Quo Vadis, Mathematics?

gist

Christian Szegedy likens pure mathematics to exploring an unmapped wilderness and AI to the first airplanes over it. He says recent systems have already landed on rocks nobody had climbed, meaning a few solved conjectures, while mathematicians still honor heroic effort more than publicity flags or useful tools. Claims that AI cannot conjecture, theorize, or explain describe last spring's models. He expects the status of lone climbs to fade, and mathematics to graduate into the infrastructure of scientific and technological progress.

ideas

• Pure mathematics is wilderness exploration. Recognition goes to heroic climbs and the maps they sketch; widely used tools and deposits that help ordinary people earn less reverence than a hard rock earlier explorers failed to climb.
• AI is the first airplane over that terrain. Szegedy says recent systems have planted flags on unclimbed rocks, and that "airplanes cannot reach the real mountains" is a static-thinking fallacy about models that will improve within months.
• Flag-planting is a demonstration, not the point. Mathematicians climb conjectures to hone tools; once anyone can charter a plane, that status game loses its point, and casual climbers can buy tools instead of forging them.
• The field is graduating, not ending. Universities will look similar for years, but respect shifts from lone heroic climbs toward choosing terrain, steering fleets, and explaining results, with a grief like the emptiness after competition math ends.

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