Emmy Noether ~ the "backbone of modern Physics", revolutionized abstract algebra, with special attention to rings, groups, and fields, filled gaps in relativity. Saw relationships that traditional algebra experts could not. Was not allowed to fill a paid teaching position, as a woman.
Emmy Noether. Amazing woman, amazing mathematician. Noether did trail-blazing work in a number of areas, especially abstract algebra. Rather than focusing on real numbers and polynomials she was interested in abstract structures, like rings or groups, that obey certain rules. She went on to prove fundamentals that now underpin modern physics: Noether's theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.