Smile of the Day Friday, January 8, 2021

Friday Jan. 8, 2021’s Smile of the Day: Fermat’s Last Theorem

On this Day:

Sophie Germain is the first woman to win a prize from the Paris Academy of Sciences for her paper on elasticity.

Marie-Sophie Germain (1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father’s library, including ones by Leonhard Euler, and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss (under the pseudonym of «Monsieur LeBlanc»). One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat’s Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. Before her death, Gauss had recommended that she be awarded an honorary degree, but that never occurred. On 27 June 1831, she died from breast cancer. At the centenary of her life, a street and a girls’ school were named after her. The Academy of Sciences established the Sophie Germain Prize in her honor.

The modern view generally acknowledges that although Germain had great talent as a mathematician, her haphazard education had left her without the strong base she needed to truly excel. As explained by Gray, “Germain’s work in elasticity suffered generally from an absence of rigor, which might be attributed to her lack of formal training in the rudiments of analysis.” Petrovich adds: “This proved to be a major handicap when she could no longer be regarded as a young prodigy to be admired but was judged by her peer mathematicians.”

Notwithstanding the problems with Germain’s theory of vibrations, Gray states that “Germain’s work was fundamental in the development of a general theory of elasticity.” Mozans writes, however, that when the Eiffel tower was built and the architects inscribed the names of 72 great French scientists, Germain’s name was not among them, despite the salience of her work to the tower’s construction. Mozans asked: “Was she excluded from this list … because she was a woman? It would seem so.”

Concerning her early work in number theory, J. H. Sampson states: “She was clever with formal algebraic manipulations; but there is little evidence that she really understood the Disquisitiones, and her work of that period that has come down to us seems to touch only on rather superficial matters.” Gray adds that “The inclination of sympathetic mathematicians to praise her work rather than to provide substantive criticism from which she might learn was crippling to her mathematical development.” Yet Marilyn Bailey Ogilvie recognizes that “Sophie Germain’s creativity manifested itself in pure and applied mathematics … [she] provided imaginative and provocative solutions to several important problems”, and, as Petrovich proposes, it may have been her very lack of training that gave her unique insights and approaches. Louis Bucciarelli and Nancy Dworsky, Germain’s biographers, summarize as follows: “All the evidence argues that Sophie Germain had a mathematical brilliance that never reached fruition due to a lack of rigorous training available only to men.”

Germain was referenced and quoted in David Auburn’s 2001 play Proof. The protagonist is a young struggling female mathematician, Catherine, who found great inspiration in the work of Germain. Germain was also mentioned in John Madden’s film adaptation of the same name in a conversation between Catherine (Gwyneth Paltrow) and Hal (Jake Gyllenhaal).

In the fictional work “The Last Theorem” by Arthur C. Clarke and Frederik Pohl, Sophie Germain was credited with inspiring the central character, Ranjit Subramanian, to solve Fermat’s Last Theorem.

A new musical about Sophie Germain’s life, entitled The Limit, premiered at VAULT Festival in London, 2019.

The Sophie Germain Prize (French: Prix Sophie Germain), awarded annually by the Foundation Sophie Germain, is conferred by the Academy of Sciences in Paris. Its purpose is to honour a French mathematician for research in the foundations of mathematics. This award, in the amount of €8,000, was established in 2003, under the auspices of the Institut de France (per Wikipedia).

First, a Story:

There are three kinds of people in this world. Those who get math and those who don’t.

Second, a Song:

The Simpsons is known for its blink and you’ll miss it mathematical references. But perhaps the most ingenious one of all is located in Series 10 Episode 2 ‘The Wizard of Evergreen Terrace’ in which it appears that Homer Simpson has successfully disproven Fermat’s Last Theorem.  Here is a clip explaining Homer’s apparent insight into one of the most challenging mathematical problems ever…I hope you enjoy this even if you hated math…but liked The Simpsons…(from the Full Fat Podcast).

Here is the Epic Simpsons Maths Joke that Broke the Internet. I hope you enjoy this!

(https://www.youtube.com/watch?v=pSh-lY6XoKY)

Thought for the Day:

“I loved doing problems in school. I’d take them home and make up new ones of my own. But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem – Fermat’s Last Theorem.” – Andrew Wiles

Have a great day!

© 2021 David J. Bilinsky and Colleen E. Bilinsky