When I first thought of this question, I wanted to ask: If you could give one mathematician his remaining life until an average age for the time he lived in, who would you choose? However, this question is a bit too subjective for SE. So I decided to modify it to: Which mathematicians died very young or in a tragic way?
Two obvious candidates are Galois and Abel. I included more detail about them in an answer. But I'd like to know whether there are more examples.