Thoughts & Posts

The practical future of math is written in its past:

Cardano was chronically short of money and kept himself solvent by being an accomplished gambler and chess player. His book, Liber de ludo aleae (“Book on Games of Chance”), written around 1564 but not published until 1663, contains the first systematic treatment of probability, as well as a section on effective cheating methods. He used the game of throwing dice to understand the basic concepts of probability.

The point is not to be short of money, but to be problem-oriented.

It goes without saying that AI is having a profound impact on academia and, more directly for us, on the fields of Statistics and Mathematics. We have seen amazing advancement in solving long-standing problems, which should be a net positive for science itself. Yet anxiety and confusion are everywhere: what will be the purpose of our profession in the future? I have been hearing these concerns, discussing them with others, and thinking deeply about them in the middle of the night (and early in the morning). The prevailing pessimism and nihilism have prompted me to write down some of my thoughts and share them with people who care.

Please share your thoughts and feedback. The eventual equilibrium of the scientific community should be what we actively think about and contribute to, rather than something we get cynical about or exploit amid the disturbance of the status quo.

So, what do I think overall? I remain hopeful in this era of AI-driven disruption. The paradigm of academia will shift—and, in my view, in a positive direction. Terence Tao said, “In short, we will transition from an era of proof scarcity to an era of proof abundance.” I would not try to place an upper bound on what AI will eventually be capable of, and I happily admit that I used to underestimate it. For theoretical research, the consequence is a shift from:

“I discover this wonderful thing”

to

“I discover this wonderful thing”

I am hopeful precisely because this shift can make us healthier human-beings. When the purpose of research is no longer limited to studying only what our abilities and tools allow us to study, doctoral students and senior researchers alike may be happier with their lives. I knew many of my friends, predominantly in mathematics, spent five to ten of the best years of their lives studying problems they had never heard of, did not care about, or were not truly interested in, simply because these problems were the natural next steps in their fields or the subjects on which their advisors had focused for decades. In principle, the liberation made possible by AI-assisted reasoning and an expanded research frontier should allow us to choose problems that more deeply engage our innate curiosity or matter more for advancing our fields and understanding ourselves as human-beings. The current transition, however, can be very painful for those of us who have worked on difficult problems for years and invested heavily in the ego of “only I can solve this important problem.”

So, what should be our response? I believe we should embrace and adopt the new reality responsibly. The eventual stable point may teach us to value “important problems” more and “only I” less. If the problem itself is what truly fascinates us, we shouldn’t be too upset when AI cracks it—perhaps a little upset, understandably, but then we should just laugh it off! We should be excited to see the problem solved because it helps us understand what we want to understand and allows us to study even more interesting and difficult questions—of course, unless you are nihilistic and don’t believe anything is important.

I will update this page regularly as I develop these thoughts further. Several crucial questions follow from my overall view of where our attention should shift and why we should remain hopeful:

• How can we, as individuals, use AI responsibly to advance our research during this period of disruption, as opposed to exploitation and irresponsible practices?
• How can we, academia as a whole, evaluate research and evolve our institutions to encourage advances and high-quality work in this new era? What should be the focus and meaning of our profession if it were to change substantially?
• How can we, as mentors and teachers, educate students while continuing to encourage their curiosity and exploration? How should we advise them, and how can we fulfill our responsibilities as advisors?
• How can we, as a scientific community, make the best use of an abundance of proofs through a standardized, responsible, and verifiable process? How should we institutionalize that process through policies rather than rely on self-disclosure?

More to come.