An essay based on a public lecture delivered at the 2026 International Congress of Mathematicians explores how the mathematical community might respond to the arrival of artificial intelligence tools capable of performing research-level mathematical tasks.

Rather than debating the capabilities of such tools, the author conditions on the hypothesis that these capabilities will arrive, and examines instead a question that is orthogonal to it: what the goals and values of mathematical research actually are.

The problem-solving component of mathematics is used as a case study to investigate how human mathematicians can preserve their unique contributions and purpose in an era where machines can assist with or even surpass human computational abilities.

Authored by Terence C. Tao, the submission history shows the initial version was posted on August 17, 2026, with a file size of 3,396 KB. The essay emphasizes maintaining human agency and meaning in mathematical discovery despite advancing AI.