Sophie Germain: Revolutionary Mathematician

This is a second edition, with a change in title and publisher, of Prime Mystery: The Life and Mathematics of Sophie Germain, which we reviewed in 2015.

Our review of the first edition discussed author Dora Musielak’s detailed treatment of both the mathematics and personal life of Sophie Germain, the first woman we know who did important original research in mathematics (indeed, in two completely different subject areas). This is an appropriately broad scope, since so little of Germain’s mathematical work was ever published, and source material on both her life and work is much harder to come by than for a typical male professional. Despite the fact that little effort was made at Germain’s time to preserve knowledge of her life and work, Dora Musielak has found an amazing amount of material. In this biography she presents her results painstakingly and engagingly while also discussing tantalizing remaining mysteries.

The second edition has considerable new material. The biggest addition is to the discussion of Germain’s research in number theory, now expanded and split into two chapters. An early chapter elucidates more fully Germain’s research via correspondence with Gauss during the years 1804–1809, mostly on power residues, partly on Fermat’s Last Theorem. A later chapter expands discussion of the plan Germain subsequently developed and followed for proving Fermat’s Last Theorem, centered over several years around 1819. This chapter includes the broader historical context before and since and discusses the people with whom Germain interacted about Fermat’s Last Theorem, especially Legendre and Gauss. This reworking and enlargement tremendously enhances the second edition.

The second edition contains several other improvements. Considerable detail from around the year 1829, perhaps one of Germain’s last productive years, has been added: correspondence involving her or about her, her last letter to Gauss, and her final two published papers in Crelle’s Journal, on curvature and number theory.

There are new translated excerpts throughout that further support Germain’s story. The author has provided valuable translations of 9 of the 14 letters between Germain and Gauss, for which Germain initially used a male pseudonym. She also includes two other letters shedding light on the revelation of Germain’s true identity to Gauss. Finally, the author has added a very comprehensive list of references, while encouraging readers to explore historical archives to uncover yet more about Sophie Germain.

Musielak regularly suggests stimulating interpretations, poses questions that we currently do not have sufficient evidence to resolve, and speculates and conjectures on possibilities, always making clear what is and isn’t supported by current evidence. This makes the story incredibly interesting, gets the reader thinking and guessing, and provides avenues for future research.

The new edition preserves the coherent and engaging organization by topical chapters while retaining the essence of a chronology, and gives equal emphasis to Germain’s two areas of research as well as her life and its social and historical context. The special chapters titled “Friends, Rivals, and Mentors”, “Unanswered Questions”, and “Princess of Mathematics” are fully justified by the extraordinary nature of Germain’s situation. The latter chapter puts Sophie Germain in the context of other women in mathematics and science from her era and before, also in the context of education and women’s access to it from her time almost to the present, and discusses her legacy both mathematically and in terms of subsequent recognition.

The revised title and the book itself make the case that Sophie Germain was an extraordinary one-off, a remarkable woman who overcame incredibly unfair obstacles to achieve greatness, and paved the way for others. The documentary evidence discovered and synthesized here by Dora Musielak is far richer than I would have thought possible, and supports the title’s claim that Sophie Germain was a “Revolutionary Mathematician”.

David Pengelley is professor emeritus at New Mexico State University and courtesy professor at Oregon State University. His research is in algebraic topology and history of mathematics. He has studied the handwritten manuscripts of Sophie Germain and published “Voici ce que j’ai trouvé”: Sophie Germain’s grand plan to prove Fermat’s Last Theorem in Historia Mathematica. David develops the pedagogies of teaching with student projects and with primary historical sources, and created a graduate course on the role of history in teaching mathematics. He relies on student reading, writing, and mathematical preparation before class to enable active student work to replace lecture. He has received the MAA’s Haimo teaching award, loves backpacking and wilderness, is active on environmental issues, and has become a fanatical badminton player.