Comment by zarzavat
Fermat was alive in the 1600s, long before the advent of mathematical rigour. What counted as a proof in those days was really more of a vibe check.
Fermat was alive in the 1600s, long before the advent of mathematical rigour. What counted as a proof in those days was really more of a vibe check.
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.
It is possible to discover mathematical relation haphazardly, in the style of a numerologist, just by noticing patterns, there are gradations of rigor.
One could argue, being a lawyer put Fermat in the more rigorous bracket of contemporary mathematicians at least.
Not true. Even if it’s more strict it’s just a matter of inserting more care and steps, not changing the original idea.
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.