Emmy Noether's  doctoral thesis was completed in 1907 under the supervision of  Paul Gordan, who gave a constructive proof on the existence of invariant forms in n variables. David Hilbert had already proved the existence of such forms in a non-constructive manner. Noether extended Gordan’s results, listing 331 covariant forms in her dissertation. One does not need to know much about the theory of covariant forms to be impressed by the magnitude of her work.

Noether later adopted Hilbert’s more abstract and general approach to the problem. This resulted in her famous theorems known to physicists as Noether’s Theorems. These were published in a 1918 paper entitled, Invariente Variations Probleme. Noether’s theorems in physics establish a relationship between certain groups of symmetry and field equations in the context of the theory of general relativity. When Albert Einstein published his famous 1910 paper on general relativity, he could not establish the principles of conservation of energy and momentum within that theory. Noether’s theorems provide the mathematical framework to do this. She does so, by establishing a correspondence between two major areas of mathematics: algebra (group theory) and analysis (field equations)

Among mathematicians, Noether is also known as the "mother of modern algebra". Her landmark paper in 1921 on the theory of ideals generalized the idea of expressing a natural number uniquely as a product of powers of primes to commutative rings satisfying the ascending chain conditions on ideals.  Today, such rings are called Noetherian Rings and their properties are of far reaching importance in the study of commutative algebra, algebraic number theory and algebraic geometry