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There is the striking quote by the English mathematician G. H. Hardy. He received a letter, out of the blue, from Ramanujan (who was unknown and impoverished), saying that he had been working on some mathematics. The letter gave some extraordinary number-theoretic formulas. Hardy knew at once that this wasn't a hoax or joke, because no one would have had the imagination necessary to dream up such formulas if they weren't real. In the event, nearly all of the formulas proved correct. Anyway, what Hardy said was that this was the only genuinely romantic episode in his life. ("Romantic" in the older sense, as Merriam Webster defines the word: marked by the imaginative or emotional appeal of what is heroic, adventurous, remote, mysterious, or idealized.)

Evariste Galois is one of the true tragedies of mathematics. The romantic version of the story is that he frantically wrote down his mathematical discoveries the night before his certain death in a duel with one of France's best duellists. Indeed, he died at 21 in this duel. It isn't clear what the duel was over: a woman, or politics. The truth is that Galois had already detailed his work months earlier in a manuscript he had already sent to the best French mathematicians. "Galois theory" is still the subject of active research in modern mathematics.

Another tragic early death in mathematics was that of the Norwegian mathematician Niels Abel, who made several spectacular discoveries (some related to the math Galois also worked on) before his death at 26 of tuberculosis. Abel died in 1827; Galois in 1832.

If any of this interests anyone, there's a marvelous web site: The MacTutor History of Mathematics Archive