Mathematics and Physics Revolution

Henri Poincaré dominated French mathematics, contributing to topology, celestial mechanics, and relativity theory. His philosophical writings explored mathematics' foundations and science's limits. "Science is built up of facts, as a house is built of stones," he wrote, "but an accumulation of facts is no more a science than a heap of stones is a house."

The Nancy school where Poincaré taught became mathematics center rivaling Paris. Provincial universities, previously overshadowed by the capital, developed specialties attracting international students. Scientific decentralization strengthened French research overall.

Paul Langevin advanced physics through work on magnetism and ultrasonics. His sonar development during WWI would save ships from submarines. His leftist politics—he later joined the Communist Party—showed scientists engaging social questions beyond laboratories.

Women mathematicians remained virtually invisible. Sophie Germain had died in 1831, and no French woman approached her achievements during the Belle Époque. Foreign women like Sofia Kovalevskaya visited Paris but found no positions. The École Normale Supérieure admitted women in 1881 but segregated them completely.

The International Congress of Mathematicians in Paris (1900) posed famous problems shaping twentieth-century mathematics. David Hilbert's 23 problems, though proposed by a German, reflected international collaboration transcending nationalism—temporarily. Mathematics seemed universal language promising human unity through reason.