The life of Sophie Germain - Lukas Brantner

Añadido: 2026-05-11

[00:00:02][music] [music] >> So, thank you all for coming to this special day on life of Sophie Germain.

[00:00:23]As mathematicians, we have a maybe quite special tradition of looking at the lives of the people who came before us and taking a real interest.

[00:00:31]And many of us will know the story of Archimedes or Galois or maybe Grothendieck, but uh Sophie Germain's story is, I think, a story that has fallen a little bit out of the spotlight. And today, um well, it's a special day where we celebrate her 250th birthday and look back at her life and uh what she accomplished.

[00:00:50]So, my name is Lukas Brantner and I thank ICMS and Oxford University for supporting this event. And I'm going to start with a talk on the life of Sophie Germain.

[00:01:01]On the 26th of December, 1815, so on Boxing Day, um the Parisian Academy of Science met and they found that um you know, they discussed uh a prize and they decided that the committee proposes to award the prize to the only work that was submitted and the note attached to this memoir was opened and one finds the name Mademoiselle Sophie Germain. So, what we learn from this is, well, she won the prize and at the time, uh evaluation was anonymous. So, in practice, as we'll later see, it wasn't all that anonymous in reality, but at least in theory, it was.

[00:01:38]Um then a bit later, there was a public ceremony to honor the recipient of this prize in the Institute of France. It was apparently well attended, but the day after this ceremony, the Journal des Débats politiques et littéraires notes that the public's expectation was disappointed. This young lady did not come to receive a palm that is an honor that no woman had yet won in France. So, she didn't show up to the prize ceremony. So, the question is, why didn't she come and who was this person who was the first woman to win a major competitive prize in mathematics?

[00:02:16]So, let's start with what she looked like. So, we actually don't have a single depiction of what she looked like during her life. So, this is a image that is produced from the statue that was made probably from her death mask. So, death mask is the only thing that we have of her.

[00:02:35]And as you will note, um well, the head is a little bit deformed, which was probably due to some practice that was common in France at the time of wrapping up the head of the baby when it was very young uh to protect it or maybe also to achieve a different form. So, that is something noteworthy, but I guess not all that relevant for the rest of the talk.

[00:02:58]So, she was born near the Fontaine des Innocents. So, back in the day, this looked like uh the building on the left. Nowadays, you can still see it depicted on the right. They basically took the front of the structure and turned it into the free-standing fountain we know today.

[00:03:15]And back then, it wasn't just decorative. It was a working water source for the neighborhood.

[00:03:19]And let me just give you some context what time this was. So, Louis XVI had just taken the throne 2 years earlier.

[00:03:26]And around the time she was born, uh America had declared independence. Jane Austen was born as well roughly then.

[00:03:34]And Gauss was born a bit more than a year later.

[00:03:39]She died only 55 years later of breast cancer in this house on the Rue de Savoie.

[00:03:45]At the time, the second French Revolution had just taken place. Louis Philippe, the Citizen King, had taken the throne and shortly after Sophie died, Galois passed away as well. So, the question now is, what did she achieve during her life? What were her mathematical contributions?

[00:04:01]So, much of what we learn, we learn from um an obituary written by Libri. So, Libri himself was a good friend of hers, very colorful figure. So, he at the time was still well regarded in France. At some point, he started stealing manuscripts and then fledged to England um because But anyway, so he wrote a very nice obituary about her life. So, and it starts with um she was one of those women who appear from time to time through the centuries to show that the intelligence of their sex is in no way inferior to ours.

[00:04:31]This line is obviously pretty sexist, but it is also revealing because it shows that men of her own time saw her as a kind of proof that women were capable of the same intellectual achievements as men.

[00:04:43]Her family was um quite distinguished, a distinguished Parisian family, not aristocracy, but bourgeoisie. Her father was a silk merchant.

[00:04:51]Um she had two sisters. Um Then there's also François-Thomas Germain, who's a sort of famous silversmith who you might know from Beauty and the Beast. Um No, but uh seriously, he's Wikipedia claims it's her uncle, but it can't quite be that simple because they're born only like 5 months apart or something like this.

[00:05:12]But he sort of doesn't play a big role.

[00:05:14]He does appear in a character in Assassin's Creed. So, he is a So, but this revolution played a big role. Now, we're back in the first revolution.

[00:05:23]So, at the age of 13, the obituary says, Mademoiselle Germain was deeply struck by the revolution's extent from the very beginning she had predicted and towards which she her thoughts were continually drawn by the conversations held in her father's house. So, her father um was shortly before elected as a representative of the Third Estate. And you know, when King Louis XVI kicked out the Third Estate and they sort of they formed a Constitutional Assembly and then the Bastille was stormed, this is apparently when Sophie Germain became interested in mathematics. And you know, then there was the Women's March on Versailles, so it was a pretty wild time in Paris.

[00:06:04]And she felt that only intense and sustained occupation could divert her fears when chance placed before her eyes and before her eyes, chance placed a book called The History of Mathematics by Montucla. More precisely, apparently, she was very impressed by the story of the death of Archimedes, which is depicted here. So, Archimedes was, you know, this great geometer who allegedly died while doing mathematics because he told a Roman soldier during the sacking of Syracuse that he should not disturb his circles and then the soldier killed him.

[00:06:38]Um and apparently, this immense focus really impressed Sophie Germain. And at once the young Sophie was fixed upon a science whose very name she scarcely knew.

[00:06:50]So, apparently, this was met with resistance from her family. So, getting up at night in such cold that the ink often froze in her inkwell, working wrapped in blankets, and by the light of a lamp to force her to rest, her clothes, the fire, and the candles were taken from her room. So, this is a scene that really stays with you, this young Sophie wrapped up in blankets. And that scene has also inspired um artists to depict this scene. So, and apparently, during this time, she read two books. Um one of them, Bézout's Éléments d'arithmétique, and the other one, uh Cousin's Leçons de calcul différentiel et de calcul intégral, which she found in her father's library.

[00:07:32]So, apparently, it was a sort of educated Parisian family where you could find these books in the library.

[00:07:37]And at that time, she also taught herself Latin, we learn from Libri's obituary, um and started reading Newton.

[00:07:46]And then the revolution got really, really bad. La Terreur set in. And she was absorbed in these studies while the she lived through the Terror. So, you know, thousands of people in Paris were executed. Here we see the execution of Marie Antoinette and Olympe de Gouges, who was a female rights activist at the time.

[00:08:06]So, you know, the revolution did not sort of include women uh in the group of people who worked to get equal rights, as we will see in a moment again.

[00:08:15]What the revolution did during the Terror is to abolish all universities.

[00:08:20]So, they seized the endowments of colleges and universities. So, before the revolution, the old University of Paris operated in many ways like Oxford and Cambridge. So, it had faculties, colleges with endowments, and strong ties to the church. The National Convention ended all of this and founded um the École Polytechnique, which was meant to be this university with equal access for everyone. Students would receive a stipend, they were paid for to study.

[00:08:45]They were recruited on meritocratic uh principles, but again, it was a military school that completely excluded women. But apparently, during this time, Sophie managed to access uh notes from the École Polytechnique. And specifically from Lagrange.

[00:09:03]And under the name of a student of the École Polytechnique, she sent her observations to Lagrange, who apparently liked them very much. So, the student's name was LeBlanc. So, we don't know much about LeBlanc. LeBlanc um Well, he Here's a student card at the École Polytechnique. At the bottom, you can see that he was set to transfer to another prestigious école, but that school's records show that he had been admitted, but never matriculated because he died before he could attend.

[00:09:30]So, yeah, this person must have had a very short life.

[00:09:34]But Lagrange took an interest in Sophie and started supporting her. So, here's a letter that says it's sort of a proof of this where he tries to arrange a meeting with Sophie.

[00:09:45]So, after learning the true name of the author, he came to her home to express his astonishment and in the most flattering terms. So, this caused a stir in the Parisian math community. And not just Lagrange, but also other learned men wanted to be in touch with this young woman. So, she received encouragement from Cousin, whose book she read earlier. So, the appearance of a young geometer caused quite a stir, and Miss Germain soon saw scholars of superior merit come to her home. So, this is a letter from citizen Cousin.

[00:10:16]So, this would have been a very revolutionary way of referring to oneself, where he writes to Sophie's mother to arrange a meeting between them and offers his full support in her scientific career. So, we can see, you know, she was noticed and she received support once Lagrange had sort of recognized her.

[00:10:36]There was a difficult encounter with Lalande, who was a famous astronomer at the time, who wrote her a letter the day after they met saying, "It would have been difficult to make me feel more keenly to make me feel more keenly than you did yesterday the indiscretion of my visit and your disapproval of my intentions."

[00:10:56]He mentioned that you had read Laplace's Systeme du Monde, but that you had no desire to read my book.

[00:11:02]So, he wrote this book Astronomie des Dames, which was astronomy for women.

[00:11:08]Um But it's sort of a little bit more interesting than it appears in the first instance because this book also um acknowledged the contributions of the women who did his calculations. So, he ran a sort of observatory where a lot of the computations that were sort of done by women. So, um anyway, so this encounter did not go well and Sophie did not want to join him, and she in fact did not want to see him again. So, there's a note where later someone told her that she can come to some dinner because Lalande wasn't going to be present.

[00:11:41]Um Then Sophie picked up an interest in number theory.

[00:11:46]Um and she started reading Legendre's book Essai sur la théorie des nombres, which came out in 1798.

[00:11:54]And then and here it's becoming important again that she was acquainted with Latin, she started reading uh Gauss's Disquisitiones Arithmeticae in 1801 under the guidance probably of uh Lagrange.

[00:12:10]Um And then something quite special happened, namely that she was bold enough to do the following. So, after much research on the subject, she entered still under the assumed name of a former student. So, this was this LeBlanc chap, who was dead by now, of the École Polytechnique into correspondence with the author. The author being Gauss.

[00:12:29]Here's a picture of Gauss what he apparently looked like at the time.

[00:12:34]And let's just look at this letter right away because it's quite it's it's all these letters all preserved, so we can read them and it's quite amazing how quickly she gets to the point somehow. So, "Monsieur, your Disquisitiones have long been the object of my admiration and my studies. The last chapter of this book contains among other remarkable things the beautiful theorem expressed by the equation 4x to the n minus 1 over x minus 1 equals y squared plus minus n z squared." And then she goes on how she thinks she can generalize this from n a prime to n a prime power, odd prime I should say.

[00:13:11]So, then there follow pages of computation.

[00:13:16]And at some point she also writes that, "I've added to this letter several other considerations. The last concerns Fermat's celebrated equation x to the n plus y to the n equals z to the n." So, already in 1804 she was sort of aware and interested in Fermat's Last Theorem that we'll hear more about in later talks today.

[00:13:35]Um Gauss responds to this uh after a few months and says that, "I'm pleased that arithmetic has found a very capable friend. Above all, your new demonstration concerning the prime numbers for which two is a residue or non-residue pleased me exceedingly. It is very fine, although it seems isolated and incapable of application to other numbers."

[00:13:57]And Gauss valued this exchange. So, they exchanged more letters over the coming months and years.

[00:14:04]And the fact that he valued this we can see from a note that he sent to his good friend and colleague Olbers. So, he says, "I've been led by various circumstances, partly by letters from LeBlanc in Paris, who has studied my Disquisitiones Arithmeticae with true passion and has become completely familiar with it and has made some very nice communications about it to resume my beloved arithmetic investigations."

[00:14:26]So, this this exchange meant something to to Gauss. So, Olbers by the way is a fine astronomer in his own right, so there's a lot one could say about him, but let's not get distracted on this point.

[00:14:39]And then after a few letters history sort of breaks in again.

[00:14:43]Um so, Napoleon took the power in 1799, was crowned emperor in 1804 and then launched war against the various German states soon after.

[00:14:53]And this really mattered for Sophie's story because at some point during the Battle of Auerstadt the Duke of Brunswick, who was sort of Gauss's duke and Gauss's supporter, died. He didn't quite die in battle, he was just mortally wounded and died a few weeks later, but um back in the day, you know, dukes still fought in real battles and that didn't go well for him.

[00:15:18]Sophie at the time was very worried about Gauss, and we look sort of there's two historic sources which tell us this story. One of them is from Major Chandel to General Pernety.

[00:15:32]Um and the major tells this general, "Just after arriving in this city, the city being Brunswick, I asked several people for the residence of Monsieur Gauss, whom I see whom I went to see in order to inquire after his health on your behalf and that of Mademoiselle Sophie Germain.

[00:15:50]He replied that he had not had the honor of knowing either you or the young lady."

[00:15:55]Pernety forwards this letter the day before Christmas from the battlefield near Breslau to Sophie Germain.

[00:16:01]And he writes, "Mademoiselle, I hope this letter will satisfy your wishes concerning this worthy successor to Archimedes, who has been treated better than Archimedes, as you will see."

[00:16:11]So, Sophie was sufficiently highly connected that she could talk to generals um in Paris and she cared sufficiently much about Gauss that well, she wanted to make sure that he doesn't have that fate.

[00:16:27]Um Soon after she learned this, she writes to Gauss and makes a confession.

[00:16:32]She writes, "Monsieur Pernety informed me that he had made my name known to you.

[00:16:37]This circumstance leads me to confess that I'm not quite so completely unknown to you as you suppose. Rather, fearing the ridicule attached to the title of a learned woman, I borrowed the name of Monsieur LeBlanc in order to write to you.

[00:16:49]I hope that the singularity of what I confess today will not deprive me of the honor you granted me under a borrowed name and that you will devote a few moments to giving me news of yourself directly. Your very humble servant, Sophie Germain."

[00:17:05]And before then Gauss always took his time responding to her letters, but this time he responds immediately. And he says, "The keen interest you took in my fate during the disastrous war deserves my sincerest gratitude. Fortunately, the events and aftermath of the war have not affected me too closely so far, although I'm convinced they will have a great influence on the future course of my life." And this was going to become true.

[00:17:32]"A taste for the abstract sciences in general and especially for the mysteries of numbers is exceedingly rare. This is not surprising. The charms of this sublime science are revealed in all their beauty only to those who have the courage to study it deeply." And then comes maybe the most beautiful quote of all these letters of Gauss. So, he says, "But when a person of this sex, who by customs and prejudices must encounter infinitely more obstacles and difficulties than men in familiarizing themselves with these thorny problems, nevertheless knows how to overcome these obstacles and penetrate that which is most hidden, she undoubtedly has the noblest courage, extraordinary talents, and superior genius."

[00:18:12]And then, you know, after a little bit more time, he continues and gets back to mathematics. So, this is really Um he then gives a counterexample to something Sophie asserted, namely her claim that if the sum of the nth powers of two numbers is of the form a squared plus n f squared, then the sum of the numbers themselves has this form.

[00:18:32]So, he gives this very big example and this maybe shows you the nature of the exchange. You know, it was all these pleasantries and these things about the war and so on, but there were also pages and pages of mathematics, which are actually very very interesting to read.

[00:18:47]So, Sophie writes him again um showing more of her work and asking him questions and so it's trying to continue this exchange and Gauss responds just once more.

[00:18:57]Um so, this uh is the last letter that we have preserved of Gauss, where he says that he has changed residence in order to accept a post of professor at the University of Göttingen. "I shall say nothing to you of the circumstances that finally led me to take this step." So, Gauss, I think, lost lost funding because the sort of um you know, he was privately supported by this Duke of Brunswick and when he died that arrangement sort of wasn't there anymore, so he had to uh move to Göttingen.

[00:19:30]And then he makes a few more comments about mathematics and [snorts] then closes the letter as follows, "May you always be happy, my dear friend, as your rare qualities of mind and heart deserve and continue from time to time to renew for me the sweet assurance that I may count myself among the number of your friends, a title of which I shall always be proud."

[00:19:51]So, this is the last letter that we have preserved of the two. Now, it's not the last time they had an exchange indirectly.

[00:20:00]Um so, soon after let me just say this little episode.

[00:20:03]So, Gauss's first wife uh died pretty early and so, he was left there with children. So, he remarried and he asked a friend that he had in Paris to ask Sophie Germain to help him pick out a pendulum clock as a present for his new wife. So, they they clearly had some exchange that was still going on. Later, he asked his students who visited Paris to give Sophie Germain his latest books.

[00:20:28]So, he still counted her amongst his friends, but this whole exchange of letter from his side had come to an end.

[00:20:33]So, she kept writing to him, but we don't have any responses recorded.

[00:20:38]But, at the same time something completely different happens. So, Ernst Chladni, who was a German scientist, came to visit Paris and he showed uh Napoleon that when you take a metal plate and you sprinkle sand on it and you make it vibrate with a violin bow, then interesting patterns emerge.

[00:20:57]And so, this we'll actually see later today.

[00:21:00]And so, he had written a whole book where he wrote hundreds of these patterns and you know, tried to classify them, but the mathematics behind this was not understood. And Napoleon, who was himself very keen supporter of mathematics, was so impressed by this that he urged the Academy of Sciences to um create a special prize for the person who would explain this phenomenon. So, this on the right is the first prize announcement. Um competition opened on the 13th of March, 1809 and it closed in 1811. So, let's just hear Sophie herself on what she had to say on this topic.

[00:21:40]So, she said as soon as Mr. Chladni uh Monsieur Chladni uh his first experiments became known to me, it seemed to me that analysis could determine the laws to which they are subject. But, I had occasion to learn from a great geometer, so this is Lagrange in this case, her mentor, that this question contained difficulties that I had not even suspected. I stopped thinking about it. So, you she was interested, she thought she could do something, but a great person told her that it's probably too difficult.

[00:22:09]Um at the time of Monsieur Chladni's stay in Paris, the sight of his experiments again aroused my curiosity. I studied Euler's memoir on the linear case, certainly not with the intention of competing for the extraordinary prize.

[00:22:25]And then she continues, in the linear case, elastic forces are supposed to be proportional to the inverse ratio of the radius of curvature.

[00:22:33]The hypothesis that instead of the inverse ratio of the radius of curvatures of a simple curve, one takes the sum of the inverse ratios of the radii of the two principal curvatures of a surface, struck me by its analogy and its simplicity. So, here she has the right idea. And neither my sense of inadequacy nor the lack of practice in calculation, nor the little time remaining before the competition could prevent me from submitting to the Institute a memoir in which I proposed the hypothesis I had imagined. Even then, I felt how worthy of attention the hypothesis was and I was most eager to submit it to the judgment of the Academy.

[00:23:13]So, you know, she was bold, she submitted her hypothesis and it went wrong. So, Legendre, who was by that time her good friend, I think, um and a member of the jury, uh told her that he had not good news, that it has been found that your principal equation is not exact, even if one admits this hypothesis that elasticity can be expressed by 1 / R + 1 / R prime.

[00:23:38]Monsieur Lagrange It's a bit confusing because there's Legendre and Lagrange and they sort of sound the same, but Lagrange is the old one, Legendre is the young one.

[00:23:48]So, Monsieur de Lagrange, and he's also the Italian one, actually, even though the name doesn't reveal it, has found that under the hypothesis, the true equation ought to be of this form.

[00:24:00]So, Lagrange, who was stuck on this problem before, understands Sophie's hypothesis and then suggests this equation.

[00:24:08]So, this was all communication about the supposedly anonymous evaluation process.

[00:24:13]And then he continues, I nevertheless do justice to efforts that are praiseworthy in themselves, even though they have not had the outcome I would have wished. But, that is all the more reason to preserve your anonymity and I promise on my side to keep the most profound silence.

[00:24:29]I imagine that the same question will be proposed again with a new deadline. So, all hope is not lost.

[00:24:36]And then so, that is indeed what happens. The Academy finds that there's the only submission, so hers was the only submission, it wasn't good enough.

[00:24:47]So, they reopened the contest.

[00:24:49]And then she submits again and her submission, well, it's anonymous, but she starts with that quote in her submission by Francis Bacon. So, by far the greatest obstacle to the progress of science, to the launching of new projects and the opening of new fields of inquiry, is that men despair and think things impossible.

[00:25:08]So, this is what Sophie Germain starts her second submission with.

[00:25:13]And her second attempt receives an honorable mention this time because the Academy finds that while the equations and the proof of the equation is still incomplete and defective, they it is quite good at proposing well, it aligns with observation.

[00:25:31]So, this happens shortly before the end of the year in 1813.

[00:25:36]And then Poisson, who you might have heard of, pulls an interesting stunt.

[00:25:39]So, Poisson was sort of on the jury of the second submission.

[00:25:43]And so, the following is from the minutes of the Parisian Academy. These minutes, by the way, are great. They sort of are exactly like minutes of similar meetings that happen nowadays. Well, maybe nowadays it's less exciting because this is kind of interesting. So, Monsieur Poisson requests permission to read a memoir on the mathematical theory of elastic surfaces. And then Legendre, who's, remember, Sophie's friend, proposes that the section should not hear any memoir on a question set for prize competition before the prize for that competition has been awarded.

[00:26:14]And then Monsieur Poisson declares that the memoir he is about to read is not of the kind that would prevent the competition prize from being awarded and continues reading it anyway.

[00:26:25]And then Legendre's proposal is referred to a commission that is meant to be formed in the next meeting.

[00:26:32]And then the next meeting never forms this special commission, so that sort of doesn't really happen. But anyway, Poisson, using the knowledge that he acquired as a uh judge, um you know, started working on the problem and makes this very, I think, improper move that was called out by Legendre.

[00:26:51]So, then so, the prize was reopened again and um Germain this time submits again and she in fact wins. So, this is an invitation, an official invitation, two days before the ceremony when the permanent secretary of the Parisian Academy sends her two tickets and he says, "Here are two tickets and if you need more for your friends, you can ask for more."

[00:27:14]And this is a quite interesting point. So, Sophie had a hard time accessing the Parisian Academy of Science because she was outranked not just by the members, but also by the members' wives. So, there are sort of these exchanges when someone has to say, "Oh, you know, my wife probably won't come to so, you can have her ticket." Um so, it was quite difficult for her to, you know, connect with other mathematicians at the time and she always had to arrange private meetings rather than going to the usual meeting spaces.

[00:27:43]Um the public session happened on the 8th of January. It was apparently very well attended in this very nice building, but she didn't come as I said in the beginning. And one can speculate why she didn't come.

[00:27:58]Some think it's because of this ticket thing, that she was not given enough tickets, but what seems more likely is that she was very upset with Poisson because Poisson sort of, I think, at the time spread the news that actually it wasn't all that good and you know, it wasn't all that complete yet and even though she'd won the prize, she there was a lot of negativity around it.

[00:28:18]And this sort of continued in the years afterwards.

[00:28:22]On the left, we see her first publication on this topic, which was in fact self-published.

[00:28:27]In response to it, she received the following letter from Legendre, where he said, "You offer your opinion in the most modest manner and if there were anything to reproach you for, it would be the compliments with which you somewhat overwhelm the geometer whose opinion you are contesting. This is Poisson.

[00:28:45]May he respond worthily to this assault of civility, that is more a desire than a hope."

[00:28:53]So, yeah, this is her first ever publication. She self-published more.

[00:28:58]Later, she also published regularly in Crelle's Journal, Journal für die reine und angewandte Mathematik, that's still around today.

[00:29:07]On the So, yeah, this is the first sort of the resonance part of this special day.

[00:29:13]So, later we'll see like a demonstration of these Chladni figures and hear more about the mathematics behind behind this by Laura Munoz.

[00:29:20]And but once this sort of prize has happened, the next prize that the Paris Academy proposes is for the solution of Fermat's Last Theorem.

[00:29:33]Um so, you know, problems weren't easy, somehow.

[00:29:37]And so, Sophie picks up her work on Fermat's Last Theorem again and sends Gauss, after a long silence, I think about 10 years, a long long letter where she sort of sets out her grand plan.

[00:29:52]And she says, "I never cease thinking about number theory.

[00:29:55]I can give you some idea of how preoccupied I am with this kind of research by confessing that even without any hope of success, I preferred to other work which is sure to yield yield results when I think about it."

[00:30:09]So, this I think was maybe her true passion and so she started working on this again.

[00:30:16]And later we will hear from Anna Galiani and James Maynard about Fermat's Last Theorem in general and about Sophie's work on this in particular.

[00:30:25]So, she continues to write long before our academy proposed a prize for the demonstration of the impossibility of Fermat's equation, this kind of challenge to modern theories posed by a geometer deprived of the resources we possess today, often preoccupied me.

[00:30:42]And then she starts with here's what I found and she starts setting out her her grand vision of how Fermat's Last Theorem could be proven.

[00:30:50]Her work on Fermat's Last Theorem received attention and was in fact mentioned in a footnote in a book by Legendre where he writes, "This proof, which one will undoubtedly find very ingenious, is due to Mademoiselle Sophie Germain."

[00:31:04]Legendre's footnote in fact refers to case one of Fermat's Last Theorem. So, x to the p + y to the p does not equal z to the p where p is a prime number which does not divide x * y * z. And using Sophie Germain's method, one can sort of show this for primes less than 100. She also did a method is sort of more interesting than this once you read the letter, but this footnote maybe didn't do full justice to this and I think for the longest time this footnote was all that was sort of remembered. Um Then Sophie's life uh came to an end um in 1831. So, she wrote two letters to Libri who, remember, was the person who wrote her obituary and was I think a good friend of hers.

[00:31:52]So, the first of these two letters is quite interesting for historic reasons because she says that student Galois, who is in spite of his impertinence, displays a good disposition, has managed to be expelled expelled from the École Normale for being too politically active and saying negative things about the director.

[00:32:11]He's without fortune and his mother is very has very little.

[00:32:14]The woman has left her house leaving him enough to live in a mediocre way and has been forced to place herself as a lady-in-waiting. One hears that he is becoming totally insane and I believe it.

[00:32:26]So, she was connected to the young rising talent in Paris, obviously.

[00:32:32]Um But the if you look at the letter, you can already see that um it's written slightly differently from the ones before. So, I think she was really very unwell at this time. So, the next letter says, "I'm also very ill. I made a great effort during your stay here not to close my door to you, but my condition has worsened considerably since then. I'm in the grip of horrible suffering. My life is a true torment."

[00:32:56]So, a few weeks later after the second letter, she died of uh breast cancer.

[00:33:02]And the obituary by Libri continues and says, "She has also displayed this noble character in her actions always marked by virtue which she loved. She said like a geometric truth.

[00:33:14]For she added, she could not conceive that one could love ideas of order in one way without loving them in another.

[00:33:21]And the ideas of justice and virtue were in her eyes ideas of order that the mind should adopt even when the heart was not inclined to cherish them."

[00:33:30]So, Sophie Germain also has worked in philosophy and even the theory of music, which is sort of outside of today's uh meeting.

[00:33:42]Um but she was had many interests that that I think are maybe worth exploring with more time.

[00:33:51]And the last slide I want to show you um is a letter that comes back to Gauss. So, this is a letter from Weierstrass to Fuchs um where Weierstrass says, "When the honorary doctorates were being conferred at the last jubilee of the celebration at the University of Göttingen, Gauss regretted nothing more than the fact that Sophie Germain was no longer alive."

[00:34:18]And then so this is the first bit, but then the second bit is maybe even more interesting.

[00:34:26]Um she had proven to the world that a woman too was capable of achieving something worthwhile in the most rigorous and abstract of the sciences and therefore would have been rich would have richly deserved an honorary diploma.

[00:34:37]Following this, I had no qualms about encouraging Miss von Kovalevsky to apply to your faculty for doctorate. So, Kovalevsky, for those who know, was the first female uh math professor in the world at the University of Stockholm.

[00:34:51]And I think this sort of letter shows that already back then Sophie Germain's story served as an inspiration and the sort of proof that um you know, this could be achieved.

[00:35:04]So, this was um all for my talk and now I'm looking forward to take a brief break uh take questions before and then we'll have Anna.

[00:35:16]>> [applause]