The first species is the pure problem solver. Tao is the poster child for this group. Their currency is interesting problems and solutions to those problems.
The second species is the pure theory builder. The poster child for this group is Conway. Their currency is theories and ideas rather than theorems, they are most interested in expanding the territory of mathematics and discovering new mathematical lands.
The third species is the applied mathematician. They see mathematics as a means to an end, they have some problem outside of mathematics and they want to use mathematics to solve it.
It seems like the first group (the problem solvers) are the most immediately threatened by AI, although so far AI is better at solving problems than finding new conjectures.
The second group (the theory builders) are more distantly threatened by AI, since thus far AI has shown limited ability to come up with novel and interesting mathematical ideas and nobody has any clue how to train an AI to do such a thing.
The third group stands to gain the most from AI. If an AI can answer your mathematical question then you can spend less time doing mathematics and more time on whatever it is outside of mathematics that you wanted to use mathematics to help solve.
I'm cautiously optimistic that the theory camp will benefit as much the applied guys, but later. They dream and scheme and shape fields by making vague intuitions and questions sharper, but they also need interesting patterns to work with as their raw material.
Identifying suitable problems in this sense rather than solutions is an AI use-case you don't hear about much. We don't quite have the infrastructure for this yet but by combining language models / anomaly detection / knowledge-bases we might be in a position to give a Conway 25 interesting high-quality puzzles before breakfast. Funny that it's like a kids nightmare, chatgpt giving them homework instead of solving it, but if it had good taste, people would love it for research.
Anyway, for now, dreamers will probably find more inspiration by cross-pollination with colleagues from different disciplines, or just going for a walk.
Yes, I should have just said "explorer" or "inventor" rather than theory builder which is too specific.
Grothendieck is a better specifically for building theories. Conway is famous for his various ideas and inventions so he also fits the bill as an "anti-Tao".
The first species is the pure problem solver. Tao is the poster child for this group. Their currency is interesting problems and solutions to those problems.
The second species is the pure theory builder. The poster child for this group is Conway. Their currency is theories and ideas rather than theorems, they are most interested in expanding the territory of mathematics and discovering new mathematical lands.
The third species is the applied mathematician. They see mathematics as a means to an end, they have some problem outside of mathematics and they want to use mathematics to solve it.
It seems like the first group (the problem solvers) are the most immediately threatened by AI, although so far AI is better at solving problems than finding new conjectures.
The second group (the theory builders) are more distantly threatened by AI, since thus far AI has shown limited ability to come up with novel and interesting mathematical ideas and nobody has any clue how to train an AI to do such a thing.
The third group stands to gain the most from AI. If an AI can answer your mathematical question then you can spend less time doing mathematics and more time on whatever it is outside of mathematics that you wanted to use mathematics to help solve.