The evolution of mathematical problem solving from Euclid to AI

Mathematicians have shifted their focus from documenting geometric propositions to solving complex problems that drive new scientific fields.

Euclid established one of the first lists of mathematical problems in his book Elements, written 300 years before Christ. However, the modern goal of solving specific problems gained prominence in 1900 when German mathematician David Hilbert proposed a list of 23 problems.

While French mathematician Henri Poincaré argued that the true goal of mathematics is understanding deep meanings, Hilbert pushed for the resolution of specific challenges. To date, 11 of those 23 problems remain unsolved. In 2000, the American Clay Institute created the Millennium Prize Problems, a list of seven difficult challenges with a 1 million dollar reward for each solution. These problems connect to fields like physics and computer science.

Russian mathematician Grigori Perelman solved the Poincaré conjecture in 2002 but refused the associated prize. Recently, OpenAI claimed to have used 10,000 AI agents to find a solution to the Navier-Stokes equations in under 4 days, a result that still awaits verification by the scientific community.