A week ago 25 Fields Medalists wrote a declaration on their misgivings about the impact of AI on mathematics. While I can empathasize with their concerns, I found much of their statement problematic. So I gathered my thoughts and wrote an X post, which I also cross-posted on proofsandprompts:
The Fields medalists’ objections to AI will not age well.
Yes, the true value of mathematics lies in understanding. But what counts as mathematical understanding, and indeed even a valid proof, evolves. First came geometric construction and thereafter symbolic calculation, numerical algorithms, computer-assisted proofs, and, in cases such as the classification of finite simple groups, arguments dispersed across thousands of pages and decades of work that exceed what any individual mathematician can fully absorb.
Frontier AI systems will be another chapter in this progression.
It may take a village of mathematicians to interpret and understand the mathematical artifacts produced by an AI system, just as with humanly produced ones. But that is not necessarily a bug. It may instead be a useful feature that forces mathematicians to confront more directly what is actually worth understanding.
Even here there is creative license, since understanding is not canonical but relative. Mathematicians stand on the shoulders of those who came before them, routinely invoking theorems they haven’t fully digested. Ultimately, expertise is not exhaustive; it is selective. So that building upon formally verified machine-generated proofs is an expansion of the mathematical toolkit, not a diminishment of it.
Understanding is also, in some sense, a luxury. The natural world is full of objects, structures, and phenomena we don’t fully understand. To the extent that mathematics has value in discovering what is true independently of our ability to understand it, those of us who are Platonically inclined should welcome AI’s capacity to generate and confirm mathematical truths that we find useful.
There will obviously be social consequences with powerful AI. It disrupts the traditional value system that awards prizes and prestige to the first to solve a “difficult” problem. But history is full of once-valuable skills made obsolete by technological progress.
Determining exact time and longitude had been a major scientific and navigational challenge, attracting enormous intellectual effort and institutional rewards. But today, atomic clocks and GPS allow us to measure time and location with extraordinary precision and no expertise. And we do not mourn the convenience that modern technology affords us.
Likewise, if some of the most celebrated problems in mathematics turn out not to be especially difficult in the age of AI, that should not be viewed as a loss. It would itself be a discovery: that what we regarded as requiring exceptional human ingenuity to overcome can, in fact, be solved by machines equipped with enough compute.
The appropriate response is not nostalgia for approaching problems with our unassisted minds, but curiosity about what lies beyond and a willingness to set our sights on new horizons.