March 23, 2019 • 27 mins
Today we revisit a 2015 episode about Emmy Noether pursued a career in mathematics in the early 20th century in Germany, despite many obstacles in her path. She became one of the most respected members of her field, and developed mathematical theory that's still important today.
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Episode Transcript
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Speaker 1 (00:02):
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
(00:30):
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
(00:53):
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
(01:16):
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
(01:37):
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
(01:59):
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.
(02:21):
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.
(02:44):
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
(03:06):
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
(03:28):
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
(03:51):
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
(04:12):
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
(04:36):
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,
(05:00):
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,
(05:23):
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.
(05:44):
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
(06:06):
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
(06:27):
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
(06:49):
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
(07:10):
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
(07:32):
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
(07:54):
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,
(08:15):
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
(08:36):
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
(08:56):
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
(09:17):
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
(09:38):
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
(10:00):
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
(10:23):
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
(10:45):
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
(11:09):
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
(11:30):
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,
(11:53):
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
(12:17):
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
(12:40):
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,
(13:02):
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
(13:23):
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
(13:45):
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
(14:05):
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,
(14:28):
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
(14:50):
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
(15:13):
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,
(15:33):
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
(15:57):
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
(16:17):
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.
(16:42):
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
(17:06):
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.
(17:30):
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
(17:52):
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,
(18:14):
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
(18:38):
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
(18:59):
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,
(19:20):
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
(19:41):
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,
(20:02):
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
(20:25):
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
(20:48):
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
(21:09):
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
(21:31):
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
(21:53):
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
(22:17):
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
(22:38):
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
(22:58):
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
(23:19):
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.
(23:42):
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
(24:03):
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
(24:23):
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
(24:47):
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,
(25:12):
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
(25:32):
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
(25:53):
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
(26:15):
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
(26:38):
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,
(27:01):
and wherever else you listen to podcasts. For more on
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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
(00:30):
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
(00:53):
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
(01:16):
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
(01:37):
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
(01:59):
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.
(02:21):
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.
(02:44):
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
(03:06):
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
(03:28):
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
(03:51):
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
(04:12):
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
(04:36):
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,
(05:00):
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,
(05:23):
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.
(05:44):
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
(06:06):
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
(06:27):
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
(06:49):
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
(07:10):
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
(07:32):
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
(07:54):
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,
(08:15):
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
(08:36):
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
(08:56):
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
(09:17):
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
(09:38):
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
(10:00):
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
(10:23):
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
(10:45):
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
(11:09):
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
(11:30):
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,
(11:53):
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
(12:17):
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
(12:40):
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,
(13:02):
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
(13:23):
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
(13:45):
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
(14:05):
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,
(14:28):
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
(14:50):
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
(15:13):
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,
(15:33):
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
(15:57):
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
(16:17):
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.
(16:42):
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
(17:06):
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.
(17:30):
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
(17:52):
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,
(18:14):
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
(18:38):
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
(18:59):
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,
(19:20):
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
(19:41):
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,
(20:02):
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
(20:25):
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
(20:48):
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
(21:09):
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
(21:31):
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
(21:53):
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
(22:17):
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
(22:38):
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
(22:58):
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
(23:19):
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.
(23:42):
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
(24:03):
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
(24:23):
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
(24:47):
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,
(25:12):
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
(25:32):
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
(25:53):
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
(26:15):
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
(26:38):
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,
(27:01):
and wherever else you listen to podcasts. For more on
this and thousands of other topics, visit how staff works
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