One could make an interesting biography comparing the Ακουσματικοι
with the proto-Catholics and the Μαθηματικοι with (at least) the
Valentinian Gnostics. Could we say that much of our intellectual
history has been shaped by the Gnostics winning, and the
mathematicians losing, at the wrong time?

That's the akousmatikoi ('listeners'), and mathēmatikoi ('learners') -- the two sects or schools into which pythagorianism roughly split -- if like me you're not into all this wanky ostentatious and entirely superfluous ejaculation of greekiferous fluids onto the otherwise pure and chaste breasts of sensible glyphage.