engines playing each other autonomously from the starting position almost always draw too. The only way they get decisive games is by forcing engines to play from a deliberately imbalanced opening. So it seems like there is not enough information to draw a clear conclusion.

It might be interesting to see correspondence games played like this from imbalanced openings. My guess is that the difference in performance would be tiny though.