Terence Tao: Mathematics in the Age of AI and Our Community Values
Terence Tao: Mathematics in the Age of AI [pdf]
I argue that as AI tools rapidly advance in solving research-level mathematical tasks, our community faces a crisis in values rather than just foundations. We must move beyond debating AI capabilities to critically examine our true goals, from solving problems to building enduring knowledge. This shift forces us to define what mathematics means when human effort is no longer the sole driver of discovery.
I believe we are entering a similarly turbulent period—a crisis in the foundations of mathematical values and practices. But once we thoroughly examine and codify these foundations, our community will emerge stronger and more resilient than before.
- yurimo
I think it is important to divine what currently AI is good for and what it is not even in such verifiable environments like math. Current hyped announcements about breaking conjectures are notable and are a marker of how much improvement was made. But as I read them, and maybe I am wrong, I see it as a large model+ harness executing a broad brute force search and trying solutions until something sticks. There are lots of problems like that and they should be solved, as often they are perhaps less important or overlooked, or just a slog, any field of research has these, math even more so.
However, this is very different from inventing new mathematical machinery that allows to break old problems, I think it will be a while until AI will be able to do it if at all. For now I think we will be moving to a symbiosis where an AI cracking a problem and giving a solution, inspires a human to invent new techniques.
- Syzygies
I loved the appearance of Bill Thurston. He proved enough of what he saw to be considered one of our greatest mathematicians, but his brilliance was what he saw.
The obvious question Terry Tao seems not to address: AI mops up our unsolved problems? Whose unsolved problems? The architecture of mathematics will remain a human endeavor long after we replace human construction workers with machines.
- light_triad
This is the taste question applied to Mathematics in a similar way it's been applied to code. In an era of AI abundance, the question becomes what the goals are and what gets verified and digested (adopted by users). Goodhart’s law: the goal of producing code is not just about maximizing the number of tokens used, but the productivity gains and economic surplus.
This could serve as the template for any field in the age of AI:
"We are not trying to meet some abstract production quota. The measure of our success is whether what we do enables people to
understand and think more clearly and effectively about math (or products, or science, or hardware...)"
- doomrobo
Recording of a talk with the same title. I’m not certain it’s the same content as the linked PDF though
- megaloblasto
This is the thought process that I fail to see many people take (both here and other places). AI is changing many fields, ok what does that look like and how do we adapt? What can we do now that we couldn't before? What skills should I learn to adapt to this changing world? I think this is how we move forward. If you can get past the scary aspects of AI (not talking about datacenters or billionaires, that is a different subject) then you might be able to see how exciting this can be.