Quiddital Mathematics

Atiyah, Lax, Connes, Kontsevich


Since its very beginnings, mathematics has been very close to physics. The observation of natural phenomena has sought to avail itself of the mathematical apparatus at every moment of history. Mathematics, which has always been described as the universal language of the sciences, had, at the beginnings of modern mathematics (thanks to Riemann’s spectacular revolution) come to understand itself as a sort of structural machinery for the sciences. In Riemann’s vision, far from being reduced to a mere language, an expedient that would serve only to display what other sciences had discovered, mathematics would in fact be the discipline that allows us to codify the deep structures underlying the natural world. The situation was complicated even further in the last half of the twentieth century, with some of the most formidable advances in contemporary mathematics…