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About this book

This biography of the mathematician, Sophie Germain, paints a rich portrait of a brilliant and complex woman, the mathematics she developed, her associations with Gauss, Legendre, and other leading researchers, and the tumultuous times in which she lived.

Sophie Germain stood right between Gauss and Legendre, and both publicly recognized her scientific efforts. Unlike her female predecessors and contemporaries, Sophie Germain was an impressive mathematician and made lasting contributions to both number theory and the theories of plate vibrations and elasticity. She was able to walk with ease across the bridge between the fields of pure mathematics and engineering physics. Though isolated and snubbed by her peers, Sophie Germain was the first woman to win the prize of mathematics from the French Academy of Sciences. She is the only woman who contributed to the proof of Fermat’s Last Theorem.

In this unique biography, Dora Musielak has done the impossible―she has chronicled Sophie Germain’s brilliance through her life and work in mathematics, in a way that is simultaneously informative, comprehensive, and accurate.

Table of Contents

Frontmatter

Chapter 1. Unforgettable Childhood

Abstract
Sophie-Marie Germain was born in Paris on 1 April 1776, ten months after Louis XVI was crowned King of France and his wife Marie Antoinette became Queen. That was a time when France was the most powerful country in Europe, and its cultural influence was such that nobles, monarchs, and the educated people in many other countries often spoke elegant French instead of their native languages.
Dora Musielak

Chapter 2. Lessons from l’École Polytechnique

Abstract
Following the brutal Reign of Terror, an emergency council was set up in Paris. Its main task was the creation of a new engineering school called the École centrale des Travaux publics, which had the objective to train engineers, both civilian and military.
Dora Musielak

Chapter 3. Sophie’s Sublime Arithmetica

Abstract
It is the autumn of 1804. Sophie Germain is twenty-eight, a woman ready to assert her worth as a serious scholar. By her own account, she had been studying the theory of numbers and had built the necessary skills to understand the theorems in Legendre’s Essai sur la théorie des nombres. Now Germain began courting the affirmation of her mathematical efforts from the pre-eminent authority in the purest of mathematical science: Gauss. Three years earlier, Gauss had captivated Germain with a new approach to study “higher arithmetic” or arithmeticae sublimiori, as Gauss called it. This is the branch of mathematics dedicated to the general study of the proper, particular properties of the integers, which now we call number theory.
Dora Musielak

Chapter 4. Chladni and His Acoustic Experiments

Abstract
In early 1809, a peculiar acoustics demonstration by Chladni, a German physicist, arose in Sophie Germain her intellectual curiosity. At that time, the learned community in Paris was once again vibrant, spurred by the support of Napoléon. The first graduates from the École Polytechnique were working alongside senior researchers, paving new roads in applied mathematics and physics. Scientists from abroad were descending in Paris to learn from the French and to share with them their own scientific discoveries. Acoustics and elasticity theories were emerging.
Dora Musielak

Chapter 5. Euler and the Bernoullis

Abstract
Sophie Germain set out to derive the mathematical theory to describe the complex phenomena manifested on Chladni’s vibrating plates. To do that, Germain sought to obtain a clear understanding of the theories advanced by Euler, the Bernoullis, d’Alembert, and Lagrange, and she tried to extend and improve their analysis. This was a daunting task. Her predecessors had worked for many years to formulate the mathematical foundation for elasticity that was in place in 1809.
Dora Musielak

Chapter 6. Germain and Her Biharmonic Equation

Abstract
What prompted Sophie Germain to enter the prize competition to derive a theory for vibrating surfaces? Did she see the contest as a source of mathematical knowledge and sought to advance her own intellectual development?
Dora Musielak

Chapter 7. Experiments with Vibrating Plates

Abstract
When Sophie Germain attempted to develop a theory for vibrating plates of variable thickness, she was aware of the complexity and importance of the problem. She had to build especial plates to carry out her own experiments. Her memoir of 1825 begins with a review of the relevant literature, citing papers by Euler, Bernoulli, Lagrange, Chladni, Poisson, Navier, Savart, and Italian physicist Giordano Riccati.
Dora Musielak

Chapter 8. Elasticity Theory After Germain

Abstract
The mathematical theory of elastic vibrating plates originated in 1811, when Sophie Germain first developed the first valid hypothesis. This led to the first fourth-order partial differential equation now known as the Germain-Lagrange equation. Much more work had yet to be done, of course. The governing equation for the equilibrium of thin elastic plates was derived from that basic formulation.
Dora Musielak

Chapter 9. Germain and Fermat’s Last Theorem

Abstract
On the same day Sophie Germain won the prize for her mathematical work on vibrating plates, the commissioners of the Academy of Sciences announced the (last) theorem of Fermat as the topic for the 1818 contest of mathematics. A happy coincidence? Germain kept her feelings secret, or at least there are no written words to shed light on her intellectual delight, as the new competition would carry her back to her first love—number theory. It would give her a fresh impetus to pursue once again the proof of the célèbre équation de Fermat, as she called it, an effort she had begun years earlier.
Dora Musielak

Chapter 10. Pensées de Germain

Abstract
Sophie Germain was a mathematician, a physicist, and a philosopher. She left us a legacy that portrays a deeply sensitive woman who was curious about the world and studied diverse subjects such as astronomy, chemistry, history, and geography.
Dora Musielak

Chapter 11. Friends, Rivals, and Mentors

Abstract
Sophie Germain was ill at ease by unwelcome attention. She may have been rude and even quick-tempered with those who treated her condescendingly. At the peak of her career, she displayed arrogance unexpected in a woman of her time, and she fought back with those who did not take her work seriously.
Dora Musielak

Chapter 12. The Last Years

Abstract
In 1824, France had reverted to the splendor of the Bourbon monarchy. On September 16, the ailing King Louis XVIII died. His brother succeeded him to the throne as King Charles X of France. In the first few months of his rule, the government passed a series of laws that bolstered the power of the nobility and clergy, which met with particular public disapproval. This reign dramatized the failure of the Bourbons, after their restoration, to reconcile the tradition of the monarchy by divine right with the democratic spirit produced in the wake of the 1789 Revolution.
Dora Musielak

Chapter 13. Unanswered Questions

Abstract
There are many unanswered questions about Sophie Germain. Who taught her basic mathematics when she was a child? What exactly drove her to take a man’s name to communicate her work to the leading mathematicians of her time? Why did she pursue research in mathematical physics while her desire was to work in number theory? What gave her the inspiration and the extraordinary courage to compete in the most prestigious mathematical prize in Europe? Answering these and many other questions would help us paint a better portrait of the woman behind the mathematics.
Dora Musielak

Chapter 14. Princess of Mathematics

Abstract
The leading number theorists at the turn of the nineteenth century were Legendre and Gauss, and right between these two great men we always find Sophie Germain.
Dora Musielak

Backmatter

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