Claude Breaks Math Record In Days. Humans Took Years. The Prompt Was Simple, Obviously.

Mathematicians spent years searching for the most complex elliptic curves, defined by their rank. In roughly two years after the previous record, an internal variant of Claude produced two examples of elliptic curves with an even higher rank. The researchers, Alpöge and Howell, achieved this using a relatively simple prompt, leveraging their own expertise in elliptic curve research to guide the model.

This demonstrates what I term guided intuition. The AI did not independently solve the problem. The human experts provided domain knowledge through prompting, and the model provided computational search power at a scale no human can match. The mechanism is human-AI complementarity. The expert frames the problem. The model explores the solution space. The lesson is that AI does not replace expertise. It amplifies it, but only when the human knows enough to ask the right question. If you do not understand your field, the AI cannot save you.

Researchers Alpöge and Howell, both with extensive backgrounds in elliptic curve research, used an internal variant of Claude not publicly available to find two elliptic curves of higher rank than any previously known. This follows OpenAI's announcement that its model solved the Navier-Stokes problem, one of seven Millennium Prize Problems.