André Weil and the Hodge Conjecture

Discussion (7 Comments)Read Original on HackerNews

bee_rider•about 1 hour ago

I wonder if we’ll end up in a weird situation a decade from now, where every conjecture will collapse into one of two states: counterexample found by AI, or assumed to be true.

AIiscoming•41 minutes ago

Might be a lot faster than you think.

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?

glimshe•37 minutes ago

How does AI's mathematical abilities affect the commercial future of software like Mathematica?

mlh496•25 minutes ago

I think Mathematica will survive because the alternative is for AIs to write the code to do a computation or use an open-source library. And there are many calculations for which there simply isn't an open-source tool for evaluating.

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.

QuesnayJr•about 1 hour ago

I wonder if this is a hint to a more-specific rumor. Weil constructed what are now known as "abelian varieties of Weil type". In low dimensions the Hodge conjecture has been proven for abelian varieties of Weil type, but it's open in higher dimensions. Maybe that's where they found their counterexample.

pmdulaney•5 days ago

Two factoids of interest:

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.

bananaflag•about 1 hour ago

3. He is not to be confused with Hermann Weyl.

André Weil and the Hodge Conjecture

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Discussion (7 Comments)Read Original on HackerNews