At the dawn of the 20th century, European mathematicians exchanged ideas extensively, especially those from France and Germany, the two leading nations in this branch of science. The Franco-Prussian War of 1870–71 had admittedly left lingering resentment, but the mathematical community saw itself as the bearer of a universal science and believed that advances should be made with everyone's participation. Across the Rhine, Felix Klein and David Hilbert reigned supreme, while in France, following Henri Poincaré's untimely death in 1912, the ageing Camille Jordan remained a leading figure in French mathematics. On both sides of the Rhine, younger mathematicians were transforming the landscape with new theories: Émile Borel, Henri Lebesgue, Maurice Fréchet and Jacques Hadamard in France, and Felix Hausdorff, Georg Cantor and Ernst Zermelo in Germany.
The end of an era -------------------
Initiated by Felix Klein, Heinrich Weber and Wilhelm Franz Meyer, an Encyclopédie des sciences mathématiques pures et appliquées enlisted the most eminent scientists of the day. They included the French mathematicians Émile Borel, Paul Painlevé and Maurice Fréchet, as well as the Italian Guido Castelnuovo and the American William Osgood. A French edition was produced under the direction of Jules Molk, a French professor in Nancy and former student of the German mathematician Leopold Kronecker. In 1914, more than a third of the members of the Société Mathématique de France were foreign! The outbreak of war thus ended a golden age in the development of mathematics and forced everyone to rally to their own side.
In France, most scientists declared their commitment to their country as soon as war was declared. Not one of the most influential among them raised a pacifist voice. The same was true in Germany, where some declarations were particularly extreme, especially those made by the signatories of the Manifesto of the Ninety-Three (see box). Only one mathematician was among them, but he was a giant: Felix Klein, who had reigned supreme over mathematics at the celebrated University of Göttingen until leaving in 1913. The scientific community in Italy was more divided. Although Italy was formally committed under the Triple Alliance to fighting alongside Germany, it initially remained outside the conflict before eventually siding with the Allies (France, England and Russia). Even mathematicians disagreed over what course to take. The most influential among them was Vito Volterra. Having become a senator in 1905, he had forged numerous ties with French academics before the war. Two weeks after war was declared, he sent Émile Borel a letter expressing his faith in France's righteous struggle for "the cause of civilization against the most odious and brutal imperialism". He campaigned for Italy to enter the war alongside the Allies. Castelnuovo and Federigo Enriques, soon followed by Francesco Severi—all three representatives of the Bologna school of algebraic geometry—followed his lead. Others would have preferred neutrality, such as Tullio Levi-Civita and Corrado Segre, while some favored joining the opposing side outright.
The decimation of the normaliens ---------------------------------