Forget formalism: mathematics was built on infighting and emotional turmoil

"In the weeks leading up to September 1891, mathematician Georg Cantor prepared an ambush. For years he had sparred - philosophically, mathematically and emotionally - with his formidable rival Leopold Kronecker, one of Germany's most influential mathematicians. Kronecker thought that mathematics should deal only with whole numbers and proofs built from them and therefore rejected Cantor's study of infinity. "God made the integers," Kronecker once said. "All else is the work of man.""

"But Cantor had a proof that he hoped would confound his competitor. Armed with an innovative method, now known as Cantor's diagonal argument, he could demonstrate that some infinities are larger than others and he planned to confront Kronecker with it in public at the inaugural meeting of the German Mathematical Society in Halle. But the showdown never came. Weeks before the meeting, Kronecker's wife was fatally injured in a climbing accident, preventing him from going to Halle, and Kronecker himself died that December."

Georg Cantor developed a revolutionary proof, the diagonal argument, demonstrating that infinities can have different sizes. Leopold Kronecker rejected studies of infinity, insisting mathematics should concern whole numbers and constructions from them. Cantor planned to confront Kronecker publicly, but a climbing accident that fatally injured Kronecker’s wife and Kronecker’s subsequent death prevented the showdown. The period saw a transformation from rigorous analysis to the birth of set theory, formal logic and topology. Debates over the foundations redefined what counts as a valid proof and whether mathematical truth is discovered or invented. Personal temperaments, loyalties, neuroses and chance heavily influenced the intellectual revolution.

Read at Nature