Pythagoras explains in first person his celebrated theorem, complete with diagrams and shaded triangles. It is a source of substantial chagrin to him because it naturally leads to the irrational numbers. As he puts it humorously:
“The ratio of the diagonal to the side is not a ratio of integers. It is not even a fraction or recurring decimal. I can’t begin to express my frustration with this one. […]. We’ve been sitting on it for a while now, keeping it quiet. If people found out, all hell will break loose […] and we’re going to look miserable and stupid when we sit there and shrug. There’s no reason to it, it’s completely irrational. Makes you think, though, if only it had been 1.5. Or 1.4, I’d have settled for that. But no, it had to be 1.4142135…. goes on forever. Sometimes, the Gods really piss me off”
Archimedes, on the other hand, is having problems of his own. As he jogs, geometric thoughts stat crossing his head. He feels like a hamster treading a giant wheel but on the outside. The dome of the sky, the horizon, the progressive shortening and lengthening of his shadow as he runs, they all crowd in [e.g. “The Horizon is not a plane but a circle of constant size with him as its center”]. Suddenly, he stumbles and falls, getting knocked on his head. When he comes around, he has a distinctly odd experience where he is as large as the earth – it is quite funny to read and has implicit link to his statement about moving the earth if only he could find the place to stand and a proper lever.
The thoughts of Sisyphus are not mathematical though quite poetic.