In the comments on my thread, several people pointed out that
(1) You are still better off with a "straight line" AI solution.
(2) Mathematicians remain free to wander around the path if they like (possibly with help from that same AI that found the proof.)
This is true, but there are reasons why it can’t happen today:
- AI models are heavily trained to nuke hard problems, not to marvel at the beautiful flowers found on the way to the bombing site
- As long as AI companies collect solutions to hard problems like hunting trophies, they have little incentive to make that exploration a priority
- For human mathematicians, the current research ecosystem does not reward exploring the territory around a known solution
But none of this is inevitable, and I hope that collaboration between mathematicians and open-source AI builders can help make that "post-solution" exploration process happen.
Mathematicians are angry at AI solving their problems, and it's easy to dismiss this as gatekeeping.
"A proof is a proof. They just want to keep their jobs / prestige / fun !"
But I do think mathematicians have a point, and I'll try to explain using old Civilization-style maps
Understanding the Navier-Stokes blow-up?
I created a new Tangible lesson to explain the concept of blow-up: from ordinary differential equations, to gravity, heat equation…and Navier-Stokes !
If you do research, apparently "closed model for you" = "open bar for them"...
...and all your unpublished ideas are what's on tap ! 🍺
Sounds like a paradox, but if you care about it, open models are actually the private option. 🤷♂️