Emmy Noether
Her main area of research changed over time. From 1908 to 1919, she studied algebraic invariants and number fields.  Her work on Noether's theorem has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics". From 1920 to 1926, she developed the theory of ideals in commutative rings.  From 1927–35, she published works on noncommutative algebras and hypercomplex numbers. In addition to her own publications, Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.