Preface: Alphaproof and Alphageometry

In July 2024, New York Times reported the DeepMind researchers celebrated what Alex Davies, a lead of Google DeepMind’s mathematics initiative, described as a “massive breakthrough” in mathematical reasoning by an A.I. system. A pair of Google DeepMind models, Alphaproof and Alphageometry, tried their luck with the problem set in the 2024 International Mathematical Olympiad, or I.M.O., held from July 11 to July 22 about 100 miles west of London at the University of Bath. The event is said to be the premier math competition for the world’s “brightest mathletes,” according to a promotional post on social media.

The human problem-solvers — 609 high school students from 108 countries — won 58 gold medals, 123 silver and 145 bronze. The A.I. performed at the level of a silver medalist, solving four out of six problems for a total of 28 points. It was the first time that A.I. has achieved a medal-worthy performance on an Olympiad’s problems.