Sophie Germain – A Life Between Numbers and Freedom

1880 illustration of a young Sophie Germain (circa 1790)

                                                                  

We know that women also worked on Mathematics, but their interest encountered several limitations due to their gender.

For example, Sophie Germain, born on 1st April 1776 in Paris, made important contributions to the field of Mathematics, in particular to number theory and the applied mathematics of acoustics and elasticity.

Sophie's interest in mathematics sparked at the age of 13 when she read about Archimedes' death. She thought that maths must be an interesting subject, if someone could love it so much to die for it.

She learned Latin and Greek by herself to be able to read Euler and Newton works. Furthermore she read every mathematics book in the home's library.

Her parents, initially opposed to her wishes, assigned her a private tutor for her mathematical studies, but Sophie was not satisfied and wanted to attend the University, forbidden to women during her time.

She thus decided to enroll at the École Polytechnique using the pseudonym Monsieur Antoine-August Le Blanc.

Lagrange 

Sophie studied independently on the course notes without attending, in order not to be discovered. Lagrange, at the time a teacher at the École, was struck by Le Blanc's skill and wanted to meet him. So Sophie had to reveal her true identity.

Lagrange introduced her into the mathematical community.

Under his guidance, Sophie devoted herself to advanced study, especially of Number Theory and Fermat's Last Theorem.

During the study of the theorem that  provided a foundation for mathematicians exploring the subject for hundreds of years after, she found a type of prime number: Sophie Germain's prime.

Carl F. Gauss

In 1804, she began an epistolary correspondence with Carl F. Gauss, still using the same pseudonym, to deepen her studies of number theory. Gauss was thrilled when he learned she was a woman, confirming his esteem for her.

Sophie subsequently devoted herself to the study of vibrating plates and, with the help of Lagrange, obtained the correct solution to the plate problem. This solution, however, due to the prevailing machismo, went down in history as Lagrange's differential equation, and is only recently mentioned as the Germain-Lagrange plate equation.

This important contribution is a work full of brilliant insights that lays the foundations of the modern theory of elasticity.

I suggest the book 'Sophie Germain: An Essay in the History of the Theory of Elasticity'.

It took her several years of work to be recognized and appreciated for her contributions to the field of mathematics and science: the Academy of Sciences of Paris finally awarded her work on elasticity in 1816.

Sophie Germain is considered an icon of feminism for the fight against the social and cultural prejudices of her time.

Sophie Germain (Œuvres_philosophiques, 1896)

A brilliant and tenacious mind, she has left an indelible mark not only on the history of mathematics and science, but also on the cultural and social fabric of humanity. Her cultural legacy is a song of perseverance, an ode to the strength of the intellect that rises against the storms of prejudice.

Born in an era when women were excluded from academia and relegated to the margins of intellectual life, Sophie immersed herself in numbers and equations with a passion that defied convention. Her contributions are jewels of a legacy that shines with rigor and genius. But what makes her cultural legacy so poignant is the price she paid to pursue it: years of clandestine study, letters exchanged with giants like Gauss, who only later discovered the true identity of that extraordinary mind. Her life was a slow, painful chipping away at the walls of exclusion, an act of creation that was not limited to formulas, but redesigned the boundaries of the possible.

Socially, Sophie Germain emerges as an icon of feminism ante litteram, a beacon of resistance against the prejudices that chained women to silence. It was not only her intelligence that made her a symbol, but the courage with which she faced a world that denied her space. In an era in which female education was seen as an aberration, she appropriated knowledge with a determination that had the flavor of rebellion. Each step towards recognition was not only a personal victory, but a collective one, a silent cry for all women crushed by the weight of social expectations.

Sophie did not just fight for herself: her example became an inspiration, a reminder that the fight against cultural and gender prejudices requires time, sacrifice and an unyielding obstinacy. Although she did not live to see the full recognition of her genius, her name resonates today as a symbol of emancipation, an echo of what a woman can achieve when she dares to challenge the destiny that was imposed on her.

Her legacy, therefore, is twofold: a mathematical heritage that still illuminates science today, and a living testimony to the transformative power of those who refuse to be forgotten.

Sophie Germain is not just a scientist; she is a sentiment, a breath of hope for anyone fighting to be heard in a world that too often closes its doors.

On 27 June 1831, she passed away from breast cancer.

The plaque on Sophie Germain house at 13, rue de Savoie. Source

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Images: they come from Wikimedia Commons and are in the public domain, except the last one (the plaque) which is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

References:

Sophie Germain (on Wikipedia) 

Badass Wimmin of History Presentes Sophie Germain

Sophie Germain, la boss des maths

Marie-Sophie Germain - Biography

Paul Erdős: The Wandering Genius Who Loved Only Numbers

 

On 26 March 1913, Paul Erdős was born: one of the most prolific and influential mathematicians of the 20th century, a legendary figure not only for his academic contributions, but also for his eccentric lifestyle and his unique vision of mathematics as a collaborative and universal activity.

Born in Budapest, Hungary, to a Jewish family, Erdős lived a nomadic existence, traveling incessantly between conferences, universities and colleagues' homes, with a suitcase and a few personal belongings, dedicating his life entirely to mathematics.

He is known for his work in fields such as number theory, combinatorics, graph theory and probability. He published over 1,500 papers before his death in 1996, collaborating with more than 500 co-authors, a record that gave rise to the famous "Erdős number", an index measuring the collaborative distance between a mathematician and Erdős himself through joint publications. Among his most famous results are the Erdős-Kac theorem (also known as the fundamental theorem of probabilistic number theory), his contributions to Ramsey theory, and his work on prime numbers. His ability to pose deep and challenging problems often opened up new avenues of research.

Erdős’s legacy goes beyond his theorems. He embodied an approach to mathematics as a collective, almost mystical enterprise: for him, mathematical problems were part of an ideal “Book,” written by some kind of transcendent entity, which mathematicians were tasked with discovering. His recurring phrase, “my brain is open,” reflected his willingness to collaborate with anyone, regardless of age, nationality, or prestige. This spirit inspired a culture of openness and sharing in the mathematical community. Erdős was also a symbol of cultural resilience. Growing up in a time of political turmoil and persecution of Jews in Europe, he transformed personal hardship into tireless creative energy. His minimalist lifestyle – he owned little, lived as a guest of others, and donated much of his earnings in prizes for solving mathematical problems – reflected an almost monastic dedication to knowledge.

Morally, Erdős represents an ideal of intellectual altruism. He did not seek personal fame or material wealth, but the advancement of knowledge for the common good. His generosity manifested itself in the monetary prizes he offered for solving problems he proposed, a way of stimulating the curiosity and talent of others. Furthermore, his refusal to conform to social conventions – he never married and did not have a permanent home – can be seen as a rebellion against materialism and a call to pursue what truly matters. Erdős was also deeply human: he loved to joke, invented terms such as "epsilons" for calling children (referring to the small mathematical quantity ε), and had an inclusive ethic that made him a friend to all. His death from a heart attack, while attending a conference in Warsaw on 20 September 1996, was emblematic: he died doing what he loved, surrounded by the community he had helped build.

Paul Erdős left a legacy that intertwines mathematical brilliance, a collaborative cultural approach, and a moral example of selfless dedication. His life demonstrates that true greatness lies not only in achievements, but in the way one lives and inspires others. To this day, his name is synonymous with creativity, connection, and a passion for discovery.

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Image: Erdős with Terence Tao (ten-year-old ), 1985. Via Wikimedia Commons 

References and further reading

Paul Erdős- Biography 

PAUL ERDŐS 

N Is a Number: A Portrait of Paul Erdös 

The Man Who Loved Only Numbers 

Emmy Noether: The Queen Of Mathematics Who Revolutionized Physics

Born on 23 March 1882, Emmy Noether, considered by Einstein the most important woman in history of mathematics, had a great passion for theoretical physics and abstract algebra.

She made many relevant contributions to the field of mathematics.

In 1915, Noether accepted an invitation from Hilbert and Klein to move to Göttingen, the "Mecca of Mathematics."

Many of the faculty did not want her there, but she worked hard and soon was given a job as a lecturer.

Even though she still was not paid for her efforts, for the first time, Noether was teaching under her own name.

Three years later, she began receiving a small salary for her work.

There she became a world-class algebraist who attracted students and younger colleagues who themselves became leading mathematicians.

In fact, during her time at the University of Göttingen, Emmy accumulated a small following of students known as "Noether's boys".

In 1933, Hitler and the Nazis came into power in Germany.

Noether moved to the USA, where Bryn Mawr College offered her a position teaching. There she taught until her death in 1935, being an inspiring teacher for her students.

"In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians. Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature."

- Albert Einstein, Princeton University, May 1,1935 (Source)

Emmy discovered the symmetries of a physical system are inextricably linked to physical quantities that are conserved, such as energy. These ideas became known as Noether’s theorem, the foundations of modern physics.

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References

Celebrate the mathematics of Emmy Noether

Emmy Noether, Mentors & Colleagues 

Emmy Noether

Image: Portrait of Emmy Noether, before 1910 (Public Domain)

Author: unknown

Image Source 

La Matematica È il Segreto Nascosto per Capire il Mondo

Pubblico un interessante video da TED Ideas worth spreading, in cui Roger Antonsen (logico, matematico e informatico norvegese) spiega come un piccolo cambio di prospettiva può rivelare schemi, numeri e formule quali passaggi verso l'empatia e la comprensione.

Il filmato è sottotitolato in lingua italiana, ma, se preferite la lettura, più avanti trovate la traduzione della TED translator Silvia Fornasiero.

Teoria dei Numeri: La Regina della Matematica

Fonte dell'immagine

Si dice che Carl Friedrich Gauss, uno dei più grandi matematici di sempre, avesse affermato:

"La matematica è la regina delle scienze e la teoria dei numeri è la regina della matematica".

Le proprietà dei numeri primi giocano un ruolo cruciale nella teoria dei numeri, che studia le proprietà dei numeri interi; una domanda intrigante è come essi siano distribuiti all'interno degli altri numeri interi.
Nel 19° secolo ci sono stati indubbi progressi nella risposta a questa domanda con la dimostrazione del Teorema dei numeri primi, ma abbiamo anche visto Bernhard Riemann proporre quello che molti considerano il più grande problema irrisolto in matematica - l'Ipotesi di Riemann.

La teoria dei numeri è un'antica disciplina. Le prime formulazioni dei problemi della teoria dei numeri, e le soluzioni di alcuni di essi, risalgono, infatti, a Pitagora e alla sua scuola e sono enunciate negli Elementi di Euclide.
Euclide ha dimostrato l'infinità dei numeri primi con il metodo della reductio ad absurdum, un metodo di dimostrazione che procede con la formulazione di una proposizione che poi si risolve in una contraddizione, dimostrando così che la proposizione è falsa.
Un altro problema è, sin dai tempi più antichi, quello della risoluzione di equazioni a coefficienti interi: Pitagora risolveva equazioni quadratiche legate ai triangoli rettangoli, Euclide utilizzava equazioni lineari per calcolare il massimo comun divisore di due numeri interi e Archimede studiava equazioni quadratiche, note oggi come equazioni di Pell.