# What famous theorems or results were proven by female mathematicians?

We know that there were/are many famous female mathematicians who influenced the mathematics as we know it today, but their numbers are few compared to male mathematicians. While we have numerous famous results by many male mathematicians like Gauss, Euler and many others, what are famous results bearing the name of a female mathematician which also have a very deep impact on our understanding of mathematics?

• en.wikipedia.org/wiki/Hypatia – rickz Oct 19 '15 at 1:56
• I started thinking about all the important theorems named "Somebody's theorem/lemma/etc." that I know, and realized that, for a substantial fraction of them, I actually don't know the gender of the person they're named after, at least not beyond the default cultural assumption that a majority of them are probably male. Even knowing their given name doesn't always help, if it's non-gender-specific or from a culture whose names I don't easily recognize as male or female specific. – Ilmari Karonen Oct 19 '15 at 9:13
• The MRDP theorem solved Hilbert's tenth problem (to the negative). The R in MRDP references Julia Robinson. – David Hammen Oct 19 '15 at 12:03
• The question is trivial. Easy search on the internet gives plenty of examples. Therefore I vote to close. – Alexandre Eremenko Oct 19 '15 at 19:10
• @R.. that may be so, but it seems people want to close this one because they are uncomfortable with the question. I've researched it, and while there are lists of women mathematicians, and famous ones, there is little which places their achievements in the context of all mathematics, or their results in the context of all "famous results". I would post a proper answer but I don't have the rep. – Ben Oct 21 '15 at 9:36

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.

• This answer massively underplays the significance of Noether's work, really hugely! – CameronJWhitehead Oct 18 '15 at 21:21
• I agree with @CameronJWhitehead. It is not possible to overstate Noether's importance. Her theorem in theoretical physics is foundational for 20th century physics, but her work in algebra is much much more extensive and is utterly foundational to all of: number theory, commutative algebra, invariant theory, and algebraic geometry. – benblumsmith Oct 20 '15 at 22:12
• Whereas laws of physics explains how the world works, Noether's theorem explains how laws of physics works – slebetman Oct 21 '15 at 6:50
• @KprimeX: While Emmy Noether's accomplishments are remarkable, and she surely belongs near the top of any list of notable mathematicians, marking an answer mentioning only her as accepted seems rather dismissive of all the other important female mathematicians mentioned in the other answers. – Ilmari Karonen Oct 21 '15 at 11:41
• Actually I am not accepting Noether as the only female mathematician of highest class, I know every other female mathematicians mentioned in the answers are also as important as Noether, but I can only accept one answer and when I accepted this answer there were only 2 answers, now it grows to 10, and I am unable to accept anymore so I give +1 to every other. @IlmariKaronen – Kushal Bhuyan Oct 21 '15 at 15:50

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.

• I'd like to point out that Liskov's LSP is still used as a design rule in modern object-oriented programming. It is the thing you have to follow if you want polymorphism to make any kind of sense. – Kevin Oct 19 '15 at 3:04
• You forgot Grace Hopper, who in 1969 won the inaugural (and incongruously named) Man of the Year award from the Data Processing Management Association. – David Hammen Oct 19 '15 at 12:11
• @DavidHammen they also forgot Ada Lovelace. Not any theorem holds her name (at far as I know) but a famous programming language instead. – ypercubeᵀᴹ Oct 19 '15 at 13:41
• Wow, while knowing the principle I never knew that the Liskov substitution principle is named after a woman. (Well, I didn't really care, in the same sense that I don't know the gender or nationality of most other people theorems are named after.) – Josef says Reinstate Monica Oct 19 '15 at 14:10
• @ypercube: While Ada Lovelace is mostly noted as the world's first programmer, her most important contribution to computing is the invention of subroutines. Babbage wasn't convinced about the usefulness of subroutines (functions) when Lovelace described it to him until she demonstrated an example program that made good use of subroutines. So Babbage added hardware that made it possible to return from a jump. While the theoretical foundations of functions came from mathematics, the practical use of it in computer hardware was introduced by Ada Lovelace – slebetman Oct 21 '15 at 6:55

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.

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).

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

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 $\mathbb{K}[y_1, y_2, \ldots, y_k]$.

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.

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

• I'm not sure that this satisfies the fame requirement in the question. – HDE 226868 Oct 19 '15 at 22:18
• Danica McKellar is famous. Her name gets 50% more hits on Google than Emmy Noether and anyone who cares about high school math education should know McKellar. But it is true the Chayes-McKellar-Winn theorem is not widely known or influential in mathematics. – Colin McLarty Oct 22 '15 at 16:32

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.

• Hypatia of Alexandria was mathematician. – ch7kor Oct 21 '15 at 9:25

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.

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.

• ... and, just to quibble, she is still alive and working! :) No past tense necessary! :) – paul garrett Jul 17 '18 at 22:34
• The question was... past. – Laurent Duval Jul 18 '18 at 2:40

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.

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.