“Proof:” Carl Friedrich Gauss & Sophie Germain

By Barry Honold

Author Elizabeth Klaver asks, why does “Auburn choose the prime numbers and not some other area of mathematics?” Her answer: Sophie Germain, Catherine’s character, and Germain Primes provide a rather “nice connection.” Catherine is working on a proof involving prime numbers. Germain was one of the first professionally-accepted female mathematicians, and her story ties directly into that of her mentor: Carl Friedrich Gauss (1777 – 1855).

Gauss is arguably the greatest mathematician who ever lived. His skill first manifested itself at the age of nine. He was clearly meant to enter academia. Under Gauss, Germany would become the “mathematical Mecca of Europe.” A colleague thought him the perfect man to finally solve Fermat’s Last Theorem. Gauss declined, replying that one could easily “lay down a multitude of such provisions, which one could neither prove nor disprove.” He made a number of advancements in optics, map-making, magnetism, non-Euclidean geometry, and invented an early telegraph. He was a master of the Romance languages and spent his sunset years learning Sanskrit and mastering Russian to correspond with colleagues there in their native tongue. He was, to quote one biographer, “a master in the deepest and most abstract questions of knowledge.”

He corresponded with many mathematicians on the Continent, though he never left his native Germany. One in particular fascinated him: an inquisitive and bright young Frenchman by the name of Monsieur Leblanc. When the French occupied his native Brunswick, an officer paid a visit, and said that he had been instructed by a certain Mademoiselle Germain to inquire about Gauss’ health. Gauss was confused; the name “Germain” meant nothing to him. His colleagues began to needle him about keeping a Frenchwoman as a lover.

Three months later, the mystery was solved: in a letter, one Sophie Germain admitted to having “previously taken the name of Leblanc” in writing to Gauss. Gauss was an open-minded individual, and pleasantly surprised at her little trick. He replied:

“How can I describe my astonishment and admiration on seeing my esteemed correspondent M. Leblanc metamorphosed into this celebrated person. . . when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men in familiarizing herself with [number theory’s] knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius.”

Germain (1776 – 1831) defied all expectations of her time. She received a Grand Prix from Napoleon for her work in acoustics and prefigured Comte’s positivism. When she was thirteen, she was in her father’s study reading a copy of History of Mathematics. Upon reading the legend of Archimedes’ death, she developed an interest in mathematics. Her parents were fiercely opposed to her studying math, so she studied at night. When they discovered this, they took her candles. She responded by hiding candles, and using them after bedtime. This escalation continued until her parents gave up in exasperation. Later, she realized that she needed to know Latin to read Newton and Euler. Having no instructors, she went about it “alone and unaided.” 

Germain realized that this bias against her would be the norm, and adopted the name of “M. Leblanc” to correspond with noted mathematicians. One in particular, Joseph Louis Lagrange, took note of her skill and the two routinely wrote.  As Jess Fernandez-Martinez wrote, she “procured for herself students’ notebooks,” particularly those in Lagrange’s classes. She then went over them thoroughly, and began sending in notebooks of her own. Lagrange was immediately intrigued by this student’s exceptional skill and began touting the pupil to anyone who would listen. Lagrange arranged to meet “him,” and met her. So delighted was he that he lent his prestigious name to her cause, and she was soon meeting with some of the foremost minds in France.

The French government had a call to solve a problem regarding acoustics, which she did on her third try, while none of her male colleagues would touch the problem. Gauss recommended that she be granted an honorary degree. Unlike him, she did try her hand at proving FLT.  As a result, we have the Germain Primes, without which FLT would have taken even longer to prove. Unfortunately, she died of breast cancer before receiving her honorary degree.