The following passage is from Mathematics and Its History (Page 295)by John Stillwell.
It was discovered by Riemann that rational curves (curves that can be parameterized by rational functions) are essentially the same as the sphere, but nonrational curves have “holes” and hence are essentially different. This discovery reveals the role of topology in the study of algebraic curves.
Can anyone please tell me which theorem is he talking about? If yes, I would further appreciate a proof of it mentioned in some book or article. Thank you!