Originally Posted by sjastro
Personally I think Emmy Noether is head and shoulders above everyone else.
Yet sadly largely unknown.
The mathematics behind particle physics which includes the theory behind the Higgs boson stems from her work.
I'm also a Noether fan. As someone with a degree across physics and pure maths, the thing that amazes me is that her big contribution to Physics (symmetries equaling conservation laws), while often regarded as the most profound piece of mathematical physics around, is actually small beer in the context of her algebraic work.
She was largely responsible for turning abstract algebra into the key element of maths that it is today, developing much of the sophisticated machinery for handling rings and modules.
On top of that, she seems to have been a generous person, happy to suggest productive ideas to others, and then decline to take credit when they turned out to be hugely important.