女數學家證明了哪些著名的定理或結果？

See at least Emmy Noether :

was a German mathematician known for her contributions to abstract algebra and theoretical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading mathematicians of her time, she developed the theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws.

Of course, this is only an example; there are many others: see answers below.

Perhaps because of its youth, the mathematical end of Computer Science has several notable women in its history.

Sheila Greibach was a pioneer in the field of formal language theory, particularly in the area of context-free languages. At the time, that would have been considered more a branch of mathematics, as Computer Science wasn't really a thing of its own.

In particular, she developed Greibach Normal Form, which is fairly instrumental in the theory of parsing, which is extremely critical to modern programming languages.

Continuing down programming language theory, Barbara Liskov developed the Liskov Substitution Principle, which was critical in developing a formalized model for object-oriented languages. She won the Turing Award (CS equivalent of the Fields medal) for her contributions.

Did these have a "deep impact" on our understanding of mathematics? Not in the classical sense, but they've led to some amazing developments, arguably as many as the 400 years of calculus/analysis theory.

There is Sophie Germain's theorem, a theorem in number theory, related to Fermat's last theorem and proved by the French mathematician Sophie Germain (1776-1831).

There are not female mathematicians who have had quite so much impact as Gauss or Euclid, for example, but this is to be expected because of historical reasons which everyone is familiar with. A quick google will have told the questioner that there are many important female mathematicians in history, but I think the question is asking for a really important mathematician, or at least a well known mathematician, like Galois who has Galois Theory named after him, or Hilbert, who has Hilbert spaces named after him.

The first person who I thought of when I read this question was Emmy Noether, who, in terms of fame, isn't quite Newton (obviously) but is at least Galois.

You probably aren't going to see the names of any women in the titles of any undergrad maths courses, but if you are, it will probably be Noether.

It is possible that many Ancient mathematicians were actually woman. This is certainly the case for Egypt but probably less so for Greece (although who knows?) Even in more modern times, a few woman have worked under male pseudonyms and there may be many more that we do not know about (although it is unlikely that any of the 'big name' mathematicians like Newton and Euler were actually women because their lives have been well documented). It is also possible (in fact very likely) that work by women has been plagiarised by men, so some theorems named after males may have actually been developed by females, we probably will never know how many.

I found an existence theorem for the Cauchy Problem in partial differential equations which has been proven by Sofia Vasilyevna Kovalevskaya.

There is the work by Ada Lovelace.

In the annotations, which were called "Notes", Ada Lovelace described how the analytical engine could be programmed and gave what many consider to be the first ever computer program.

In particular, she found and corrected a bug in Babbage's algorithm for computing Bernoulli numbers:

We discussed together the various illustrations that might be introduced: I suggested several, but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.

(from C Babbage, Passages from the Life of a Philosopher (London, 1864).)

Of course, the programming language Ada is named after her.

Danica McKellar is the McKellar in the Chayes-McKellar-Winn theorem,

Olga Ladyzhenskaya proved a result related to the Navier-Stokes equations.

The result by itself is not very famous, but the Navier-Stokes equations are.

The Denjoy–Young–Saks theorem gives some possibilities for the Dini derivatives of a function that hold almost everywhere.

Grace Chisholm Young extended Denjoy's result on continuous functions to measurable functions. Her husband was William Henry Young.

The following would be my top picks:

The Sophie Germain identity says that $a^4+4b^4=(a^2+2b^2+2ab)(a^2+2b^2-2ab)$ for $a, b \in \mathbb{Z}$. This is a very simple identity but is quite useful in many problems of elementary number theory.

The Noether normalization lemma is a result in commutative algebra that is taught probably in the very first week of a graduate level course in algebraic geometry. One version of the result says that, for any field $\mathbb{K}$ and any f.g. commutative $\mathbb{K}$-algebra $A$, there exists a non-negative integer $k$ and algebraicly independent elements $y_1, y_2, \ldots, y_k \in A$ such that $A$ is a f.g. module over the ring $\mathbb{K}[y_1, y_2, \ldots, y_k]$.

Ingrid Daubechies did pioneering work in harmonic analysis, which led for instance to the development of finite support wavelets (orthogonal and biorthogonal). This enabled wavelet theory to enter the domain digital signal processing, perhaps similarly to the invention of the Fast Fourier Transform with respect to the mathematical Fourier transform.

Two of these wavelets, called CDF 5/3 or CDF 9/7 for Cohen-Daubechies-Fauveau, are at the core of the image compression algorithm JPEG 2000, and the Motion JPEG 2000 used in the Motion Picture industry.

She was the first woman to be president of the International Mathematical Union. She was a Noether lecturer, where you can find other influential mathematician women. And she is a baroness now.

Her mathematical results not only made the path through industrial applications, but strongly modified the way people analyse data, in a multiscale (zoom-in/zoom-out) fashion.

To continue on jmite's excellent answer, Nancy Lynch is a pioneer in the theory of "Distributed Systems" in Computer Science. For example, her work with Michael J.Fischer and Mike Paterson showed that "In an asynchronous distributed system, consensus is impossible if there is one processor that crashes" which is a fundamental result in the field.

Karen Uhlenbeck made huge contribution to gauge theory and more.

She worked on several researches most significant of which included her commentaries on the Greek text-book, Arithmetica and On the Conics of Apollonius. She is remembered especially for her detailed description of the early hydrometer.

1. Émilie du Châtelet (1706-1749)

A French physicist, mathematician and writer during the Enlightenment era in Europe. In 1740, Châtelet published a book on philosophy and science called Institutions de Physique and later translated and commented on Newton’s Principia Mathematica which is its best known translation.

1. Maria Agnesi (1718-1799)

She wrote a book on math that still survives, that is: Analytical Institutions for the Use of Italian Youth in English. Another pioneering contribution was the Witch of Agnesi- a curve that she wrote the equation for.

1. Sophie Germain (1776-1831)

Sophie Germain’s paper on elasticity theory made her the first woman to be awarded from the Paris Academy of Sciences in 1816. She was also a major contributor in proving Fermat’s Last Theorem.

When asked to translate the memoir of Charles Babbage, the Analytical Engine, Lovelace went ahead and added her own comments and notes about a method of calculating a sequence of Bernoulli numbers: what is today known as the world’s first ever computer program subsequently making Lovelace renowned as the world’s first computer programmer.

1. Sofia Kovalevskaya (1850-1891)

She gave the Cauchy-Kovalevskaya Theorem its end result in 1875, worked on a paper in which she invented the Kovalevskaya Top and published ten papers based on mathematics and mathematical physics.

1. Emmy Noether (1882-1935)

Emmy Noether is famous for coining the Noether’s Theorem that clarifies the relationship between conservation laws and symmetry, as well as Noether’s Ring that changed the basics of abstract algebra. Noether is also famous for other theories based on non-commutative algebras, hyper-complex numbers and commutative rings.

1. Mary Cartwright (1900-1998)

She authored over a 100 papers which include her work on level curves, functions in the unit disk, topology and ordinary differential equations among others.

1. Julia Robinson (1919-1985)

She is well regarded for her work on Hilbert’s Tenth problem and decision problems.

1. Shafi Goldwasser (1958-Date)

Her research emphasizes on zero-knowledge proof, complexity theory, computation number theory and cryptography.