Hot take: the author sneaks in a premise that synthetic mathematics is per se "reactionary", but this is itself pure reactionary copium for not getting it: https://ncatlab.org/nlab/show/synthetic+mathematics https://en.wikipedia.org/wiki/Synthetic_mathematics . There's nothing wrong with wishing to pursue a "coordinate-free" approach to any mathematical field: the old geometers were quite right about this.

I don't understand how you got that at all. The impression I got was the synthetic mathematicians were wary of applying the new "analysis" methods because lack of rigor made them question how safe and valid it was to use.

> Using another set of metaphors: Analysts followed the fast flights of their feverish and uncontrolled imagination, while synthetics kept their feet on the ground. Their procedures were slow but safe.