Welcome to Stuff you missed in History Class, fun how Stuff Works dot Com. Hello, and welcome to the podcast. I'm Polly Fry, 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 gonna 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. True. Uh so, it's Emily Nurture. You will sometimes also hear it pronounce more like neuture. Well, and then when I looked it up at four though that 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 pas full of 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 eighty 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 especially 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 eighteen 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 backup 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, and we went to the University of our Langen to continue her education. But because she was a woman and it was nine hundred, she couldn't just enroll in classes. She had to get special permission from every instat after 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. Yes, 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 nineteen o three and he 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 Guttingen, and that started in the winter of nineteen o 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, influence saying his famous student Albert Einstein and 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 messages 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 Churcholo 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 significan get 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 PhD work at Erlangen, her former teachers David Hilbert and Felix Klein asked her to come back to gutting In in nineteen fift 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 and Kline's work. She went to Gutchingen, 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 Norture couldn't be granted faculty status, Hilbert and Klein wanted her to at least have what's called a priv discent, which is a position similar to a post doc. It would have given Emmy at least an officially recognized post within the Good and 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 provent, 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 Nurtare 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 of 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 Emmy 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 privat sent. After all, the Senate is not a bathhouse, 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 in Kline had to convince Nurture 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 nurts Or 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 nurtures 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 relating 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 of theoretical physics, and her peers at the time recognized its significance so much so that the following year, Emmy Notre was finally officially recognized as an academic lecture with the private zodes and title that we've been talking about for so long she had 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, uh Emmynure 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 that 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 nine four years after she was made of vits In. Yeah, we don't know exactly where the money was coming that supported her. H This is one of those kind of wiggly 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 nineteen twenty she collaborated with colleague Werner Schmidler to write concerning moduli and 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 twenties, she was often on the road lecturing throughout Germany, and from nineteen twenty six nurtures 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 concept ups, but this was in terms of her personal life a period of ups and downs for Emmy. In ninety 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 nineteen twenty three. Just two years later, Andy's first student to complete a doctorate under her mentorship received her PhD. Amy had mentored another woman, Greta Herman, through her thesis process, and Herman finished her doctorate in February nineteen twenty five. Around nineteen twenty four, while she was working with Greta herman and 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 Moscowna 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. So in n 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 ur there's work in this area yielded a theory that enabled the 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 in their Representation in ninety twenty 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, nineteen thirty three would prove to be a pivotal year for Nurture, and we're going to talk about it after we paused chat about one of our awesome sponsors who keep our show going. In nineteen thirty 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 ninety three to move to the United States. She'd been offered a one year guest professor spot at brent Mark Hall Edge. 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 gutting 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 ren Mar was extended the following academic year of nine 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 had a 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 Notare 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 few weeks later, on May third of nineteen thirty five, 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 far 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 information 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 uh Nurture 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 Alexandro 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 ninety 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 is 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 seemed 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, and 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 is 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. 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 one where I kept zooming in on my phone, azing tex Gorge, 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 fabulous gift. We're very, very lucky. If you would like to write to us, you can do so at history Cast at how stuff works dot com. We're also at Facebook dot com, slash mist in history, at Twitter at miss in History, on pinterest dot com slash mist in history. Are you seeing a miss in History theme. It continues where at miss in history dot com, Ware dot com and at mist in history dot spreadshirt dot com. If you want to pick up some mist in History goodies for your person, or your parcels or your pals, I'm just gonna alliterate all of that. We're also on Instagram at miss in history if you want to see some sometimes silly and sometimes informative photos about history and the things we cover. Uh. If you would like to do a little bit of research related to what we talked about today, you can go to our parents site, how Stuff Works, and you can type in how math works in the search barring you'll get a fabulous article written by Robert from stuff to blow your mind about math. We just don't want to read about that. Don't say you don't, because it's really interesting. If you would like to visit us, you could do so at mist in history dot com, where we have all of our episodes archive from forever. We have show notes from any episodes trade see and I have worked on so over the last two and a half years or so. 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Welcome to Stuff you missed in History Class, fun how Stuff Works dot Com. Hello, and welcome to the podcast. I'm Polly Fry, 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 gonna 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. True. Uh so, it's Emily Nurture. You will sometimes also hear it pronounce more like neuture. Well, and then when I looked it up at four though that 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 pas full of 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 eighty 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 especially 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 eighteen 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 backup 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, and we went to the University of our Langen to continue her education. But because she was a woman and it was nine hundred, she couldn't just enroll in classes. She had to get special permission from every instat after 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. Yes, 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 nineteen o three and he 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 Guttingen, and that started in the winter of nineteen o 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, influence saying his famous student Albert Einstein and 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 messages 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 Churcholo 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 significan get 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 PhD work at Erlangen, her former teachers David Hilbert and Felix Klein asked her to come back to gutting In in nineteen fift 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 and Kline's work. She went to Gutchingen, 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 Norture couldn't be granted faculty status, Hilbert and Klein wanted her to at least have what's called a priv discent, which is a position similar to a post doc. It would have given Emmy at least an officially recognized post within the Good and 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 provent, 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 Nurtare 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 of 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 Emmy 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 privat sent. After all, the Senate is not a bathhouse, 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 in Kline had to convince Nurture 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 nurts Or 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 nurtures 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 relating 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 of theoretical physics, and her peers at the time recognized its significance so much so that the following year, Emmy Notre was finally officially recognized as an academic lecture with the private zodes and title that we've been talking about for so long she had 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, uh Emmynure 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 that 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 nine four years after she was made of vits In. Yeah, we don't know exactly where the money was coming that supported her. H This is one of those kind of wiggly 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 nineteen twenty she collaborated with colleague Werner Schmidler to write concerning moduli and 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 twenties, she was often on the road lecturing throughout Germany, and from nineteen twenty six nurtures 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 concept ups, but this was in terms of her personal life a period of ups and downs for Emmy. In ninety 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 nineteen twenty three. Just two years later, Andy's first student to complete a doctorate under her mentorship received her PhD. Amy had mentored another woman, Greta Herman, through her thesis process, and Herman finished her doctorate in February nineteen twenty five. Around nineteen twenty four, while she was working with Greta herman and 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 Moscowna 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. So in n 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 ur there's work in this area yielded a theory that enabled the 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 in their Representation in ninety twenty 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, nineteen thirty three would prove to be a pivotal year for Nurture, and we're going to talk about it after we paused chat about one of our awesome sponsors who keep our show going. In nineteen thirty 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 ninety three to move to the United States. She'd been offered a one year guest professor spot at brent Mark Hall Edge. 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 gutting 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 ren Mar was extended the following academic year of nine 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 had a 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 Notare 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 few weeks later, on May third of nineteen thirty five, 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 far 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 information 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 uh Nurture 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 Alexandro 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 ninety 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 is 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 seemed 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, and 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 is 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. 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 one where I kept zooming in on my phone, azing tex Gorge, 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 fabulous gift. We're very, very lucky. If you would like to write to us, you can do so at history Cast at how stuff works dot com. We're also at Facebook dot com, slash mist in history, at Twitter at miss in History, on pinterest dot com slash mist in history. Are you seeing a miss in History theme. It continues where at miss in history dot com, Ware dot com and at mist in history dot spreadshirt dot com. 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