The Neurosurgery Resident Who Proved Crouzeix’s Conjecture:

It is remarkable to realize that a longstanding conjecture was first solved by someone with no specialized training in mathematics, working with a large language model. Only a few years ago, it was difficult to imagine an AI system contributing the decisive idea in a proof of a major conjecture. Now it has happened in our field.

We suspect that episodes like this — in which people outside professional mathematics make major contributions with the help of AI — will become increasingly common, even if the burden of verification continues to fall largely on experts. We do not yet know whether academia has the capacity to absorb the flood of results that may be coming or have time to digest them all. This is surely the beginning of a golden age for results in applied mathematics, but what it means to be an applied mathematician may be about to dramatically change.

The AI takeover of mathematics has begun:

For Maynard and other mathematicians The Verge spoke to, the announcement has added to a complex swirl of emotions about where their field is headed. There is palpable excitement at the prospect of accelerating mathematical discovery — but also apprehension, and in some cases despair, about what this could mean for the people who have dedicated their lives to the pursuit, and for the generations of future mathematicians who will follow them. Few doubt that a profound upheaval is already underway.