A remark of Simone Weil, which I learned from Karen Olsson’s book The Weil Conjectures.
In the original, “Pour moi, je pense bien que Dieu, selon la parole pythagoricienne, est un géomètre perpétuel – mais non pas un algébriste.” Here’s the letter to her brother from which this is taken.
I wanted to write more in Shape about the complicated moral weights people assigned to the difference/tension between algebra and geometry. I wrote a little about what Poincaré thought about it, who saw the two subjects as representing two temperaments, both indispensable, though any given mathematician might possess them in different proportions.
But then there is this, from S.I. Segal’s “Topologists in Hitler’s Germany”
“the … Nazi movement saw “truly German” mathematics as intuitive and tied to nature, often geometrical, and certainly not axiomatic. Axiomatics, “logic chopping”, too great abstraction, was Franco-Jewish.”
It is grimly funny to imagine the Nazi ideologues locating in abstract algebra and the insolubility of certain equations in radicals the ultimate origins of rootless cosmopolitanism.