Hello everyone, we have another birthday edition of our Saturday Classics. Today it is Emmy Nurture, who was a groundbreaking mathematician and was born March two. We hope you enjoy her mathematical world. Welcome to Stuff you Missed in History Class from how Stuff Works dot com. Hello, and welcome to the podcast. I'm CALLI Frying. I'm Tracy B. Wilson, and today we're going to talk about a subject that was directly inspired by a listener mail. And we're going to talk in some detail about that listener mail at the end, but just know that it did and we'll credit the person when we get to the end, because it's pretty spectacular. We're gonna talk about a really important lady mathematician and her the pronunciation of her name is a matter of some debate here at the office and online. Uh so it's Emily Nurture. You will sometimes also hear it pronounced more like nuture. Well, and then when I looked it up at four vough, the one German speaker pronounced it more like yeah, and I was like, we can't say it that way. That's not gonna work. So I think we decided we're going to hover right around Nurture that with all our possible respects to Emmy, and I hope we do not offend her ghosts should it exist, or German speakers, or German speakers, or people who love math and love her as a figure. So we're just going to jump right into talking about her. Emmy was born Emily Emmy Nurture on March two in Erlangen, Germany, and her father, Max Nurture, was a mathematician. Her mother, Ida Amalia Kaufman, was from a very well to do family, and after Emmy was born, Max and Ida had three sons, although two of them died when they were very young, only Emmy's brother, Fritz, survived to adulthood. And as a young child, by most accounts, Emmy did not really stand out as a specially gifted. She was a bright child, but nobody was like, this is the future of mathematics. She attended the State Girls School in Erlangen from ninety seven, studying the basics of school curriculum, and she also took piano lessons, and she learned to speak French and English, and as she grew into her teen years, she loved dancing and she was known as a very friendly, clever girl. When she was eighteen, she was certified to teach both French and English, and the series of exams that she had to go through to get this certification was pretty strenuous that it took four days for her to do this. But instead of settling into a career teaching in girls schools, she decided that she would go to university and study mathematics. And this was a pretty big jump to suddenly make. And we don't know why Emmy had this sudden shift in interests. Her life up to this point had seemed to follow a pretty standard course for a young woman in that period of time in Germany from an intellectual, middle class family. You know, she would potentially get married, but if not, she had this cup job as a teacher. And none of her personal writing from this time has survived to offer us any clues why she suddenly decided that what she really wanted was to pursue a mathematics career. Yeah, we do know that it wasn't a completely foreign subject to her. Her brother Fritz was studying mathematics at the time, and her father also entertained other mathematicians in their home from time to time. So she had been around the subject of math her whole life. So while it does seem like quite a shift to go from teaching French and English to studying math, it wasn't something that was completely new to her. And just the same though, this desire to take university courses was incredibly ambitious. So the schooling that girls received at this time in Germany was vastly different from the way that the boys were educated. The goal for a girls school was to turn out proper young ladies or trade workers, depending on the young woman's family background, and they just simply did not receive the kind of educational groundwork that would make a transition to university studies a natural step. Regardless of exactly how it was that she arrived at this decision, Emmy went to the University of our Langen to continue her education. But because she was a woman and it was she couldn't just enroll in classes. She had to get special permission from every instructor of every class, and then she couldn't actually enroll as a regular student. She could only audit the class. She had to once again get special permission to actually take the exams from the instructors. Yeah, so she uh really had to jump through every imaginable hoop just to get this math education that she had decided she wanted. Um. In July three, Emmy took the enrollment exam for the university at the Royal Gymnasium in Nuremberg and she passed, basically, proving at that point that she was even with male classmates despite having missed their educational background. After the exam, in the summer and he started auditing advanced mathematics courses at the University of Linen, and that started in the winter of nineteen oh three oh four. During these winter courses, she learned from teachers who would make incredible contributions in the world of mathematics. Herman Minkowski, for example, developed the geometry of numbers. He contributed to number theory, and he worked on relativity, influencing his famous student Albert Einstein. David Hilbert, another of her instructors, set the foundations for functional analysis. Felix Klein influenced the development of mathematics is it related to representing the properties of space and spatial relations through geometry. So she was learning from serious heavy hitters. But in nineteen o four she went back to the University of Erlangen because the school had started actually accepting women as for real legitimate students. On October nineteen o four, she was officially enrolled as student number four eighties six, and she was the only woman student in a field of forty seven. Emmy's mentor during this time was Paul Gordon, who was a friend of her father's as well as an influential mathematician in his own right, and Emmy had known him since she was just a child. He was very close with her family and he has often described as sort of a second father figure to her. He was, however, in terms of personality, a stark contrast to her father. Max Air Nurture was gentle and warm. He was passionate about his work, but he is always described as sort of having this overlying sense of calm about him. Gordon, who was nicknamed the King of invariant Theory, was unlike Max, a more dramatic figure. He was impulsive, He was expressive in very unbridled ways. He was given to wild gesticulation while he was talking, which I can identify with. Emmy was the only doctorate student that that he ever mentored, and she was really devoted to him. She kept a photo of him on her wall for the rest of her life. And it's interesting when people describe Emmy's behavior, she is sometimes described as having traits that are in some ways more similar to Paul Gordon than her father, like she too was given to serious gesticulation and kind of would make messes and be very dramatic and very excited and so passionate that she would kind of lose herself. But she received her PhD in mathematics from Erlangen after several years as Gordon's protege, and her thesis was a dissertation on algebraic invariance, which she successfully defended on December thirteenth of nineteen o seven. She was given her degree sumakun lauda on July two of the following year. This timing is really significant because co ed classes were not a thing in Germany until nineteen o eight, the year after she successfully defended her thesis. Any woman who had gone through the education system prior to that had, like Emmy, had to get special permission and was not granted equal students status. Yeah, just for clarity, we mentioned that she returned to Erlangen because they were doing it, but in terms of Germany wide, women were still not considered equal until that year after she defended her thesis, and in nineteen o eight, Emmy attended the International Mathematical Congress in Rome, Italy, and she attended that along with her father. She was at this point still a young woman and relatively unknown, despite sort of making this name for herself as an unusual figure being a woman in a very male dominated field, so it seems that during this particular conference she really kept a fairly low profile. After Ms Nurture received her PhD, she continued her research work at their Lingen, although she wasn't paid for any of this work. She assisted her father in his research and then she was invited in nineteen o eight to join the Cholo Mathematico in Italy and then in nineteen o nine the German Mathematical Union. Emmy's first sort of professional lecture was in nineteen o nine at the Salzburg meeting of the German Mathematical Union. She lectured at the Vienna chapter of the group several years later in nineteen thirteen, and not long after that she also started guest lecturing for her father as a substitute and during this same period. Although as we said, we don't have writings from her, so we don't really know how this impacted her, but surely it did. Emmy's mentor, Paul Gordan, died in nineteen twelve, so just as her career was taking off. So next up we're going to talk about a significant move in Emmy's life. But before that, let's have a word from one of our awesome sponsors, who keep the lights on here in our studio. That sounds grand. So after eight years of post pH d work at er Langen, her former teachers David Hilbert and Felix Klein asked her to come back to gutting In in nineteen fifteen. And this was right after Albert Einstein had published his Theory of General Relativity and Klein and Hilbert wanted Nurture to work with them on unraveling the mathematics that were involved in Einstein's work. And Nurture had published several papers of her own by this time, and she had really exhibited some insightful approaches to mathematical concepts, so she was the perfect candidate to assist in Hilbert Incline's work. She went to Goettingen, but this move turned out to be extremely controversial. Many faculty members objected to the idea of a woman on the teaching staff. If Emmy notre couldn't be granted faculty status, Hilbert and Kline wanted Hurt to at least have what's called a privat descent, which is a position similar to a post doc. It would have given Emmy at least an officially recognized post within the Good Educational system, would also grant her sufficient title and permission to teach for nurtures thesis to be accepted, and for her to be granted this privat, the entire philosophy faculty had to vote on it. And this umbrella of philosophy, keep in mind, included not only philosophy, but also history, natural sciences, and mathematics. And it turned out that the math people there were pretty cool with Emmy, but the non mathematics people in the mix, we're really vehemently arguing against having a woman teach students. The arguments against Nurture were that giving her a provactance and position would mean that she was on track to be faculty and what would the returning soldiers think when they came back to war to find that they're supposed to take classes from a woman. Yeah, they really framed it like what a slap in the face that would be these young men who had gone to defend the ideals of Germany and they then come back and find a lady teacher. Well yeah, and keep in mind, this wasn't even soldiers saying this. This was kind of the weird trumped up argument that the non mathematics faculty was trying to put together to keep Eman Nurture off of their cool kids club. And her mentor and now colleague Hilbert's response was, gentlemen, I do not see that the sex of the candidate is an argument against her admission as a privatdot sent After all, the sent it is not a bath house, and he meant like the educational Senate, not their uh government Senate. And his argument, though, didn't sway the detractors, and Emmy was not granted this title. Hilbert and Klein had to convince Nurta to stay for obvious reasons, but she couldn't lecture under her own name, so they had to come up with a sneaky kind of work around. The lectures were listed under Hilbert's name, but Nurture was the one who actually delivered them. Yeah, she worked under his name for quite some time. Um in eighteen. However, she has been doing this sort of sneaky workaround plan for several years. At this point, she had developed at through her work with Hilbert Kleine Nurture's theorem, which deals with the relation between what are known as the symmetries of a physical system and its conservation laws. So among the revelations of this theorem is the linkage between time and energy, directly related to the idea of conservation of energy, so that in case you do not remember, is that energy can neither be created nor destroyed, but merely changes form. And this is incredibly significant stuff. I mean, this is really a huge part of physics as we know it, right. It's an incredibly important concept at theoretical physics, and her peers at the time recognized its significance, so much so that the following year, Emmy not Are was finally officially recognized as an academic lecture with the privit zodes and title that we've been talking about for so long she had to lecture without. She no longer had to lecture under a male mentor's name, and this was obviously incredibly significant, but uh, it's not maybe the huge win that we would all be hoping for, because, just to be clear, at this point, emmy noture was in her thirties, she had published numerous influential and important papers, and she was working with the best mathematicians at the time as a respected peer of theirs on the mathematics of relativity. And despite all of that, she had up to this official um you know, kind of track to be in a faculty position. She had zero stability or safety in her career. But even though she now had a title but made it okay for her to lecture as herself, her position did not actually come with any pay. She would not get any pay as a lecture until nineteen three, four years after she was made of private dotes in. Yeah, we don't know exactly where the money was coming that supported her. Uh, this is one of those kind of wiggily fuzzy points. Presumably she was getting some from like a family fund and possibly sort of private grants from other mathematicians, but we don't really knew. In she collaborated with colleague Werner Schmidler to write concerning moduli in non commutative fields, particularly in differential and difference terms, and this publication really established, like without question, Nurture as a mathematician at the very top of her field. While the start of World War One kept her from traveling to speak at gatherings of mathematicians, starting in nineteen twenty she was often on the road lecturing throughout Germany, and from ninety and nineteen twenty six Nurture's work focused on what's called the general theory of ideals, no more commonly in modern times as commutative algebra. Her work during this time united a lot of different mathematical concepts, but this was in terms of her personal life a period of ups and downs for Emmy. In one, for example, her father died, so at this point she was left without both of her father figure mentors in mathematics, and in the middle of all that work, as we said, she was given a lecture ship specifically in algebra in ninety three. Just two years later, and he's first student to complete a doctorate under her mentorship received her PhD. Emmy had mentored another woman, Greta Herman, through her thesis process and Herman finished her doctorate in February nine, twenty five. Around nineteen twenty four, while she was working with Greta Herman and lecturing and doing her research, Nurture was at the center of this sort of interesting walking and talking phenomenon on campus. Students and scholars alike would take long walks with Emmy around the school of grounds, talking about what else mathematics and math theory, and this informal group, which came to be known as Nurtures Boys, included Russian scholar Pavel Alexandrov, who was a visiting professor from the University of Moscow. Nutter and Alexandrov became friends, and she was eventually invited to Moscow as a guest lecturer in the nine academic year. This was not the only international recognitions she was receiving during this time, though. She also delivered a paper at the International Mathematical Congress in Bologna, Italy that was in nine and then a few years later in nineteen thirty two, she addressed the same group in Zurich. In nine seven, nursers focus shifted almost exclusively to noncommutative algebras, and these are algebras where the order in which the numbers are multiplied affects the outcome and nur There's work in this area yielded a theory that enabled a conceptual unification of all of them, and during her work in this phase of her career, she collaborated with Helmet Hass and Richard Brauer and published papers hyper Complex Number Systems and their Representation in nine and non Commutative Algebra in nineteen thirty three. From nineteen thirty to nineteen thirty three she also worked as an editor on the German Mathematical Annual. Throughout all of her research, writing and editing, she was also still teaching regularly, but even so she was still employed at a level far below what her colleagues thought she deserves. Yeah, even as male mathematicians were rising up through the ranks in the Gutting gutting in educational system at a rate that really easily outpaced Emmy, they were so hugely influenced by her work that many of them tried to point out how wrong this was and tried to petition for an improved title on her behalf. It generally came to not with the greater university system, but in terms of the mathematics world. She was regarded not just as a peer, but as a leader. At this point, n three would prove to be a pivotal year for Nurture, and we're going to talk about it after we paused to chat about one of our awesome sponsors who keep our show going. In ninety three, Germany changed, obviously pretty significantly when the Nazi Party came into power. Emmy Nurture, who was Jewish, lost her job, as did many of her colleagues. The Nazi Party had actually passed a number of laws that were intended to keep Jews out of civil service jobs, and that included academics. For a while, Emmy gave informal lectures at her home, and she certainly had students who were eager to continue learning from her. She was apparently not even bothered when a student or two showed up in their Nazi uniforms. She just wanted to talk about math. Meanwhile, her friend Pablo Alexandrov was working to get the University of Moscow to appoint her to a position, and his efforts were really passionate, but they were getting slow response, and finally Emmy just had to make a decision about her future. As tensions mounted in Germany, she left Germany in October to move to the United States. She'd been offered a one year guest professor spot at brent Mark College. Unbeknownst to Nurture, when she accepted the offer, the school was also setting up a graduate fellowship in her name for the academic year she would be teaching there. She also lectured and worked on her math research in Princeton, New Jersey, at the Institute for Advanced Study, and while interest in her lectures was initially slow to catch on, eventually Emmy did get a following of students, and she sort of found this mirror group to the Nurture Boys of gut In, but this group was called the Nurture Girls, and they would go on hikes on Saturdays all the while, just as she had in Germany, discussing mathematical concepts. Her one year invitation to teach at bren Mar was extended the following academic year of nineteen thirty five, but before it started, she went back to Germany to visit her brother Fritz and his family before they moved to Siberia for a teaching position there. Like Emmy, Fritz lost his job at the Institute of Technology under the Nazi government. Emmy also visited her old campus and her friends at gutting In, but she soon headed back to Pennsylvania for another year at Bryn Mar and during her second year there she mentored her first American PhD candidate, a young woman named Ruth Halfer. The life of Emmy Nore ends rather abruptly. In the spring of nineteen thirty five. She went into the hospital to have an ovarian sister moved, and while she seemed to be recovering well initially, she died quite suddenly on April fourteenth, four days after her surgery. Just a weeks later, on May third, of the New York Times ran a letter that was written by Albert Einstein about Emmy Nutter, and he wrote, within the past few days, a distinguished mathematician, professor I mean Notre, formerly connected with the University of Guttingen and for the past two years at Renmark College, died in her fifty third year, and the judgment of the most competent living mathematicians, Fraeulein Notre was the most significant creative mathematical genius thus bar produced since the higher education of women began in the realm of algebra, in which the most gifted mathematicians have been busy for centuries. She discovered methods which have proved of enormous importance in the development of the present day younger generation of mathematicians. And now while we have reached the point in emmy story where she has departed this earthly plane, there's a little bit more to talk about in terms of her politics. And the reason that we're putting that this at the end is because the primary infra nation we have about it isn't from things that came up in her actual lifetime or again her writings, which we don't have. It's stuff that came up in eulogies and memorials from colleagues after her death, specifically two of them. In nineteen nineteen, Nature joined the independent Social Democrats group and getting in and to some the group was considered an extremely radical Bolshevik group. It was a splinter group that broke away from the Social Democratic Party in nineteen fourteen as a centrist group between the Social Democratic Party and the Communist Party of Germany. But two of her close friends and fellow mathematicians interpret her politics very differently. When they spoke about her life. First Herman Wile while worked in analysis, number theory, foundational mathematics and quantum mechanics, among other areas, and he met Nature in gutting In in nineteen thirteen, and they remained quite close throughout the rest of Emmy's life. And when while spoke of Emmy's political stance, it was very much in the vein that she was a pacifist and she definitely was, we know that with great hopes for Germany's future, and that really she saw the independent Social Democrats as the next stage of the Social Democrats, not as a radical shift, but as a gradual evolution. And he also wrote of Emmy that quote, without being actually in party life, she participated intensely in the discussion of the social and political problems of the day. On the other hand, Pavel Alexandrov characterized Emmy as very pro Soviet. He said that quote, she always had a lively interest in politics and hated war and chauvinism in all its forms, and with her whole being, her sympathies were always unwaveringly with the Soviet Union. So it seems based on the fact that Alexandrov was working to get Emmy a position in Moscow in nineteen thirty three, that she was comfortable with the idea of living in the Soviet Union, and the Bolshevik Revolution took place while she was working in academia, so it's really unlikely that she was blind or ignorant to the political events that were playing out around her. But since both of these men likely saw Emmy's political stance through their own lenses and in the way they wished to see her, and since we do not have any of her own writing on the subject to reference, we really don't know where she truly stood. What's really indisputable as that I mean notre was a major figure in mathematics, both in her time and today, as many others have built upon her work, and she seems simply unflappable in the face of the difficulties she faced as she made a name for herself in a field that had very few women in it. And so I wanted to end with a quote from her friend Pavel Alexandrov, because it describes Emmy in such a way that I think anybody would want to know her. It says, quote her great sense of humor, which made social gatherings in personal contacts with her so pleasant enabled her to counter the injustices and absurdities that beset her academic career easily and without anger. In such circumstances, instead of being offended, she would simply laugh. But she was very offended indeed, in protested sharply when even the smallest injustice was directed at one of her students. I love that quote. Um, there's really no substantiation in any way, but there are. It will come up as theory sometimes that she was connected romantically to either While or Alexandrov, although we don't know, and none of them, none of their letters ever hinted any of that, so we just have no idea. But we do know that she was very close with both of those men. So I love that that sort of lovely description of her. Yeah. Um, And now we'll get to the listener mail and inspired this whole thing. And this is from our listener, Mark, who is amazing, and he writes, Hi, Holly and Tracy, I enjoyed listening to your podcast, and I thought you might like a laser engraving of one of my favorite mathematicians, Emmy Nurture. I did the engraving on one millimeter aircraft Plywood, hoping that would make it a little more unique. I listened to your podcast when I'm on the road or in the lab a guitar lab. Really keep up your great work. And Mark sent us this absolutely beautiful engraving of Emmy and I just was so struck by it that we had to do an episode. Yeah, and we're going to post a picture of it. It's great and it's uh So we've talked about how I don't normally work in the same office as Holly anymore, and so Holly will send me pictures of the things that come into the office and are amazing. And that was whe where I kept zooming in on my phone usually text Gorget like WHOA, what's happening. It's really it's very beautiful. I love it. Mark, thank you so much. That was so thoughtful and cool, and I appreciate that you took time to make us a really famulous gift. We're very, very lucky. Thank you so much for joining us on this Saturday. If you have heard an email address or a Facebook you are l or something similar over the course of today's episode. Since it is from the archive, that might be out of date Now. You can email us at History podcast at how stuff works dot com, and you can find us all over social media at missed in History. And you can subscribe to our show on Apple podcasts, Google podcasts, the I Heart Radio app, and wherever else you listen to podcasts. For more on this and thousands of other topics, visit how staff works dot com

Hello everyone, we have another birthday edition of our Saturday Classics. Today it is Emmy Nurture, who was a groundbreaking mathematician and was born March two. We hope you enjoy her mathematical world. Welcome to Stuff you Missed in History Class from how Stuff Works dot com. Hello, and welcome to the podcast. I'm CALLI Frying. I'm Tracy B. Wilson, and today we're going to talk about a subject that was directly inspired by a listener mail. And we're going to talk in some detail about that listener mail at the end, but just know that it did and we'll credit the person when we get to the end, because it's pretty spectacular. We're gonna talk about a really important lady mathematician and her the pronunciation of her name is a matter of some debate here at the office and online. Uh so it's Emily Nurture. You will sometimes also hear it pronounced more like nuture. Well, and then when I looked it up at four vough, the one German speaker pronounced it more like yeah, and I was like, we can't say it that way. That's not gonna work. So I think we decided we're going to hover right around Nurture that with all our possible respects to Emmy, and I hope we do not offend her ghosts should it exist, or German speakers, or German speakers, or people who love math and love her as a figure. So we're just going to jump right into talking about her. Emmy was born Emily Emmy Nurture on March two in Erlangen, Germany, and her father, Max Nurture, was a mathematician. Her mother, Ida Amalia Kaufman, was from a very well to do family, and after Emmy was born, Max and Ida had three sons, although two of them died when they were very young, only Emmy's brother, Fritz, survived to adulthood. And as a young child, by most accounts, Emmy did not really stand out as a specially gifted. She was a bright child, but nobody was like, this is the future of mathematics. She attended the State Girls School in Erlangen from ninety seven, studying the basics of school curriculum, and she also took piano lessons, and she learned to speak French and English, and as she grew into her teen years, she loved dancing and she was known as a very friendly, clever girl. When she was eighteen, she was certified to teach both French and English, and the series of exams that she had to go through to get this certification was pretty strenuous that it took four days for her to do this. But instead of settling into a career teaching in girls schools, she decided that she would go to university and study mathematics. And this was a pretty big jump to suddenly make. And we don't know why Emmy had this sudden shift in interests. Her life up to this point had seemed to follow a pretty standard course for a young woman in that period of time in Germany from an intellectual, middle class family. You know, she would potentially get married, but if not, she had this cup job as a teacher. And none of her personal writing from this time has survived to offer us any clues why she suddenly decided that what she really wanted was to pursue a mathematics career. Yeah, we do know that it wasn't a completely foreign subject to her. Her brother Fritz was studying mathematics at the time, and her father also entertained other mathematicians in their home from time to time. So she had been around the subject of math her whole life. So while it does seem like quite a shift to go from teaching French and English to studying math, it wasn't something that was completely new to her. And just the same though, this desire to take university courses was incredibly ambitious. So the schooling that girls received at this time in Germany was vastly different from the way that the boys were educated. The goal for a girls school was to turn out proper young ladies or trade workers, depending on the young woman's family background, and they just simply did not receive the kind of educational groundwork that would make a transition to university studies a natural step. Regardless of exactly how it was that she arrived at this decision, Emmy went to the University of our Langen to continue her education. But because she was a woman and it was she couldn't just enroll in classes. She had to get special permission from every instructor of every class, and then she couldn't actually enroll as a regular student. She could only audit the class. She had to once again get special permission to actually take the exams from the instructors. Yeah, so she uh really had to jump through every imaginable hoop just to get this math education that she had decided she wanted. Um. In July three, Emmy took the enrollment exam for the university at the Royal Gymnasium in Nuremberg and she passed, basically, proving at that point that she was even with male classmates despite having missed their educational background. After the exam, in the summer and he started auditing advanced mathematics courses at the University of Linen, and that started in the winter of nineteen oh three oh four. During these winter courses, she learned from teachers who would make incredible contributions in the world of mathematics. Herman Minkowski, for example, developed the geometry of numbers. He contributed to number theory, and he worked on relativity, influencing his famous student Albert Einstein. David Hilbert, another of her instructors, set the foundations for functional analysis. Felix Klein influenced the development of mathematics is it related to representing the properties of space and spatial relations through geometry. So she was learning from serious heavy hitters. But in nineteen o four she went back to the University of Erlangen because the school had started actually accepting women as for real legitimate students. On October nineteen o four, she was officially enrolled as student number four eighties six, and she was the only woman student in a field of forty seven. Emmy's mentor during this time was Paul Gordon, who was a friend of her father's as well as an influential mathematician in his own right, and Emmy had known him since she was just a child. He was very close with her family and he has often described as sort of a second father figure to her. He was, however, in terms of personality, a stark contrast to her father. Max Air Nurture was gentle and warm. He was passionate about his work, but he is always described as sort of having this overlying sense of calm about him. Gordon, who was nicknamed the King of invariant Theory, was unlike Max, a more dramatic figure. He was impulsive, He was expressive in very unbridled ways. He was given to wild gesticulation while he was talking, which I can identify with. Emmy was the only doctorate student that that he ever mentored, and she was really devoted to him. She kept a photo of him on her wall for the rest of her life. And it's interesting when people describe Emmy's behavior, she is sometimes described as having traits that are in some ways more similar to Paul Gordon than her father, like she too was given to serious gesticulation and kind of would make messes and be very dramatic and very excited and so passionate that she would kind of lose herself. But she received her PhD in mathematics from Erlangen after several years as Gordon's protege, and her thesis was a dissertation on algebraic invariance, which she successfully defended on December thirteenth of nineteen o seven. She was given her degree sumakun lauda on July two of the following year. This timing is really significant because co ed classes were not a thing in Germany until nineteen o eight, the year after she successfully defended her thesis. Any woman who had gone through the education system prior to that had, like Emmy, had to get special permission and was not granted equal students status. Yeah, just for clarity, we mentioned that she returned to Erlangen because they were doing it, but in terms of Germany wide, women were still not considered equal until that year after she defended her thesis, and in nineteen o eight, Emmy attended the International Mathematical Congress in Rome, Italy, and she attended that along with her father. She was at this point still a young woman and relatively unknown, despite sort of making this name for herself as an unusual figure being a woman in a very male dominated field, so it seems that during this particular conference she really kept a fairly low profile. After Ms Nurture received her PhD, she continued her research work at their Lingen, although she wasn't paid for any of this work. She assisted her father in his research and then she was invited in nineteen o eight to join the Cholo Mathematico in Italy and then in nineteen o nine the German Mathematical Union. Emmy's first sort of professional lecture was in nineteen o nine at the Salzburg meeting of the German Mathematical Union. She lectured at the Vienna chapter of the group several years later in nineteen thirteen, and not long after that she also started guest lecturing for her father as a substitute and during this same period. Although as we said, we don't have writings from her, so we don't really know how this impacted her, but surely it did. Emmy's mentor, Paul Gordan, died in nineteen twelve, so just as her career was taking off. So next up we're going to talk about a significant move in Emmy's life. But before that, let's have a word from one of our awesome sponsors, who keep the lights on here in our studio. That sounds grand. So after eight years of post pH d work at er Langen, her former teachers David Hilbert and Felix Klein asked her to come back to gutting In in nineteen fifteen. And this was right after Albert Einstein had published his Theory of General Relativity and Klein and Hilbert wanted Nurture to work with them on unraveling the mathematics that were involved in Einstein's work. And Nurture had published several papers of her own by this time, and she had really exhibited some insightful approaches to mathematical concepts, so she was the perfect candidate to assist in Hilbert Incline's work. She went to Goettingen, but this move turned out to be extremely controversial. Many faculty members objected to the idea of a woman on the teaching staff. If Emmy notre couldn't be granted faculty status, Hilbert and Kline wanted Hurt to at least have what's called a privat descent, which is a position similar to a post doc. It would have given Emmy at least an officially recognized post within the Good Educational system, would also grant her sufficient title and permission to teach for nurtures thesis to be accepted, and for her to be granted this privat, the entire philosophy faculty had to vote on it. And this umbrella of philosophy, keep in mind, included not only philosophy, but also history, natural sciences, and mathematics. And it turned out that the math people there were pretty cool with Emmy, but the non mathematics people in the mix, we're really vehemently arguing against having a woman teach students. The arguments against Nurture were that giving her a provactance and position would mean that she was on track to be faculty and what would the returning soldiers think when they came back to war to find that they're supposed to take classes from a woman. Yeah, they really framed it like what a slap in the face that would be these young men who had gone to defend the ideals of Germany and they then come back and find a lady teacher. Well yeah, and keep in mind, this wasn't even soldiers saying this. This was kind of the weird trumped up argument that the non mathematics faculty was trying to put together to keep Eman Nurture off of their cool kids club. And her mentor and now colleague Hilbert's response was, gentlemen, I do not see that the sex of the candidate is an argument against her admission as a privatdot sent After all, the sent it is not a bath house, and he meant like the educational Senate, not their uh government Senate. And his argument, though, didn't sway the detractors, and Emmy was not granted this title. Hilbert and Klein had to convince Nurta to stay for obvious reasons, but she couldn't lecture under her own name, so they had to come up with a sneaky kind of work around. The lectures were listed under Hilbert's name, but Nurture was the one who actually delivered them. Yeah, she worked under his name for quite some time. Um in eighteen. However, she has been doing this sort of sneaky workaround plan for several years. At this point, she had developed at through her work with Hilbert Kleine Nurture's theorem, which deals with the relation between what are known as the symmetries of a physical system and its conservation laws. So among the revelations of this theorem is the linkage between time and energy, directly related to the idea of conservation of energy, so that in case you do not remember, is that energy can neither be created nor destroyed, but merely changes form. And this is incredibly significant stuff. I mean, this is really a huge part of physics as we know it, right. It's an incredibly important concept at theoretical physics, and her peers at the time recognized its significance, so much so that the following year, Emmy not Are was finally officially recognized as an academic lecture with the privit zodes and title that we've been talking about for so long she had to lecture without. She no longer had to lecture under a male mentor's name, and this was obviously incredibly significant, but uh, it's not maybe the huge win that we would all be hoping for, because, just to be clear, at this point, emmy noture was in her thirties, she had published numerous influential and important papers, and she was working with the best mathematicians at the time as a respected peer of theirs on the mathematics of relativity. And despite all of that, she had up to this official um you know, kind of track to be in a faculty position. She had zero stability or safety in her career. But even though she now had a title but made it okay for her to lecture as herself, her position did not actually come with any pay. She would not get any pay as a lecture until nineteen three, four years after she was made of private dotes in. Yeah, we don't know exactly where the money was coming that supported her. Uh, this is one of those kind of wiggily fuzzy points. Presumably she was getting some from like a family fund and possibly sort of private grants from other mathematicians, but we don't really knew. In she collaborated with colleague Werner Schmidler to write concerning moduli in non commutative fields, particularly in differential and difference terms, and this publication really established, like without question, Nurture as a mathematician at the very top of her field. While the start of World War One kept her from traveling to speak at gatherings of mathematicians, starting in nineteen twenty she was often on the road lecturing throughout Germany, and from ninety and nineteen twenty six Nurture's work focused on what's called the general theory of ideals, no more commonly in modern times as commutative algebra. Her work during this time united a lot of different mathematical concepts, but this was in terms of her personal life a period of ups and downs for Emmy. In one, for example, her father died, so at this point she was left without both of her father figure mentors in mathematics, and in the middle of all that work, as we said, she was given a lecture ship specifically in algebra in ninety three. Just two years later, and he's first student to complete a doctorate under her mentorship received her PhD. Emmy had mentored another woman, Greta Herman, through her thesis process and Herman finished her doctorate in February nine, twenty five. Around nineteen twenty four, while she was working with Greta Herman and lecturing and doing her research, Nurture was at the center of this sort of interesting walking and talking phenomenon on campus. Students and scholars alike would take long walks with Emmy around the school of grounds, talking about what else mathematics and math theory, and this informal group, which came to be known as Nurtures Boys, included Russian scholar Pavel Alexandrov, who was a visiting professor from the University of Moscow. Nutter and Alexandrov became friends, and she was eventually invited to Moscow as a guest lecturer in the nine academic year. This was not the only international recognitions she was receiving during this time, though. She also delivered a paper at the International Mathematical Congress in Bologna, Italy that was in nine and then a few years later in nineteen thirty two, she addressed the same group in Zurich. In nine seven, nursers focus shifted almost exclusively to noncommutative algebras, and these are algebras where the order in which the numbers are multiplied affects the outcome and nur There's work in this area yielded a theory that enabled a conceptual unification of all of them, and during her work in this phase of her career, she collaborated with Helmet Hass and Richard Brauer and published papers hyper Complex Number Systems and their Representation in nine and non Commutative Algebra in nineteen thirty three. From nineteen thirty to nineteen thirty three she also worked as an editor on the German Mathematical Annual. Throughout all of her research, writing and editing, she was also still teaching regularly, but even so she was still employed at a level far below what her colleagues thought she deserves. Yeah, even as male mathematicians were rising up through the ranks in the Gutting gutting in educational system at a rate that really easily outpaced Emmy, they were so hugely influenced by her work that many of them tried to point out how wrong this was and tried to petition for an improved title on her behalf. It generally came to not with the greater university system, but in terms of the mathematics world. She was regarded not just as a peer, but as a leader. At this point, n three would prove to be a pivotal year for Nurture, and we're going to talk about it after we paused to chat about one of our awesome sponsors who keep our show going. In ninety three, Germany changed, obviously pretty significantly when the Nazi Party came into power. Emmy Nurture, who was Jewish, lost her job, as did many of her colleagues. The Nazi Party had actually passed a number of laws that were intended to keep Jews out of civil service jobs, and that included academics. For a while, Emmy gave informal lectures at her home, and she certainly had students who were eager to continue learning from her. She was apparently not even bothered when a student or two showed up in their Nazi uniforms. She just wanted to talk about math. Meanwhile, her friend Pablo Alexandrov was working to get the University of Moscow to appoint her to a position, and his efforts were really passionate, but they were getting slow response, and finally Emmy just had to make a decision about her future. As tensions mounted in Germany, she left Germany in October to move to the United States. She'd been offered a one year guest professor spot at brent Mark College. Unbeknownst to Nurture, when she accepted the offer, the school was also setting up a graduate fellowship in her name for the academic year she would be teaching there. She also lectured and worked on her math research in Princeton, New Jersey, at the Institute for Advanced Study, and while interest in her lectures was initially slow to catch on, eventually Emmy did get a following of students, and she sort of found this mirror group to the Nurture Boys of gut In, but this group was called the Nurture Girls, and they would go on hikes on Saturdays all the while, just as she had in Germany, discussing mathematical concepts. Her one year invitation to teach at bren Mar was extended the following academic year of nineteen thirty five, but before it started, she went back to Germany to visit her brother Fritz and his family before they moved to Siberia for a teaching position there. Like Emmy, Fritz lost his job at the Institute of Technology under the Nazi government. Emmy also visited her old campus and her friends at gutting In, but she soon headed back to Pennsylvania for another year at Bryn Mar and during her second year there she mentored her first American PhD candidate, a young woman named Ruth Halfer. The life of Emmy Nore ends rather abruptly. In the spring of nineteen thirty five. She went into the hospital to have an ovarian sister moved, and while she seemed to be recovering well initially, she died quite suddenly on April fourteenth, four days after her surgery. Just a weeks later, on May third, of the New York Times ran a letter that was written by Albert Einstein about Emmy Nutter, and he wrote, within the past few days, a distinguished mathematician, professor I mean Notre, formerly connected with the University of Guttingen and for the past two years at Renmark College, died in her fifty third year, and the judgment of the most competent living mathematicians, Fraeulein Notre was the most significant creative mathematical genius thus bar produced since the higher education of women began in the realm of algebra, in which the most gifted mathematicians have been busy for centuries. She discovered methods which have proved of enormous importance in the development of the present day younger generation of mathematicians. And now while we have reached the point in emmy story where she has departed this earthly plane, there's a little bit more to talk about in terms of her politics. And the reason that we're putting that this at the end is because the primary infra nation we have about it isn't from things that came up in her actual lifetime or again her writings, which we don't have. It's stuff that came up in eulogies and memorials from colleagues after her death, specifically two of them. In nineteen nineteen, Nature joined the independent Social Democrats group and getting in and to some the group was considered an extremely radical Bolshevik group. It was a splinter group that broke away from the Social Democratic Party in nineteen fourteen as a centrist group between the Social Democratic Party and the Communist Party of Germany. But two of her close friends and fellow mathematicians interpret her politics very differently. When they spoke about her life. First Herman Wile while worked in analysis, number theory, foundational mathematics and quantum mechanics, among other areas, and he met Nature in gutting In in nineteen thirteen, and they remained quite close throughout the rest of Emmy's life. And when while spoke of Emmy's political stance, it was very much in the vein that she was a pacifist and she definitely was, we know that with great hopes for Germany's future, and that really she saw the independent Social Democrats as the next stage of the Social Democrats, not as a radical shift, but as a gradual evolution. And he also wrote of Emmy that quote, without being actually in party life, she participated intensely in the discussion of the social and political problems of the day. On the other hand, Pavel Alexandrov characterized Emmy as very pro Soviet. He said that quote, she always had a lively interest in politics and hated war and chauvinism in all its forms, and with her whole being, her sympathies were always unwaveringly with the Soviet Union. So it seems based on the fact that Alexandrov was working to get Emmy a position in Moscow in nineteen thirty three, that she was comfortable with the idea of living in the Soviet Union, and the Bolshevik Revolution took place while she was working in academia, so it's really unlikely that she was blind or ignorant to the political events that were playing out around her. But since both of these men likely saw Emmy's political stance through their own lenses and in the way they wished to see her, and since we do not have any of her own writing on the subject to reference, we really don't know where she truly stood. What's really indisputable as that I mean notre was a major figure in mathematics, both in her time and today, as many others have built upon her work, and she seems simply unflappable in the face of the difficulties she faced as she made a name for herself in a field that had very few women in it. And so I wanted to end with a quote from her friend Pavel Alexandrov, because it describes Emmy in such a way that I think anybody would want to know her. It says, quote her great sense of humor, which made social gatherings in personal contacts with her so pleasant enabled her to counter the injustices and absurdities that beset her academic career easily and without anger. In such circumstances, instead of being offended, she would simply laugh. But she was very offended indeed, in protested sharply when even the smallest injustice was directed at one of her students. I love that quote. Um, there's really no substantiation in any way, but there are. It will come up as theory sometimes that she was connected romantically to either While or Alexandrov, although we don't know, and none of them, none of their letters ever hinted any of that, so we just have no idea. But we do know that she was very close with both of those men. So I love that that sort of lovely description of her. Yeah. Um, And now we'll get to the listener mail and inspired this whole thing. And this is from our listener, Mark, who is amazing, and he writes, Hi, Holly and Tracy, I enjoyed listening to your podcast, and I thought you might like a laser engraving of one of my favorite mathematicians, Emmy Nurture. I did the engraving on one millimeter aircraft Plywood, hoping that would make it a little more unique. I listened to your podcast when I'm on the road or in the lab a guitar lab. Really keep up your great work. And Mark sent us this absolutely beautiful engraving of Emmy and I just was so struck by it that we had to do an episode. Yeah, and we're going to post a picture of it. It's great and it's uh So we've talked about how I don't normally work in the same office as Holly anymore, and so Holly will send me pictures of the things that come into the office and are amazing. And that was whe where I kept zooming in on my phone usually text Gorget like WHOA, what's happening. It's really it's very beautiful. I love it. Mark, thank you so much. That was so thoughtful and cool, and I appreciate that you took time to make us a really famulous gift. We're very, very lucky. Thank you so much for joining us on this Saturday. If you have heard an email address or a Facebook you are l or something similar over the course of today's episode. Since it is from the archive, that might be out of date Now. You can email us at History podcast at how stuff works dot com, and you can find us all over social media at missed in History. And you can subscribe to our show on Apple podcasts, Google podcasts, the I Heart Radio app, and wherever else you listen to podcasts. For more on this and thousands of other topics, visit how staff works dot com