BY **FRAN RAMÍREZ** & **FRAN FENOLL**

Since March is also International Mathematics Day, we wanted to pay tribute to the **great influence that women have had on this science** from the beginnings of our civilisation to the present day.

Of course, **there are many others who do not appear in this article**, but we want this representation to serve **as a tribute and recognition to all of them.**

* * *

## Pioneering women in history

### Theano

One of the first mathematicians we know of is perhaps Theano, who was born in the 6th century BC. Apart from being a mathematician, she also mastered other disciplines such as philosophy, physics and medicine.

Treatises on polyhedra are attributed to her, as well as on proportionality, specifically the golden ratio. **Theano **is also known for being the wife of the mathematician Pythagoras, and for belonging to the Pythagorean school.

In fact, it is thanks to Theano that we can study Pythagoras today, because when Pythagoras died there was a revolt against his school, and both Theano and her daughters saved his works, extending and spreading his study years later throughout Greece and Egypt.

### Hypatia

Moving on in history, we come across another great woman, an innovator in her time, a teacher at the Neoplatonic School of Alexandria, Hypatia.

She was born around 350 AD, the daughter of the mathematician and astronomer Theon. From an early age she was taught science, but her quest for knowledge and truth led her to travel to different parts of Athens and Rome in search of knowledge.

This eagerness led her to teaching and oratory as headmistress of Theon’s school, also known as the Musaeum.

She excelled for years as a teacher of many pupils, both Christian and non-Christian. She contributed writings in fields such as Geometry, Algebra and especially Astronomy. Unfortunately she was lynched to death by a mob of Christians in 415.

## The Age of Enlightenment

### Émilie du Châtelet

At the beginning of the 18th century, Émilie du Châtelet , Marquise de Châtelet, was born in France. Although she could have enjoyed a life full of luxury and extravagance, she decided to devote herself to research and to the dissemination of her theories, some of which even provoked wide debate in Europe.

She stood out above all for her role in the dissemination of Newtonian theories, for her work in the Differential and Integral Calculus. Given her position, she received great mathematical knowledge from great professors of the time such as Pierre Louis Moreau de Maupertuis, Clairaut and **Koenig**, among others.

Voltaire‘s influence was notable on the marquise for many years, and the two made a great couple, both sentimentally and in their work.

In fact, they both came close to winning the competition in 1737 organised by the Academy of Sciences for the best scientific essay on the nature of fire and its propagation, won by the famous mathematician-physicist Leonhard Euler.

The Marquise de Châtelet was the first woman to enter the *Café Gradot* to discuss mathematics with **Maupertuis **dressed as a man, it should be remembered that at that time women were not allowed to enter such places unaccompanied. She was also the **first woman to have a public scientific debate.**

### Maria Gaetana Agnesi

During the 18th century we also meet the Italian mathematician Maria Gaetana Agnesi, considered by many to be the** first university professor**, as she took charge of her father’s courses for two years in 1748.

In 1750, after publishing her work on Analytical Institutions, the Pope appointed her to the chair of Higher Mathematics and Natural Philosophy at the University of Bologna.

## The magnificence of the Age of Enlightenment is spreading …

### Sofya Kovalévskaya

Other authors, however, claim that the Russian mathematician Sofya Kovalévskaya was the first university professor in Europe in 1881, in Sweden.

She was taught by the famous mathematician **Weierstrass **in Berlin. Her contribution to the Differential Calculus was very important, above all she managed to improve a result of the mathematician Cauchy, she enunciated and proved the theorem known today as Cauchy-Kowalevski.

This was one of the reasons why she was awarded the title of *Doctor Summa Sum Laude* at the University of Göttingen in 1874, becoming, together with Agnesi, one of the first women in the world to do so.

During her stay in Stockholm her study of Differential Calculus managed to solve one of the problems that had most disturbed famous mathematicians: the rotation of a solid body around a fixed point, which together with the known solutions of **Euler **and **Lagrange **solved the problem posed in 1850 by the Berlin Academy of Sciences.

*Sofya Kovalevsky Day,* organised by the Association for Women in Mathematics (AWM), promotes the funding of workshops in the United States to encourage girls to explore mathematics.

### Sophie Germain

Towards the end of the 18th century, we meet the French mathematician, Sophie Germain. She stood out among other things for the development of the Number Theory and Elasticity, but above all in her study we can highlight **Sophie Germain’s** prime numbers and the attempt to prove Fermat’s theorem, which despite not succeeding she was able to draw conclusions such as the theorem that bears her name.

During her lifetime she corresponded with the mathematicians **Lagrange **and **Gauss**. In both cases and given the times **Sophie Germain** passed herself off as a man, and it was only after some time that she revealed her true identity.

In 1816 she won the competition, with a paper entitled “Mémoire sur les Vibrations des Surfaces Élastiques”. She became the first woman to attend the sessions of the French Academy of Sciences. Today, the Sophie Germain Prize is awarded annually to the researcher who has carried out the most important work in mathematics.

## Ada Lovelace’s inspiration

### Mary Somerville

During the progress of Scottish universities against other European universities, led by the scientist Lord Kelvin, the figure of Mary Somerville emerged.

She was born in Edinburgh in 1740, and although at that time women were not allowed to join universities or mathematical societies, this did not prevent her from disseminating her acquired knowledge and winning a silver medal for the solution of a problem on Diophantine equations in William Wallace’s Mathematical Repository.

In addition, in 1826 **Mary Somerville** wrote her first article The Magnetic Properties of the Violet Rays of the Solar Spectrum for the Royal Society in the Philosophical Transactions, and these were the first writings signed by a woman to date.

Among her most outstanding achievements we can highlight her work in astronomy in the study of the orbit of Uranus, something which years later led to the discovery of the planet **Neptune**. This work earned her the medal of honour of the Astronomical Society and various medals and awards from different European societies and universities.

### Ada Lovelace

Mary Somerville was an inspiration to Ada Lovelace. **Ada Augusta Byron**, daughter of the poet **Lord Byron** and the mathematician **Anne Isabella Noel Byron**, was born in 1815, and is noted for her work with Charles Babagge on the construction of a differential and analytical machine (the latter was never built), possibly the forerunner of computers.

All of **Ada’s **contributions to the operation of **Babbage’s **machine had to be signed under the initials AAL and these notes have become the basis of what we now call computer algorithms.

We can therefore say that Ada Lovelace was the first female programmer in history. And despite her early death, her legacy is recognised today, with a programming language named after her as ADA.

## Great injustices and modern times

### Amalie Emmy Noether

One of the great injustices that have been done to female mathematicians because of their gender is undoubtedly that suffered by Amalie Emmy Noether.

**Emmy **was born in Germany in 1882 and was noted for her work in the field of algebra and topology, but despite her great knowledge, studies and the help of mathematicians such as **David Hilbert** and **Felix Klein,** she did not get a place at university, either during her time in Germany or in the United States at Princeton University, where she had to teach at the Bryn Mawr College for Girls.

### Maryam Mirzakhani

In recent years we would like to highlight the Iranian mathematician Maryam Mirzakhani, born in 1977 in Tehran, who has been teaching at Stanford until her early death at the age of 40.

She devoted herself to the study of Geometry, Topology and Differential Calculus, but above all to hyperbolic and **Riemann **surfaces.

**Maryam **has the honour of being the first woman to receive the Fields Medal, a prize awarded every four years since 1936, which has had academic recognition similar to the Abel Prize since 2003 and the Nobel Prize **(Alfred Nobel** did not consider awarding a mathematical Nobel Prize because of the various legends that speak of “problems” with mathematicians).

* * *

### Author’s personal note

I would like to highlight a mathematician in my life who was an inspiration and role model, her name is Fuensanta Andreu (1955-2008) Professor of Applied Mathematics at the University of Valencia.

I was very lucky to have her as a teacher, not only for all her work in functional and differential analysis, but also for the closeness and simplicity with which she transmitted her classes. Thank you for your patience and help.

Featured photo: **Max Fischer / Pexels**