Oh! I really liked the essay - the idea that French 'analysis' was seen as a dangerous modern invention and contrasted with 'synthetic' geometric understanding of the world had political implications is fascinating. There could be parallels with the present day use of computer modelling (and now AI) being seen as a risky way to organise and run societies.

I agree that there is a lot of vague language around the practice of mathematics as a social and philosophical construct ('analysts' vs 'synthetics') but I'm not sure how that indicates the author does not understand what truth is. My understanding of the history of mathematics and science is that these areas of knowledge were much more intertwined with philosophy and religion than they are considered to be today.

So Newton saw no issue with working on the calculus at the same time as being an alchemist and a non-trinitarian. Understanding the world was often a religious activity - by understanding Nature, you understood God's creation - and in Naples it seems that understanding analysis was tied to certain political and nationalist ideas.

> ...these areas of knowledge were much more intertwined with philosophy and religion...

Indeed, consider Laplace to Napoleon "I had no need of that hypothesis", ca 1799.