André Weil and the Hodge Conjecture(jiahao116.github.io) |
André Weil and the Hodge Conjecture(jiahao116.github.io) |
https://news.ycombinator.com/item?id=49748998
Make for a funny pairing.
I'm wondering though when we as a society / all the normal money flowing into universicites and research start to recupe and invest AI resources more deliberate.
Like are we working with ai on superconductors (easiest example i have, i don't know enough math).
Whats the most 'math' we need to advance for human progress?
Yes, we are. Basically, for any scientific problem worth any funding, there is someone using AI on it. That said, for materials science it’s usually not LLMs, or even transformers (unless the AI used to write slop papers count). But there is a menagerie of AI or deep learning models that people are trying to use.
It depends: there do exist some conjectures for which there don't exist any proofs, but a huge amount of results assuming this conjecture (which is very near to assuming that the conjecture is true). Examples are:
- Riemann hypothesis [1]
- Generalized Riemann hypothesis (GRH) [2], and potentially also Extended Riemann hypothesis (ERH) [3]
- Standard conjectures on algebraic cycles [4]
- perhaps Schanuel’s conjecture [5]
--
[1] https://en.wikipedia.org/w/index.php?title=Riemann_hypothesi...
[2] https://en.wikipedia.org/w/index.php?title=Generalized_Riema...
[3] https://en.wikipedia.org/w/index.php?title=Generalized_Riema...
[4] https://en.wikipedia.org/w/index.php?title=Standard_conjectu...
[5] https://en.wikipedia.org/w/index.php?title=Schanuel%27s_conj...
It can be productive to assume something is true and see what happens.
But I wouldn't be surprised to see Mathematica being used primarily as an AI plugin in the coming years. Mathematica now has an MCP which I use regularly from Claude Code. It's nice not having to write the lengthy Mathematica expressions by hand.
1. André was the older brother of philosopher Simone Weil.
2. "Weil" is a jumbled version of "Levi" adopted by some so as to be less conspicuously Jewish, and thus be less likely to be persecuted or discriminated against.
But no relation with Simone Veil (both Veil and Weil are pronounced exactly the same way in French).
4. Some of his best work was done/completed while he was in military prison (ignoring his draft orders to report to World War II duty). IIRC later when he mentioned this to some official, they offered to give him the opportunity again.
(André Weil spent some time in India, previously having apparently taught himself Sanskrit at age 14 and the Bhagavad Gita being described as his constant companion. His autobiography The Apprenticeship of a Mathematician is very interesting.)