December 8: The Prime Number Theorist

French mathematician Jacques Salomon Hadamard, whose achievements included his 1896 proof of the prime numbers theorem, which had been conjectured a century earlier (it formalizes the intuitive idea that prime numbers become less common as they become larger), was born in Versailles on this date in 1865. A lifelong academic, in 1893 he published Hadamard’s Inequality, which led to the discovery of the Hadamard matrix, which in turn led to the development of important statistical and other mathematical tools. Soon after, he was awarded the Bordin Prize of the French Academy of Sciences for his work on geodesics in the differential geometry of surfaces and dynamical systems (“where a fixed rule describes how a point in a geometrical space depends on time,” says Wikipedia). Later in life, Hadamard published Psychology of Invention in the Mathematical Field, for which he interviewed 100 turn-of-the-century physicists about their thought processes; Hadamard described his own as largely wordless, often accompanied by images that represent solutions to the problem being pondered. Politicized by the Dreyfus Affair (his wife was related to Captain Dreyfus) and by the deaths of three sons in war — two in WW I, one in WW II — he became active in the Jewish and peace communities. Hadamard was elected to the French Academy of Sciences in 1916 and to the Soviet Academy of Sciences, as a foreign member, in 1929. The French Vichy government permitted him to leave for the U.S. in 1941, where he taught at Columbia, but he returned to France at the war’s end and died in Paris at 97 in 1963. “He had a fantastic influence on his time, and... all living analysts were shaped by him, directly or indirectly,” said mathematician Laurent Schwartz on the centenary of Hadamard’s birth. “He had a fantastic influence on his time, and... all living analysts were shaped by him, directly or indirectly,” said mathematician Laurent Schwartz on the centenary of Hadamard’s birth.

“Logic merely sanctions the conquests of the intuition.” —Jacques Hadamard