Ancient Greek Mathematicians
Today I went to a lecture by Dr. Jacqueline Feke, put on by FemPhys. Her subject was ancient greek mathematicians, and in particular their tension with philosophy. With hindsight, and the towering fetishization of all things Greek not only in the Western intellectual tradition but their influence elsewhere, it’s tempting to think of them as both well-regarded and integrated with the broader philosophical movement. But, as Dr Feke argued, this was not so.
Her examples were later than classical Greece – 1st to 4th century CE. Partly it was that the works of that period had these longer philosophical introductions, where they were simultaneously situating their work and putting down philosophers.
Hero of Alexandria described mechanics, of the sort he was studying to build siege equipment, as a process of finding tranquility, and not only by keeping your enemies at bay. This seems a bit bizarre, but it was partly an attack on philosophical schools claiming to be about tranquility. In this same introduction and elsewhere, he was also putting down philosophers on this point of pure versus applied philosophy. I don’t recall precisely, but some of the context for this is Socrates saying mathematics was all very well if it was used in pursuit of philosophical growth and truth, and silly and useless otherwise. Philosophy was also divided into pure, which comprised theology, metaphysics, and mathematics, and applied – ethics, politics, and something else, perhaps commerce? But the point was he, or maybe this is now Ptolemy, had to show how mathematics was superior to the other branches of pure philosophy (it can help men lead a good life, and something else), whereas success in applied stuff meant engaging in the world anyway, so go do that and don’t write books at me.
But yeah, while all educated people at the time learned mathematics, very few researched it, and doing so had little prestige (unless you could carve some away from the philosophers). Meanwhile philosophers had tons of competing schools, and everyone did their own philosophy. These mathematicians chose not to. My addition: kind of. She talked about them only having so much time and focus and turning away, but they did have to be very conscious of at least the broad ambitions of philosophy to situate their work as they did.
And there’s other interesting tidbits, like the tension between mathematics and other disciplines or forms of authority, such as saying the division of land according to what is just as a solely geometric problem (hence removing the rather important role of lords). And at that time, mathematics was the minority, and philosophy the dominant view; a situation that has pretty significantly reversed now. Though not completely, universally, or anything. And as a last word, woo plurality! This doesn’t have to be a competition.