The Contribution of Pythagoreanism to the History of Mathematics

Sarah Fianna asks whether Pythagorean philosophers and mathematicians actually contributed anything to the history of mathematics. I'm not sure that Nicomachus proved new things, but he spends a lot of time telling us how important mathematics is. And Plato of course says that we should get into philosophy by doing mathematics. So I'm sure he'd be very pleased that we spent this episode doing mathematics before getting to Neo-Platonism.