Sophie Germain and the Routes Not Permitted

For centuries, knowledge was not simply discovered; it was guarded. Universities, academies, and scientific societies were not neutral spaces. They were shaped by hierarchies of gender, race, caste, class, and religion, and access to lectures, mentorship, correspondence networks, and degrees was restricted accordingly. Exclusion was not incidental; it was built into the structure of institutions. Yet those kept outside were never absent from intellectual life. When institutions closed ranks, parallel practices of learning emerged. For women like Mary Jackson, Ynes Mexia, Laura Bassi, and many others, formal pathways were denied, so informal ones were cultivated. Exclusion shaped the conditions of their work; it did not stop it.

Sophie Germain belongs to that lineage of persistence. Born in Paris in 1776, she came of age during the French Revolution. It was a time that promised liberty, but society still withheld education from women. Mathematics seized her imagination as a teenager after reading about Archimedes. Her parents, alarmed by what they considered an unfeminine obsession, tried to stop her. They removed candles and fire from her room at night to prevent her from studying. She wrapped herself in quilts and continued working.

When the École Polytechnique opened in 1794, it became a center for advanced mathematical instruction in France. Women were not admitted. Germain obtained lecture notes through acquaintances and began submitting solutions under a male pseudonym: Monsieur Le Blanc. One of the mathematicians who received work from “Le Blanc” was Joseph-Louis Lagrange. Impressed by the clarity of the submissions, he asked to meet the author. When he discovered Germain’s identity, he did not withdraw his support; he became her mentor. She later initiated correspondence with Carl Friedrich Gauss, again under her pseudonym, sending him her work on number theory. When Gauss eventually learned that his correspondent was a woman, he expressed admiration for what he described as the courage required for a woman to pursue mathematics in such conditions. But the fact remains: her intellect had to arrive disguised in order to be evaluated.

 Germain’s made significant advances in number theory, particularly in work related to Fermat's Last Theorem — the centuries-old problem asserting that the equation xⁿ + yⁿ = zⁿ has no whole-number solutions for n greater than 2. She developed a strategy that proved the theorem for an important class of prime numbers. These primes are now called Sophie Germain primes: a prime number p for which 2p + 1 is also prime. Her methods formed a crucial component in later progress on the theorem, long before its complete proof by Andrew Wiles in 1994.

She also turned to applied mathematics. In 1809, the French Academy of Sciences announced a prize for a mathematical explanation of patterns formed on vibrating metal plates in experiments conducted by Ernst Chladni. The problem lay at the intersection of physics and mathematics and demanded a theory of elasticity that did not yet exist in complete form. Germain submitted a paper. It was rejected. She revised and resubmitted. Rejected again. On her third attempt, in 1816, she won the prize. She was the first woman ever to do so.

And yet she was still not fully included. She was not a member of the Academy. She did not hold a university position. She never earned a formal degree. Even her prize-winning work was initially treated with hesitation and scrutiny beyond what her male peers faced. She was permitted to attend Academy sessions only later, and only because of her extraordinary reputation.

Germain is often described as someone who succeeded “against the odds.” That language suggests misfortune. In her case, the barriers were not accidental; they were structural. Her intellectual life unfolded alongside institutions, not within them.

Remembering Germain is therefore not about celebrating resilience in the abstract. It is about acknowledging that the history of mathematics includes contributions from those formally excluded from its institutions. The discipline advanced through work that its own structures did not fully recognize. And that is why we still need to think about her and people like her; not to marvel at an exception, but to remember a pattern.

Written by Janaky S. and edited by Parvathy Ramachandran

References:

1. Dalmedico, Amy Dahan. "Sophie Germain." Scientific American 265, no. 6 (1991): 116-123.

2. Musielak, Dora. Sophie Germain: revolutionary mathematician. Springer Nature, 2020.

3.Mackinnon, Nick. "Sophie Germain: or was Gauss a feminist?." The Mathematical Gazette 74, no. 470 (1990): 346-351.

4. https://www.thethinkacademy.com/blog/edubriefs-sophie-germain-math-story-a-pioneer-in-prime-numbers/