AI Solves Math Problems Worthy of a Career. PhD Students May Need New Hobbies.
The Verge's Robert Hart reports that AI models are now producing genuine mathematical breakthroughs, leaving researchers quote-unquote shell-shocked. Multiple mathematicians told him that any single one of these solved problems would have secured a full academic career for a human researcher. The concern is practical: a doctoral student who picks an obscure subdomain today may find the AI simply resolves it midway through their thesis work.
What we are witnessing is asymmetric capability arrival. The mechanism is straightforward: these models don't tire, don't need grant funding, and don't require five years to survey the literature. The mental model you need is depreciation of specialized human effort. When a general-purpose system closes the gap on a niche domain faster than a human can complete training in that domain, the economic logic of specialization breaks down. This applies far beyond mathematics. Any field where expertise is measured in years of slow human accumulation is now on the clock.
Robert Hart at The Verge has been documenting the reaction among working mathematicians. The researchers he spoke with describe these as genuine breakthroughs, not parlour tricks. Their collective response sits somewhere between professional admiration and existential dread.
- Open a free account with ChatGPT or Claude and ask it to prove a theorem you vaguely remember from undergraduate coursework. It will likely produce a coherent proof.
- Now ask it to explain where the proof might fail or what assumptions are unproven. You will see the model reason about its own gaps.
- Pick a problem from your old textbook that you never finished. Pose it to the model and compare its approach to the solution in the back. The exercise will acquaint you with the current frontier of what these systems can resolve unaided.