September 7, 2015 • 27 mins
In the early 20th century in Germany, Emmy Noether pursued a career in mathematics, 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 (00:00):
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
(00:21):
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
(00:42):
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
(01:03):
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
(01:26):
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
(01:49):
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
(02:10):
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
(02:32):
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,
(02:52):
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
(03:13):
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
(03:37):
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
(03:58):
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
(04:18):
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
(04:41):
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
(05:03):
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
(05:23):
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
(05:45):
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,
(06:08):
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,
(06:28):
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
(06:49):
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
(07:10):
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
(07:32):
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
(07:54):
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
(08:15):
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.
(08:36):
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
(08:56):
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
(09:18):
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
(09:41):
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
(10:03):
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,
(10:26):
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
(10:47):
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
(11:12):
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.
(11:32):
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
(11:54):
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
(12:19):
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.
(12:41):
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
(13:05):
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
(13:28):
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
(13:48):
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.
(14:10):
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
(14:30):
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,
(14:52):
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,
(15:13):
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
(15:37):
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
(15:59):
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.
(16:20):
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
(16:43):
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.
(17:04):
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
(17:26):
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,
(17:48):
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,
(18:08):
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
(18:31):
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
(18:52):
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
(19:14):
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
(19:37):
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
(19:59):
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
(20:22):
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
(20:45):
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
(21:05):
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
(21:26):
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
(21:47):
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
(22:10):
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
(22:33):
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,
(22:57):
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
(23:17):
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
(23:40):
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
(24:02):
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
(24:25):
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,
(24:45):
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
(25:06):
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
(25:28):
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,
(25:49):
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
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(27:14):
stuff Works dot com, m
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
(00:21):
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
(00:42):
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
(01:03):
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
(01:26):
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
(01:49):
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
(02:10):
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
(02:32):
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,
(02:52):
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
(03:13):
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
(03:37):
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
(03:58):
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
(04:18):
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
(04:41):
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
(05:03):
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
(05:23):
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
(05:45):
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,
(06:08):
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,
(06:28):
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
(06:49):
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
(07:10):
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
(07:32):
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
(07:54):
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
(08:15):
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.
(08:36):
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
(08:56):
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
(09:18):
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
(09:41):
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
(10:03):
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,
(10:26):
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
(10:47):
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
(11:12):
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.
(11:32):
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
(11:54):
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
(12:19):
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.
(12:41):
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
(13:05):
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
(13:28):
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
(13:48):
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.
(14:10):
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
(14:30):
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,
(14:52):
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,
(15:13):
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
(15:37):
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
(15:59):
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.
(16:20):
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
(16:43):
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.
(17:04):
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
(17:26):
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,
(17:48):
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,
(18:08):
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
(18:31):
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
(18:52):
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
(19:14):
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
(19:37):
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
(19:59):
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
(20:22):
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
(20:45):
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
(21:05):
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
(21:26):
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
(21:47):
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
(22:10):
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
(22:33):
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,
(22:57):
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
(23:17):
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
(23:40):
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
(24:02):
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
(24:25):
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,
(24:45):
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
(25:06):
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
(25:28):
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,
(25:49):
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
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(26:10):
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I'm just gonna alliterate all of that. We're also on
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(26:31):
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
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(26:52):
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(27:14):
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