By Lillie Therieau 

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Sophie Germain is one of the earliest and most influential women mathematicians. She overcame societal pressures to abandon her work during her life and persevered, becoming a pioneering thinker in the fields of number theory and elasticity. 

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Her story is inspiring for anyone, but especially any girls out there who sometimes feel alone in their love of math. Sophie’s life and work proves that anyone can become a mathematician, as long as they have a passion for math and a love of learning! 

Portrait of Sophie Germain aged 14 by Auguste Eugene Leray, Image: Wikipedia

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Sophie Germain’s Unlikely Introduction to Math 

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Sophie Germain was born in 1776 in Paris, France. She was born into a very wealthy family and her father was a silk salesman. He was also involved in politics, taking part in the Constitutional Assembly of 1789. She was surrounded by books as a child and often overheard her father's important friends discussing politics and philosophy in her home.

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When Sophie was 13, the Bastille fell, launching Paris into the bloodiest period of the French Revolution. The turmoil and political chaos forced her to stay inside for long periods. She turned to her father’s library of books, particularly several volumes about the history of mathematics. Sophie taught herself Latin and Greek so that she could read the work of math scholars like Isaac Newton. She was especially fascinated by number theory, a branch of pure mathematics that deals with the study of integers. 

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Sophie’s family didn’t support her interest in math and thought that it wasn’t an appropriate area of study for a young lady at the time. At first, they tried to persuade her verbally. When that didn’t work, they stole her warm clothes and firewood from her room so that she couldn’t stay up late into the night studying. 

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She continued to stay up reading anyway, using candlelight. Her parents even went so far as to take her candlesticks away. Sophie found novel ways to continue reading and teaching herself math. Eventually, her mother came around, swayed by her daughter’s stubborn insistence on learning mathematics.

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Number Theory: Sophie Germain’s Life Work 

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Number theory is a branch of mathematics that concerns the properties of integers including work with prime numbers, rational numbers, and equations. Number theory is sometimes known as arithmetic. 

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Sophie Germain is best known for her work in algebraic number theory, which is concerned with using abstract algebra to study integers. Algebraic equations are constructed to better understand the character and properties of integers, rational numbers, and prime numbers. 

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Today, number theory is critical for the functioning of computers and their calculation capabilities. It is also an important part of cryptography or the study of codes. 

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Early in her self-education, Sophie began correspondences with two monumental figures working on number theory at the time: Adrien-Marie Legendre and Carl Friedrich Gauss. Though she initially pretended to be a man in her letters, both of her penpals eventually discovered her true identity. Gauss was particularly impressed, praising her for her strength despite the hurdles society threw at her for being a woman in the maths and sciences. 

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Sophie used these correspondences to test theories and work out problems with the help of other highly skilled mathematicians. They helped her to correct her proofs and think of new approaches to old problems. 

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Fermat’s Last Theorem Revisited 

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Sophie Germain is best known for her work on Pierre de Fermat’s Last Theorem, a hastily scribbled note in the margin of one of the famous mathematician’s books that had been stumping scholars for centuries. 

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He had claimed that no three positive numbers for (n) could satisfy the equation a^n + b^n = c^n for any number larger than 2. However, he said, the proof was too big to fit in the margin of his book and he never published it. Later generations of mathematicians doubted that he had ever had a proof for the theorem, as no one could make any progress towards solving it. 

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Fermat’s Last Theorem is often known as the most difficult math problem ever created, due to the massive amount of unsuccessful proofs for the theorem created by gifted mathematicians. It took 358 years for someone to solve his theorem, stumping math experts everywhere until 1995, when British mathematician Andrew Wiles published a manuscript of his successful proof. 

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Sophie was the first person to make substantial contributions to the eventual solution of Fermat’s Last Theorem, introducing several new ways to rephrase the theorem and a partial solution dealing with integers less than 100. 

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However, she did not publish her work and it was only known as a footnote in the work of her friend, Legendre, for many years. Later rediscovery of her writings and work has allowed for her place in the cannon of number theory to be reestablished and she is finally getting the recognition she deserves. 

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Other Work and Legacy 

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Sophie Germain is also known for her work in the field of elasticity, which considers the properties of elastic surfaces through mathematical equations and systems. Her work in this area earned her the Paris Academy of Sciences’ Academy Award in 1816 when she became the first woman to win the prestigious prize. 

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However, it wasn’t an easy road to the prize. Her winning work was actually the third attempt she made to enter the competition. Her first two entries were filled with errors, as she worked through her ideas on the challenging subject. Each time she failed, however, the Academy acknowledged her innovation and creativity, and invited her to apply again. 

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She was not allowed to attend the prize ceremony when she finally won, as the only women allowed to enter were the wives of the members. However, she was able to collect the money prize, which helped her continue her work and research. 

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She was diagnosed with breast cancer in 1829, though she continued to work despite the progression of her illness. 

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Sophie died in 1831 from cancer. A street and an all-girls school were named after her. In 2003, the Foundation Sophie Germain began awarding the Sophie Germain Prize, an honor given each year to a pioneering French mathematician. 

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The Inspiring Lives of Famous Mathematicians 

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This article is the first of our series exploring the lives and achievements of famous mathematicians throughout history. They’ll be something for everyone: whether algebra, statistics, geometry, or calculus. 

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Through the lives of these brilliant folks, we hope you’ll find connections, inspiration, and empowerment.