Henri Cartan, the grand old man of French mathematics, has died at 104. He was the founder and leader of the "Bourbaki" movement in the 1930s, a group that tried to redo mathematics as a totally formalized and axiomatized system, following deep intellectual traditions in France of hyper-rationalism that go back to Descartes, if not all the way to Thomas Aquinas, and which in French socio-economics was associated with the social engineering idealism of Saint-Simon and the dirigiste tradition of French indicative central planning. The group operated, at least initially, anonymously, signing their papers with the name of a dead French general, Nicholas Bourbaki. They hoped to clarify mathematics and remove from it any mysticism or fuzzy thinking.
One of Cartan's most assiduous students in the immediate post-WW II period was the late Gerard Debreu, the more mathematical and austere half of Arrow and Debreu, who famously proved the existence of competitive general equilibrium in 1954, both of them eventually receiving the Nobel Prize in economics. Debreu was probably the most articulate and influential spokesman for axiomatizing economic theory, something now very much out of favor for many reasons. Indeed, as Roy Weintraub has noted in his book, _How Economics Became a Mathematical Science_, the trends of uses of math in economics tend to repeat trends in math itself, with the Bourbakist approach having fallen out of fashion within math itself some time ago. Simulation and many other approaches have picked up, and we see this in economics with agent-based modeling and more emphasis on empirics and induction from that now.
Even though Cartan and his allies dominated French mathematics for decades, two of the most interesting mathematicians to come out of France, Rene Thom, the founder of catastrophe theory, and Benoit Mandelbrot, the inventor/discoverer of fractals, were both very bad at proving theorems and following the Bourbakist approach. Indeed their great success, including with influence on economics, was perhaps a sign of the limits of Bourbakism more generally.