Comment by ants_everywhere
Comment by ants_everywhere 3 days ago
This is actually way false. Rigorous mathematical proof goes back to at least 300 BCE with Euclid's elements.
Fermat lived before the synthesis of calculus. People often talk about the period between the initial synthesis of calculus (around the time Fermat died) and the arrival of epsilon-delta proofs (around 200 years later) as being a kind of rigor gap in calculus.
But the infinitesimal methods used before epsilon-delta have been redeemed by the work on nonstandard analysis. And you occasionally hear other stories that can often be attributed to older mathematicians using a different definition of limit or integral etc than we typically use.
There were some periods and schools where rigor was taken more seriously than others, but the 1600s definitely do not predate the existence of mathematical rigor.
Euclid’s Elements “rigorous proof” is not the same thing as the modern rigorous proof at all.
>But the infinitesimal methods used before epsilon-delta have been redeemed by the work on nonstandard analysis.
This doesn’t mean that these infinitesimal methods were used in a rigorous way.