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.
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?
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.
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.
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.
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.)
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.
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?
How does AI's mathematical abilities affect the commercial future of software like Mathematica?
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.
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.
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.
3. He is not to be confused with Hermann Weyl.
3'. Nor with Andrew Wiles.
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.)