- Project manager mathematicians: Tao draws a future where mathematical insights are "produced" like anything else in our society. He attributes the lack of this productionalization of mathematics to a lack of tools in this area but AI and proof assistants might be revolutionary in this regard (proof assistants already are). Human interaction and guidance still needed
- Implicit Knowledge: he points out that so much knowledge is not in papers, e.g. intuition and knowledge of failures. This is crucial and makes it necessary even for top mathematicians to talk to one another to not make mistakes again.
- Formalization of mathematics: one would think that mathematics is pretty formalized already (and it is) but in the papers a lot of common knowledge is taken for granted so having proofs formalized in such a way that proof assistants can understand will help more people actually understanding what is going on.
I think this just shows how Tao always searches for new ways to do mathematical research, which I first came across in his talk about one of the polymath projects.
- Project manager mathematicians: Tao draws a future where mathematical insights are "produced" like anything else in our society. He attributes the lack of this productionalization of mathematics to a lack of tools in this area but AI and proof assistants might be revolutionary in this regard (proof assistants already are). Human interaction and guidance still needed
- Implicit Knowledge: he points out that so much knowledge is not in papers, e.g. intuition and knowledge of failures. This is crucial and makes it necessary even for top mathematicians to talk to one another to not make mistakes again.
- Formalization of mathematics: one would think that mathematics is pretty formalized already (and it is) but in the papers a lot of common knowledge is taken for granted so having proofs formalized in such a way that proof assistants can understand will help more people actually understanding what is going on.
I think this just shows how Tao always searches for new ways to do mathematical research, which I first came across in his talk about one of the polymath projects.