I'm curious as to how groups, rings, fields got their names. Did someone just start calling these structures by those names, or is there a (not entirely) arbitrary reason for them?
You should look up Evariste Galois and Niels Abel. Both were incredibly talented Mathematicians who died at very early ages (around their early twenties). I know that concerning Galois, he died in a very mysterious way involving a duel over a woman. Personally, both are some of my heroes in Mathematics.