The only ancient source that ascribes round-earthism to Pythagoras is Diogenes Laertios 8.48:

In addition, it is said he was the first to call the cosmos 'the heaven', and the earth spherical. But according to Theophrastos it was Parmenides, and according to Zeno, Hesiod.

That's all we have in favour of the idea. Against, there are multiple potent considerations.

1. The same passage ascribes round-earthism to Parmenides and Hesiod, and we know for certain that both of those are completely false.

2. The better attested cosmology that we have ascribed to early Pythagoreans indicates a doctrine where the earth, sun, and planets are attached to spheres surroundong the 'central fire' (whatever that may be); that in turn tends to suggest they're imagined as discs attached to the surface of the spheres.

3. In all natural philosophers prior to 400 BCE we see an overwhelming consensus that the earth was flat (with some minor variants on that theme). So if Pythagoras was a round-earther, it would be something absolutely exceptional. We’d expect a well-informed writer such as Aristotle, who explicitly discusses evidence on the shape of the earth, to highlight it.

We know vanishingly little about the doctrines of Pythagoras himself. Even major Pythagoreans like Aristoxenos are not very well understood. Most of the information we have -- including the Diogenes Laertios passage that ascribes round-earthism to Pythagoras -- comes from after a major transition around the 1st century CE, when the Pythagorean cult reimagined Pythagoras as a miraculous figure who performed fantastic feats and miracles. Virtually no sources about Pythagoras after the 1st century can be trusted as far as they can be thrown. And that includes Diogenes Laertios.

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