[coliveira]

> Einstein wasn't aware of most of the work on non-Euclidian geometry before developing relativity IIRC.

That's the worst example you could find, because Einstein didn't develop the mathematics for general relativity. He relied on the math invented in the XIX century for non-Euclidian geometry. If nobody had though about such a "sillY' geometry with "no practical value" it would probably take much longer because the necessary results would be out of the reach for Einstein.

[sdenton4]

Riemann's contribution is overlooked far far too often. The early non-Euclidean geometries were spaces of constant curvature - spherical and hyperbolic - and Riemann brought the idea of a manifold, and the notion of having a geometry that changes as you move around the space. And he did it in a fantastic lecture with only one equation in 1854, a good 50 years before special relativity.

Einstein was also definitely familiar with the work of Helmholtz, who did some fascinating work on non-Euclidean geometry in the context of ophthalmology: Lenses change the amount of curvature we perceive in space (think of fish-eye lenses), and provide a great jumping off point for the notion that the universe might not be as flat as it appears.

The Dover book 'Beyond Geometry' collects a bunch of the major papers in non-Euclidean geometry leading up to relativity, and is a fantastic read.

[Houshalter]

He figured out that spacetime may be non-Euclidean before he was aware that the math had been extensively studied. Then he learned about the preexisting work.

It's true it probably would have been much harder for him to work out the math on his own. But he and/or others eventually would have done it.