What OpenAI's breakthrough means for mathematics
Recently, OpenAI’s model managed to disprove Erdős’s famous unit distance conjecture. We explain the conjecture in depth and talk about what this news tells us about the future of math.
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Website: https://polylog.cc
Code: https://github.com/polylog-cs/erdos-p...
Credits
Richard Hladík: Animator, video editor. Site: https://rihl.cz
Václav Rozhoň: Narrator, animator, video editor. Site: https://vaclavrozhon.github.io
Václav Volhejn: Narrator, video editor, animator. Site: https://vvolhejn.com
Animations: Canvas Commons, a TypeScript library https://canvascommons.io/
0:00 Intro
0:45 Erdős problems
1:31 The unit distance conjecture
2:09 The asymptotic question
3:12 Erdős’s n^1.5 upper bound
5:28 Erdős’s n^(1+o(1)) construction
7:43 OpenAI's n^(1+ε) construction
9:50 Strengths and weaknesses of current LLMs
11:22 What happens next?
12:26 But we'll still be writing definitions, right?
15:09 Outro