The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic Swiss clocks of the period in which hundreds of gleaming cogs are made to celebrate not only the time and date but the phases of the moon.

An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.

In the end, every scheme and every science is justified by itself or it is not justified at all.

The calculus is the story this [the Western] world first told itself as it became the modern world.

Aristotelian logic is massive and marmoreal, but every monument accumulates graffiti.

No distinction in kind rather than degree between ourselves and the chimps? No distinction? Seriously, folks? Here is a simple operational test: the chimpanzees invariably are the one behind the bars of their cages.

No man is obliged to be what he might have been.