Lucian: Good evening and a very warm welcome
to “He denies the very existence of a woman
mathematician”. I shall explain that very
briefly, Professor June Barrow-Green’s Inaugural lecture.
My name is Lucian Hudson, I’m the Director of Communications
here at The Open University.
This evening we will hear from June about
this quote from the famous novelist George
Eliot, when she introduced the Russian mathematician
Sofia Kovalevskaya to the evolutionary philosopher
Herbert Spencer way back in 1869. Taking this
as her cue June will look at the centuries
long struggle for women mathematicians to
gain equality and explore the extent to which
progress has actually been made. So you could
say that this evening is of course about history,
‘his story’, but it’s also about ‘her
story’. We will hand you over in a few minutes
to someone who knows June in her academic
career in more detail. This is Phil Rippon,
Professor of Pure Mathematics at The Open
University.
Before I do that let me run through the format
of tonight’s event and some housekeeping.
Once Professor Rippon has done his introduction
June will deliver her Inaugural Lecture and
then there will be time for questions. For
your questions here in the audience but also
from those joining us online from social media.
We also invite you to engage on social media
about this talk and the hashtag for that is
#OUTalks. We are also keen to hear from those
of you who will be joining us via Livestream.
So please use the email address provided and
please keep your comments and questions brief
so that we can cover as many of them as possible
during the question and answer session. This
evening’s Inaugural will end at 7pm after
which we invite you here to join us for refreshments
downstairs. Before we start I’d like to
draw your attention to the health and safety
details on the slide. It now gives me great
pleasure to hand over to Professor Phil Rippon
who will introduce June.
 
 
 
 
 
 
 
 
 
 
 
 
Phil: It’s a huge pleasure to say a few words to introduce June. The Open University
is very fortunate that June has spent her
distinguished academic career here. Starting
as a PhD student in the History of Mathematics
with Jeremy Gray, then going on to a Post-Doctoral
position then to a Lectureship, then Senior
Lecturer and now of course Professor. The
OU has long had an international reputation
as a world leader in the history of maths,
as many of you know only too well, both for
research and teaching, with Jeremy Gray, Jonford
Bell, and Robin Wilson and June maintains
this reputation today.
June’s PhD was phenomenal. In it she described
an astonishing mathematical incident in 1889
around a mathematical memoire by the great
French mathematician Henri Poincaré. This
essay had won a prize offered by the King
of Sweden and Norway. The incident was a highly
significant event mathematically and personally
for those involved and it had been unknown
outside a very small circle until June unearthed
it in her PhD. Her book Poincaré and The
Three Body Problem’ described the incident
itself and the highly complicated mathematics
involved and its consequences and it was praised
by mathematical reviews as a “superb piece
of work”, that’s her PhD. Since then June’s
work has covered the history of maths from
the late 19th century through the 20th exploring
previously unknown topics such as the mathematical
contributions to aeronautics during the First
World War. She has often focused on the role
of women mathematicians. Her work has been
funded by the British Academy and the Centre
nationale de la recherche scientifique in
Paris. She spent six months as International
Research Professor at the University of Nancy
investigating the work of the great George
Birkhoff, a US mathematician who took up where
Poincaré had left off.
Just a few other highlights. June won a prestigious
international prize for her mathematical exposition.
She is a former President of the British Society
for the History of Mathematics. She is an
elected member of the International Academy
of the History of Science and a leading figure
in the London Mathematical Society. Together
with Professor Sir Tim Gowers and Professor
Imre Leader from Cambridge, she edited the
Princeton Companion to Mathematics, an encyclopaedic
work covering a vast range of mathematical
topics which of course again had excellent
reviews. You can see a copy of it upstairs
and feel the weight.
As you might expect June is in huge demand
to give talks at conferences in all corners
of the globe from the United States to China,
India, Brazil and all over Europe. Closer
to home she has done many outreach activities
based around maths history. She is in demand
as an expert contributor to the media, such
as the Story of Maths on BBC 4 and appearances
on Melvyn Bragg’s In our Time and also Woman’s
Hour. June’s vast knowledge of the history
of maths and her ability to communicate that
knowledge has fed into our teaching in many
ways. She runs a popular Masters dissertation
on 19th century geometry, and thanks to her
our undergraduate modules now contain far
more historical context than they did formerly.
Moreover, she is an excellent PhD supervisor,
currently with a group of three very able
and lively students, two of whom are here
today. As if all this is not enough, June
also runs marathons and she has represented
the OU at tennis, badminton and cricket. So
I am looking forward enormously to hearing
June’s talk “He denies the very existence
of a woman mathematician”.
 
June: Thank you very much Phil, I’m not
quite sure how I follow that. Thank you all
so much for coming. I’ve got so many thanks,
my family and my friends and of course my
OU colleagues. Just a few I want to say a
few words about. When I was doing my PhD it
never would have got finished without my friends
in the tennis and cricket club, that’s for
sure. Of course all my colleagues in the School
of Mathematics and Statistics and particularly
the historians of maths. My research students,
Craig, Rosie, Tony, Alison and Brigitte. Particular
thanks to Alison for orchestrating the posters
outside, and of course Robin Wilson, the late
John Favell who I miss terribly, and last
but absolutely not least, Jeremy Gray, who
was my PhD supervisor and has been my intellectual
guide, his friendship and generosity knows
no bounds and I can’t thank him enough.
I want to begin by telling you a little bit
about how I got to where I am today because
it does play into the story I am going to
tell. I came from a family that shall we say
was a little Victorian in its attitude towards
education of girls. As a result I wasn’t
allowed to go to university at the age of
18. I ended up beginning my working life in
an art gallery in Old Bond Street. This is
the story of me going from Old Bond Street
to Walton Hall.
I began at Thomas Agnew and Sons in Old Bond
Street. My office there would be decorated
with paintings by Rubens, Renoir, Constable,
or Turner. I’ve chosen one of the paintings
that came through Agnew’s hands while I
was there which is now in the Paul Mellon
collection at Yale. This painting by John Singleton
Copley of Richard Heber, I really like it and
the fact that he is an embryonic cricketer
and I think I never got beyond being an embryonic
cricketer so I feel I relate to it. The other
reason I like it is because I discovered that
Richard Heber when he grew up he was described
as a maniacal bibliophile. He never purchased
just one copy of a book, he always purchased
three. ‘No gentleman’ he remarked ‘can
be without three copies of a book, one for
show, one for use and one for borrowers’.
When he died his library was about 150,000
strong in books, in eight houses and it was
dispersed after he died and it took 216 days
to sell. So I relate, I haven’t quite got
as many books as him but I do like books.
So while I was at Agnews I began to think
I still really wanted to go to university.
This relatively new institution The Open University
came across my horizon and I thought that’s
what I can do. I’m far too old - I was in
my mid-20s. I’m far too old to go to a proper
University, I’ll go to The Open University.
But of course I was in an art gallery, I thought
I’m going to do an Arts degree. So I started
off by doing an Arts Foundation Course. In
those days you had to do two Foundation Courses.
By process of elimination I thought I had
liked maths at school, I’ll see what I can
still do. So I did some OU, some of you might
recognise the person there, I don’t know
if he wants to identify himself now, and of
course while I was doing the maths I realised
that actually that’s what I wanted to do.
I was very fortunate that I was able to use
my Open University courses and I found a rather
enlightened admissions tutor at Kings College
London and so I did a BSc in Maths at Kings.
It was while I was there I got really interested
in the history of maths. I’ll say a bit
more about that in a minute. I finished my
degree and I thought what I wanted to do was
a PhD in History of Maths. But is it because
I just liked being a student, it was so lovely
being a student. Also I needed to shore up
the finances a bit. So I thought right I will
go to the city. I was living in Islington,
I still do, and got a job at an American Investment
Bank. Well it certainly shored up the finances,
but I realised it wasn’t what I wanted to
do. That was the other thing, I thought maybe
I would go there and it would be what I wanted
to do. So I then realised that if I wanted
to do the history of mathematics that I wanted
to do, I wanted to do 19th/20th century French,
I needed a bit more maths. So I went back
to Kings and did an MSc in Mathematical Physics
and then looked around for where I could do
my PhD. In fact The Open University was the
only place that I could do a PhD in History
of Mathematics in a Mathematics Department.
I was pretty sure I could blag it to the historians
if I was in a Maths Department, but I didn’t
think it would work the other way round. It
turned out to be the best possible decision
I could have made. I was also very fortunate
that when I wrote to Jeremy Gray he thought
that I was worth putting a punt on. Somehow
I managed to get through the PhD with a huge
amount of help from Jeremy and the cricket
and tennis club, and then managed to convince
The Open University to carry on employing
me. So I think my story resonates with the
rest of my talk in the sense of as a girl
I had to struggle but also the fact that The
Open University really played a key role even
before I came here on a full time basis.
So let me now move on to the real meat of
my talk. I am going to start with Hypatia
of Alexandria. The reason I am choosing her
is because this is a talk about the history
of women in mathematics and of course it can’t
be comprehensive so I am just using a few
examples. I’m not even going to tell you
everything I know about each of the people
I am talking about, but I am just making a
few different points about each of them. I’ve
chosen Hypatia. She was the first women mathematician
that we really know anything about. There
is no surviving writings of Hypatia so everything
we know comes through commentaries of later
people. We have pretty solid evidence for
the fact that she was the daughter of Theon
of Alexandria. She was a philosopher. She
taught philosophy and astronomy. It’s believed
that she wrote commentaries on various other
books by Greek mathematicians. She was a Pagan
philosopher and she was killed by a Christian
mob. Of course we don’t have an image of
her so that’s hence the lunar crater, Hypatia,
so this really is a Hypatia. I’ve chosen
her because I think it’s quite interesting
to look at some of the images of Hypatia.
If you go onto the web and you Google around
you find some interesting pictures. There’s
this mosaic which I couldn’t find anything
more about other than it was somebody giving
a lecture. It comes up various times under
the name of Hypatia. It’s clearly not her,
but people think it is possibly what she might
have looked like. The next one is probably
what people’s idealised view of a Greek
mathematician or woman of that period. The
interesting one I think is this one by Charles
William Mitchell. I guess it’s not how many
people would imagine 
a woman mathematician today, I’ve always
been envious of her hair actually. Charles
Kingsley wrote a novel and he described Hypatia
in this way, so I want to make the point about
what people think about when a woman mathematician
image is conjured up. We will see more about
that in a minute.
There is one man who is going to make an appearance.
That’s Isaac Newton. He is arguably one
of the greatest geniuses that has ever walked
the planet. He was an absolutely incredible
mathematician, natural philosopher, creator
for calculus, I don’t need to say much more
about that. The reason I have bought him into
the story is a personal reason and also the
fact that in a way Newton’s reputation really
was made by the people that came after him
to a great extent, because it was very difficult
to get him to publish his writings. He wasn’t
a self-publicist in that way and we are going
to see some women who helped to spread Newton’s
ideas but there was a personal reason for
including him. Actually I have to thank Newton
for my interest in history of mathematics
in one respect. It was because when I was
at a lecture at Kings we had a calculus tutorial
and the tutor there said ‘mmm calculus’,
we thought we wouldn’t be doing calculus,
‘Issac Newton’, then he looked up, this
was in the 80s, and he said, ‘second nastiest
person to come out of Grantham’. Well I
don’t only have to thank Issac Newton, I
have to thank Maggie Thatcher as well. It
was like a lightbulb moment because I hadn’t
thought about mathematicians as being nice
or nasty. Mathematicians are like anybody
else, you get nice ones, and you get nasty
ones. Issac Newton wasn’t a very nice one.
Of course it matters because people empower.
Newton was President of the Royal Society
for example, and can influence things. I got
really interested in the names that were attached
to the theorems and the people. I wanted to
know who they were and what sort of influence
they had. So I do have to be grateful to Issac
Newton for being not very nice.
One of the people who helped to spread Newton’s
ideas was Emilie du Chȃtelet. Voltaire, the
great French philosopher and essayist wrote
about Emilie du Chȃtelet that “she was
a great man whose only fault was being a woman”.
It is a little bit disingenuous of me to include
that really because Voltaire was Emilie du
Chȃtelet’s lover. They lived together and
had a laboratory where they did experiments.
Her great work was in translation of Newton’s
Principia. She didn’t just provide a translation,
she provided commentary as well. She was responsible
for really spreading Newton’s word and getting
his work accepted in Europe in the 18th century.
There’s a whole story about that which I’m
not going to get into. I also particularly
like this portrait by Latour showing her with
her mathematical instruments and her books.
You can see by her dress that she came from
an aristocratic well to do family, and that’s
what enabled her to do her mathematics. She
could do it in a private capacity. She couldn’t
of course be a professional mathematician
as a woman in that age.
There’s another portrait by Latour of someone
who is not so well known. I really like this
portrait because Mademoiselle Ferrand chose
to have her portrait painted with her edition
of Voltaire’s edition of Newton, that was
her symbol. Of course Voltaire’s edition,
although it’s got Voltaire’s name on the
cover, he gave tribute to Emilie du Chȃtelet
on the frontispiece inside. I think it’s
interesting when you see these two French
women in a similar period showing that actually
there was a discourse about Newtonian philosophy
in France by women of a certain class of course.
But they were actually engaging with very
difficult mathematics. Newton’s Principia
is not an easy read. Emilie du Chȃtelet’s
work is remarkable. I can’t underline that
enough.
Another French mathematician, Sophie Germain.
She was an autodidact. She learnt her maths
from her books in her father’s library.
She became very interested, she wanted to
learn more. Born in 1776. In 1794 when she
was 18 the famous Ecole Polytechnique in Paris
opened. She wanted to study mathematics there,
but she couldn’t because she was a woman.
However the lecture notes were made available
for anyone to read, so she was able to get
hold of a copy of the lecture notes. She began
a correspondence with one of the lecturers
there, Lagrange but she couldn’t reveal
herself as being a woman so she corresponded
under the pseudonym of Monsieur LeBlanc. Eventually
the time came when Legrange was so impressed
with what she was doing that he wanted to
meet her. So they did meet and to Lagrange’s
credit he wasn’t remotely put off by the
fact that she was a woman and helped and encouraged
her with her studies. Sophie Germain did some
remarkable mathematics. She won a prize from
the Paris Academy for her work on elasticity.
But the work I want to draw your attention
to is her work on Fermat’s last theorem
because she was really the first mathematician
to make progress on this problem. After she
died and in the decades after her, she got
slightly wiped out of the history in a sense.
It was known she had worked on it, but it
was always considered that what she did was
as an aftermath of what some other male mathematicians,
Legendre particularly, had done. She wasn’t
really given credit for her own discoveries.
That record was only really put straight in
the 1990s when some American historians of
maths, Laubenbacher and Pengelly investigated
her manuscripts in the Bibliotheque Nationale
in Paris and were able to really see that
it was Germain who had made this major contribution.
So I think this tells us also something about
how we as historians have to go back to our
sources. It’s not enough just to read what
somebody else has written, particularly when
the situation is very different, as it was
in the 19th century, and the attitudes towards
women mathematicians. We are going to see
more about that in a minute.
As I said she wrote to Legrange as a man,
she also wrote to the great German mathematician,
Carl Friedrich Gauss, using the same pseudonym.
This is what Gauss said when he discovered
that she was a woman “How can I describe
my astonishment and admiration on seeing my
esteemed correspondent Monsieur LeBlanc metamorphose
into this celebrated person, yielding a copy
so brilliant it is hard to believe”. He
then goes on to say that “number theory”,
which is the branch of mathematics Fermat’s
last theorem is part of, “is such a difficult
branch of mathematics, it’s really hard.
So when a woman, because of our sex, our customs
and prejudices encounters infinitely more
obstacles than men, in familiarising herself
with their knotty problems yet they overcome
these fetters and penetrate that which is
most hidden, she doubtless has the most noble
courage, extraordinary talent and superior
genius”. So Gauss really recognised that
actually Sophie Germain, in order to be able
to achieve what she had, recognised that she
really was something special. Unfortunately
Gauss and Legrange were not representative
of the whole male society of mathematicians.
Unfortunately and male society in general,
dare I say, of this period.
Mary Somerville, we are coming back across
the Channel. Mary Somerville was a scientist
who was very much recognised in her time.
I want to bring her in because one of my PhD
students, Brigitte Stenhouse, who unfortunately
can’t be here, is writing a PhD on her so
I am learning a lot more about Mary Somerville
than I knew before. We do see very glowing
accounts of her and I like this one by R N
Beverly, he was a pamphleteer really, he wrote
pamphlets on the depravity of the students
at Cambridge and things like that. So no wonder
he considers Mary Somerville the most eminent
mathematician in England at the present time
in 1833. Of course Cambridge was then, and
throughout the 19th century, the beating heart
of British mathematics. In the first two or
three decades of the 19th century, mathematics
in places like the Royal Society were definitely
at a low ebb. It wasn’t the high point of
British mathematics then. Towards the end
of the 19th century the mathematical physicists
get going and things change. There were lots
of things going on at this time about the
role of mathematics and mathematicians. Mary
Somerville was also an autodidact. She wrote
various books on science as well as on mathematics.
The book I want to draw your attention to
is The Mechanism of the Heavens which was
published in 1831. This was a translation
with extended commentary of the first two
books of Pierre-Simon Laplace’s great work
on celestial mechanics. Laplace’s work was
the successor to Newton’s Principia. So
what Laplace did was really add a lot of mathematics
and explanations. Again, very hard mathematics,
no diagrams and pretty impenetrable. The British
mathematicians were really struggling with
what Laplace had managed to achieve. It was
Mary Somerville who was able to unpack it
and put words around Laplace’s symbols and
make it accessible. Particularly it was made
accessible to the students at Cambridge. That
was a great tribute to her for them to accept
a text book effectively by a woman mathematician.
I include this little sketch of George Peacock,
as a little bit of self-publicity because
a. I think it is lovely but b. it is actually
on display at the moment in the Guildhall
Art Gallery in an exhibition ‘Sublime Symmetry’
which I have helped to curate. So if you are
wandering around the City of London and you
have a few moments to spare, its free, it’s
a wonderful exhibition. You will see this
lovely drawing of George Peacock by Augustus
de Morgan who was the first Professor of Mathematics
at what was the University of London which
became University College and then he was
the first and founding President of the London
Mathematical Society. He was a very good mathematician
and logistician.
The other reason I want to include Mary Somerville
is because of her relationship with the Royal
Society. She was the first women to publish
experimental results in the philosophical
transactions for the Royal Society and the
first and only woman to have a bust which
was commissioned of her which is placed in
the Great Hall at the Royal Society. But of
course she could not be admitted as a Fellow
because she was a woman. The first woman to
be admitted as a Fellow of the Royal Society
wasn’t until 1945, and the first woman mathematician
was 1947 Mary Cartwright. At the beginning
of the 20th century she was proposed for fellowship,
you have to be proposed by other Fellows,
so a number of men proposed her. But the Council
turned her down because they said she was
married and so has no status in law so she
can’t possibly be a Fellow. This is the
kind of institutional barriers that women
were up against. I think this is a lovely
picture of Brigitte, because many of you will
know, the Royal Bank of Scotland had a public
vote as to who they should feature on their
recent £10 note and Mary Somerville won the
vote. Brigitte went up to the HQ of RBS and
gave a talk about Mary Somerville. There’s
a picture of her with a rather large £10
note.
Ada Lovelace was mentored by Mary Somerville
so there is a connection with her there. She
has always been attractive to historians of
many flavours because she was the daughter
of Lord Byron. Byron left the marital home
when Ada was only a few weeks old and never
returned. She was taught basic arithmetic
by her mother. As you can see from this portrait,
she also came from a well to do family. She
married Earl Lovelace and she began a mathematics
correspondence course with Augustus de Morgan.
So I think of her as an early OU student if
you like. What’s nice is that you can read
that correspondence for yourselves. It is
now up on the internet freely available and
you can see transcriptions of the letters
and you can see the actual facsimiles of the
letters. The thing she is most famous for
is her commentary on Charles Babbage’s Analytical
Engine, the computer that he tried to build.
Again there is another story about that. I
think the correspondence is interesting because
you see her developing as a mathematician
and you see Augustus de Morgan as a really
patient and effective teacher.
Kovalevskaya was the first woman mathematician
that I really became interested in because
she features in my thesis. One of her results
was important to Poincaré. When I started
to read about her I found myself very attracted
to her because she wasn’t just a mathematician.
She was a writer, she wrote novels and plays.
She was also described as revolutionary. She
was a campaigner for women’s rights. I could
give you a whole lecture about her, but I’m
not going to, I’m just going to tell you
a few things. Just to outline her life to
show you what a pioneer she was. She was born
in Moscow. She wanted to study maths. She
eventually persuaded her family to let her
study. She again came from minor aristocracy.
But she couldn’t study further maths in
Russia. She knew she needed to leave Russia
in order to carry on her studies. But the
only way she could leave was if she had a
male companion, either her father who certainly
wasn’t going to go, a brother but she didn’t
have one. So the only other possibility was
a husband. She was very lucky because at that
time there was a bunch of Russian men who
recognised this dilemma for women who wanted
to leave, and were prepared to marry them
in order to escort them out of the country
with no strings attached. So it was like a
fictitious marriage. In fact, Vladimir and
Sofia did consummate their marriage seven
years later but at the time he was just a
travelling companion and she goes to Heidelberg.
While she is there she travels to London,
then she comes back and she studies with the
great Karl Weierstrass and does a PhD. She
is the first woman to get a PhD in modern
Europe. She is championed by a Swedish mathematician
called Gösta Mittag-Leffler and gets a position
in Stockholm, not without a lot of opposition,
Mittag-Leffler worked hard on her behalf.
She becomes the first woman to be an editorial
board of a mathematical journal and the first
woman to be Professor of Mathematics in modern
Europe. She sadly dies rather young having
caught pneumonia while travelling.
This is where the quote comes from which is
the title of my lecture. This is Kovalevskaya
herself reporting on the incident when she
is at George Elliot’s salon. She says “George
Eliot at once turned and said “I am so glad
you have come today she said, I could introduce
you to the living refutation of your theory,
a woman mathematician. Allow me to present
my friend, she continued, turning to me still
without mentioning his name, only I have to
warn you that he denies the very existence
of a woman mathematician. Try to make him
change his mind.” Apparently they discoursed
for a couple of hours or so and George Eliot
was rather pleased with the outcome. So she
doesn’t elaborate further on what went on
in the conversation. I thought that I would
point out also that perhaps not so well-known
is the fact that George Eliot was interested
in mathematics so that’s why she was very
pleased to meet Kovalevskaya. She studied
mathematics. It’s likely that she went to
one of Augustus de Morgan’s classes because
he taught at the ladies college. She was friends
with the great William Kingdon Clifford. Mathematics
appeared explicitly in several of her novels.
I’m just going to show you one example of
that from The Mill on the Floss which many
of you I am sure will be familiar with. So
when Maggie Tulliver visits her older brother
Tom when he is at school, she realises that
she finds Euclid more interesting than he
does. This is Maggie saying “Mr Stelling
couldn’t I do Euclid in all Tom’s lessons
if you were to teach me instead of him. No
you couldn’t said Tom indignantly. Girls
can’t do Euclid can they Sir. They can pick
up a little of everything I dare say said
Mr Stelling. They’ve a great deal of superficial
cleverness but they couldn’t go far into
anything, they are quick and shallow.” Well
of course George Eliot could do Euclid and
this was a parody of the kind of prevailing
thought about what certain men thought about
women. If you look through George Eliot’s
novels you will find several references to
mathematics and there are some nice articles
written about that.
Kovalevskaya’s fame was widespread. We see
that she made the front page of The Illustrated
London News when she got her Assistant Professorship
in Stockholm. There’s a lot written about
her, but when you read the contemporary accounts,
one of the things that is repeated again and
again is how beautiful she is. There is a
kind of sense of astonishment and this is
captured by the remark of the mathematician
James Joseph Sylvester’s assistant when
he saw Kovalevskaya’s photograph. Sylvester
corresponded with Kovalevskaya and it was
absolutely the standard practice. You exchanged
photographs. He said “Why this is the first
handsome mathematical lady I have ever seen”.
So this idea that if you were going to do
maths you couldn’t possibly be beautiful
or attractive. It was clearly fixed in people’s
minds what a woman mathematician should look
like, and they certainly shouldn’t look
like Kovalevskaya.
That brings me on to women in Cambridge where
I’ve done a certain amount of work. Girton
and Newnham are founded in the 1870s and women
start studying mathematics. Up until 1880
they could sit the Mathematical Tripos but
they had to get permission. They couldn’t
sit it by right. The Mathematical Tripos was
the most prestigious university examination
in Britain and had been for the whole of the
19th century. It was fiercely competitive.
Six days of five and a half hours of exams
day after day. Gruelling beyond belief. But
there was such prestige attached to it that
many men competed to be the top of the list.
The first class of the Mathematical Tripos
were known as Wranglers. It’s like the First
Class university degree now. If you were a
Senior Wrangler that opened doors to anywhere
whether you wanted to continue as a mathematician
or whether you wanted to go into the church,
or law or so on. People were just amazed when
in 1880 Charlotte Scott sat the Mathematical
Tripos and she was ranked equal to the eighth
wrangler. This was beyond what anybody had
imagined could be possible. The results of
the Tripos were reported widely always in
the national newspapers and in local papers
and so on. She was keeping good company in
fellow students, you can see the Senior Wrangler
was Joseph Larmor. He became Lucasian Professor.
That was Newton’s Professorship, Stephen
Hawking’s Professorship, the oldest and
most senior mathematics professorship in Cambridge.
The Second Wrangler was J J Thomson who won
the Nobel Prize for physics in 1906 for his
earlier discovery of the electron. I’ll
show you this, this was to emphasise the significance
of being Senior Wrangler. When Joseph Larmor
goes home back to Belfast there’s a torchlight
procession of university students and there
are fireworks and celebrations that go on.
One can’t quite imagine that happening now
when a maths student goes home and was top
in the exams.
This was a remarkable achievement but how
did the press receive Charlotte Scott. This
is The Spectator just after the results “Miss
Scott has answered papers set for the Mathematical
Tripos in a manner which would have brought
her high on the list of Wranglers, an achievement
of no common kind. We hope that the ability
which the new system brings out and fosters
in women, will not be of a kind to give to
those who possess it, a character for deficiency
in feminine gentleness. We do not believe
that it will be so, but even in the rare cases
where it is so, the world should remember
that there have always been women of the masculine
type only that they have hitherto lacked the
means of proving what they could do though
possessing amply the means of proving what
they could not be.” So again we get this
emphasis on what women mathematicians look
like. You can read the reports about Charlotte
Scott. She did go on to have a distinguished
career but not in Britain. There was no way
she would get a Professorship in Britain at
this time. After she did the Tripos she did
stay on and lecture at Girton for a while
but then there was an opening at Bryn Mawr,
a new college for women in the United States,
and she was the founding Professor of Mathematics
there. She went on to have a very distinguished
career. She wrote very good papers in geometry,
published books in geometry, supervised PhD
students and was very active in the American
Mathematical Society. That was a career that
just would not have been open to her in Britain
at the time.
If she caused a stir then Philippa Fawcett
really caused a stir because ten years later
she was above the Senior Wrangler. People
had started to think that maybe women could
be capable of doing a certain amount but to
be above the Senior Wrangler. We see the Tripos
list is reported in The Times there. You see
the top of the list is a Dr Bennett, that’s
the Wranglers. Of course the women are not
listed with the men. They are listed underneath.
Although it does say she is above the Senior
Wrangler, she is clearly below. This was a
time when women could not get degrees at Cambridge.
They couldn’t get degrees at Cambridge until
1947. It’s really quite shocking. When Philippa
Fawcett became above the Senior Wrangler that
was a push for people to try and move and
get things changed. Of course there were a
lot of men who were supportive of women. Remember
these women were studying at Girton and Newnham,
and they had to be taught their mathematics
by someone. There were a number of the Cambridge
lecturers who went to Girton and Newnham to
teach them because the women could not go
into the lectures with the men. So there was
quite a considerable support, but there was
not enough. Even in 1920 when Oxford opened
its doors to women and gave them degrees,
that was a great argument the Cambridge women
thought for them to have degrees. But it came
back no, if you want a degree go to Oxford.
There was such a prejudice. I can’t underline
that enough really.
Philippa Fawcett was celebrated in the popular
press. There was a report about her triumph
in The New York Times. This was the first
verse of a ditty that was written about her
“Hail the triumph of the corset, hail the
fair Philippa Fawcett, victorious in the fray,
crown her queen of hydrostatics and the other
mathematics, wreath her brow in bay.” This
is a cartoon from Punch where we see her as
the Signora Fawcett because she’s Seniorora
than the other wranglers.
Moving on to World War One things change for
women dramatically because of conscription
and the number of men who left to go to the
war. There were jobs that needed to be done
by women. There were women mathematicians
who contributed to the war effort. One of
those women was Hilda Hudson. She came from
a mathematical family, her father was a mathematics
professor, her mother had studied mathematics,
she had a sister who had also studied mathematics
and was also equal to a high wrangler. She
quite unusually goes to Berlin to do some
studying. She is the only women to give a
lecture at the International Congress of Mathematicians
when it was held in Cambridge in 1912. She
goes over to Byrn Mawr and sees Charlotte
Scott. Then she gets a job at the West Ham
Technical institute. When the war breaks out
she does some war work. I want to draw attention
to her because my student Tony Royle has done
some very nice work indeed on the role of
women during the First World War, particularly
those working in the Admiralty and within
aeronautics. Hilda Hudson got an OBE for her
work and she published on the work that she
did.
You can’t talk about the history of women
in mathematics without mentioning probably
the most talented woman mathematician of all.
I don’t like putting somebody right at the
top of the pile, but it’s pretty hard with
Emmy Noether not to. Her work in abstract
algebra, completely changed it. She was the
daughter of a mathematician, she gave a plenary
address at the ICM in 1932. She was at the
University of Göttingen and of course being
Jewish she was expelled from her position
in Göttingen in 1933. She then goes to Bryn
Mawr and sadly dies young unexpectedly after
an operation. There’s a lot we could say
about her, but there are two main things.
One is that in 1915 her theorems which connect
conservation laws and symmetry’s which is
when she did the work were published in 1918.
So it’s the centenary this year. These are
incredibly important theroems for physics.
I think the thing she is most famous for.
There is a meeting at The London Mathematical
Society and the Institute for Maths and its
Applications in September this year, which
I am helping to organise, so this is another
bit of self-promotion here, to encourage you
to go to that. The thing I want to show is
some work done by my partner Reinhard Siegmund-Schultze
who has been working quite a bit on Emmy Noether
and he has uncovered some new manuscripts.
This is quite an interesting episode I think.
In September 1928 the Chair of Mathematics
at Keele became vacant and Adolf Fraenkel
who was at Keele and his friend Helmut Hasse
who was at Halle, are in the position of discussing
the possible candidates. The actual decision
is made by the Prussian Ministry. So you see
them in this correspondence going through
the different candidates. When they get to
Emmy Noether this is how the conversation
goes “There is no doubt that as a man she
would have received a call a long time ago.”
This is Fraenkel. Then Hasse says “I am
astonished that you even seriously consider
this possibility. Although I regard her highly
in scientific matters I deem her totally unfit
to fill a regular teaching position. Even
less so in a small university like Keele.
I am of the opinion that one should not make
the experiment to appoint a woman as a full
Professor as such a place as Keele. The experiment
should be tried first on a bigger scale where
an unsuccessful outcome would not do so much
harm.” Anybody who knows anything about
Noether’s mathematics will find this really
quite astonishing. Now it has to be said she
did not have a reputation as a brilliant teacher,
but then I guess most of us have also been
taught mathematics by one, but I don’t think
we would object to being taught by Emmy Noether.
If you want to read more about this, this
is in the most recent edition of the LMS newsletter
which is freely available online.
Almost finally on the historical part I just
want to make a glancing reference really to
the women codebreakers at Bletchley Park,
who Churchill famously described as ‘the
geese that laid the golden egg but never cackled’.
That description applies really absolutely
to Margaret Rock. I suspect that not many
people have heard of Margaret Rock. We’ve
all heard of Alan Turing and we’ve heard
of a number of mathematicians there. But Dilly
Knox who was in charge of the Cryptography
Department at the beginning of the war described
Miss Rock as the fourth or fifth best of the
whole enigma staff and quite as useful as
some of the Professors. I think one of the
reasons that we don’t know about her is
because she never cackled. She never ever
told her own story. So it’s really difficult
to know what she did do. I think this is true
of quite a lot of women mathematicians. I’m
not for a minute trying to say that there
was as many brilliant women mathematicians
as there were men, but I am saying there are
many stories to be uncovered and many roles
that women played in mathematics that have
stories yet to be told. I think there is a
responsibility on us as historians to try
and uncover them and to tell those stories
and to encourage the next generation of women
by telling those stories.
Coming right up to the present day, a wonderful
event happened in August 2014. Maryam Mirzakhani
won the Fields Medal. The Fields Medal is
what people loosely describe as the equivalent
of the Nobel Prize in Maths. The main difference
is that you can’t win a Fields Medal unless
you are under 40. That of course conspires
greatly against women particularly if they’ve
had time off to have a family. It was wonderful
that Maryam Mirzakhani won the Fields Medal.
Tragically even at the time she had cancer
and she died last year. But she’s a fantastic
role model and inspiration to women mathematicians
of our generation. We have the next ICM, because
the Fields Medal is always presented at the
International Congress, is in Rio this summer
so we are all hoping that the Prize Committee
will find another woman who will also blaze
a trail as Maryam Mirzakhani did.
So just to conclude I just want to give you
some figures about the place of women mathematicians
in the UK today. We see at degree level, unfortuantely
it’s quite difficult to get up to date figures,
but this was the situation in 2011, that 56%
male, 44% women, that’s not so bad but then
when you right to the other end in 2011 and
you get to Professors 94% men and 6% women.
So we have what’s called the leaky pipeline,
it just gets less and less women. We do have
some information a bit more recently. So in
2016, you can see that the percentage of women
has gone up to 9% so in real terms it’s
only a 3% increase but it’s a 50% increase
on what it was before. So we are making progress
but it’s still very slow and we need to
do more. There is work being done. There’s
very important work being done by the London
Mathematical Society and particularly it’s
Women in Maths Committee which was chaired
for several years by Gwyneth Stallard who
is here, and who was rightly awarded the OBE
for her work in supporting women in mathematics.
The Committee won the Royal Society Athena
prize for the work that they’ve done. The
Athena SWAN Charter which was established
in 2005 is a way of encouraging mathematics
and scientific departments to address this
question of the leaky pipeline, to help women
progress to senior roles and the School of
Maths and Statistics here have been awarded
the Athena SWAN Bronze Award and Gwyneth has
chaired that committee. I was very pleased
to be a member of that Committee along with
my student Tony Royle as well. We are now
pushing forwards and hoping we will get a
Silver award next time. So there is a lot
of good work being done but there still needs
to be a lot more. I would encourage all of
you to engage with this particular issue.
That’s my final slide.
 
Lucian: That was an excellent Inaugural Lecture
June, thank you very much. Perhaps you would
like to join me for taking some questions.
Now is the time for your questions here and
of course for those who have joined online.
Please indicate if you would like to ask a
question and we will make sure the microphone
gets to you. Could you kindly say who you
are and where you are from.
John Pearson: I used to tutor MA290, I regret
that there is no replacement History of Maths
course in the University at the moment because
it was a very enjoyable course to teach and
it’s sad to me that there is no replacement
now. As we have a Professor of History of
Mathematics, it would be nice to actually
have students at the Undergraduate level as
well.
June: It’s a great sadness to all of us.
It’s to do with the way the curriculum has
evolved, we do have a History of Maths course
at the Masters level in the dissertation.
Another bit of shameless publicity is that
the MA290 course is being rewritten by Robin
and Jeremy and me into book form and the first
volume is at the publishers. The second volume
should be at the publishers and hopefully
the first volume will be ready by the end
of this year. As you will know with that course,
it had a reader and we are incorporating the
extracts from the reader into the volume.
So even if we can’t actually teach undergraduates
we will have a resource for undergraduates.
From social media: Thank you very much, lots
of warmth and really welcoming comments coming
in from online and also for your ‘her story’
joke too Lucian, lots of love for that too.
So from Sundash on Facebook: What has been
the greatest shift in attitudes towards women
in mathematics in the last 50 years and what
was the catalyst for it?
June: I think the greatest shift has been
really coming through initiative. Things like
the Women in Maths Committee at the London
Mathematics Society, the recognition of the
leaky pipeline. Really before then it was
somehow expected that there weren’t so many
women, suddenly people have realised actually
this is a huge resource we are really missing
out on. We need to do something to address
this issue of implicit bias. A lot of men,
particularly in the last 50 years weren’t
excluding women it was a bit of a boys club.
We all know how clubs work. It was a bit like
those gentlemen’s club in St James, it was
recognising the problem and then looking at
ways of addressing it. I think we can see
that by the fact that the numbers are edging
up and that particularly with the Athena SWAN
Charter that that has really galvanised people
and one of the things that is really going
to be the game changer is when the funding
body stops giving funds to departments that
don’t have the Athena SWAN Charter. So people
really have got to engage with this issue
and realise that they are losing a great resource.
Barney: I’m June’s nephew. When I studied
the History of Archaeology I saw a similar
issue where you had women very under represented
for a long time. But now that has reversed
and women are in fact over represented. Mathematics
seems to have somehow developed severe structural
issues that have prevented Maths from taking
on a similar trend. Why do you think these
structural inhibitions have lasted longer
than in other fields?
June: That’s very interesting Barney. I
didn’t actually know that that was the situation
in archaeology. One of the reasons I think
for mathematics particularly is that if you
are doing research in mathematics then you
really need to be able to have a continuous
go at it. If you for some reason stop, for
example having a family, somebody else might
actually prove that theorem that you have
been trying to prove. It’s a slightly unusual
thing about maths, whereas in other disciplines,
particularly for me as a historian of maths,
people know that I work on Poincaré or Birkhoff.
If I go away for two or three years people
still know that’s my turf, there’s plenty
of other turf to dig up. Maybe that’s the
case in archaeology but in maths it isn’t.
That’s one of the really big things that
all these moves with Athena SWAN and so on
are trying to address, so that if women do
have time out they are kept in the loop and
there are things that are done to enable them
to continue their research.
Mangea: I was wondering in your work if you’ve
come across any women of colour in the history
of mathematics in say India or China or somewhere
like that. What’s the situation of women
of colour in mathematics today?
June: I personally haven’t, I have colleagues
who worked in this area in the States in particular.
Many of you will be aware of the film Hidden
Figures which really shows very dramatically
how women of colour as mathematicians were
really not appreciated. But I haven’t in
my own work come across any. I have done some
work on the mathematics in India from the
colonial perspective and certainly there were
male Indian mathematicians who came over and
studied here. The period I was looking at
was the late 19th century, early 20th century
but I didn’t come across any women. Of course
there’s the famous story of Ramanujan as
the men’s story as it were. But I think
actually there certainly has been work done
on that but I’m afraid I haven’t been
the person who has done it.
Bashar Nuseibeh: I’m from the Computing
and Communications Department. You mentioned
Ada Lovelace who is very well known in computing
circles as one of the founders of computing.
I wonder if you can say something more about
the relationship between the evolution of
mathematics into applied fields like computing
which might address some of the issues you
were talking about and where they can be founders
in the field and make bigger contributions.
My instinct is that we are still also having
problems in computing as well in getting more
women into computing. I am just wondering
if it’s a discipline issue or just a general
problem we have in society.
June: The computing story is rather different
actually because of course initially computers
were people. Often they were women because
it was just doing a lot of arithmetical calculations.
A lot of it would be piecework. So you would
get women in that sort of computing. Ada Lovelace
is certainly a singularity if you like because
of her insights that she had when she wrote
about Babbage’s Analytical Engine. That’s
what’s so remarkable because of course this
machine was never realised but she could see
the potential. She came from that class where
she was able to do that. She went to soirees
with Babbage and people like that. You know
better than I do about the evolution of computing
as a discipline. I think the story is different.
When computing starts to become more as a
discipline within an academic environment,
you get more women initially into it until
men come and take over. I think it’s a very
different story and again it’s not a story
that I’ve really worked on but again there
are people certainly who have worked on that.
Lucian: With all your study, you’ve really
brought it to life, it sounds very inspiring
to you and to all of us hearing those stories
about all these women who have made such an
achievement in their day, have you formed
a view as to what the combination of qualities
most of them have to have had to have been
successful in their day. Does that serve as
any indication as to what kind of combination
of qualities a woman might need to have now
either who is studying mathematics and wants
to make advances or is considering studying
mathematics.
June: The real answer, particularly for the
women of the 18th and 19th century, the most
important thing for them was to have men to
champion them. The fact that they had fathers
who supported them in their endeavours to
do mathematics, we see the same with Charlotte
Scott and Philippa Fawcett their family environments
were such that they weren’t prejudiced against
women, it was just the majority of society
was. I think that’s really the case and
particularly the women in the earlier period
where you certainly had to be from a certain
class to be able to afford to study, but again
you didn’t have entry into the professional
arena. I think it’s hard to draw anything
in that respect. Having said that these women
still had to really work hard to prove themselves.
Even though their parents were supporting
them, or maybe their brothers, there was still
people within their social environment who
would not. So they would still be fighting
their corner. I think women mathematicians
today still have to fight their corner sometimes.
I think the climate has changed but women
need to be out there and spreading the word
and saying you don’t have to be a women
of the masculine type to do mathematics. There’s
absolutely no difference in ability between
men and women to do mathematics. We understand
and recognise that now. We have to make sure
that everybody understands and recognises
it.
Lucian: Thank you, a brilliant way to end
the evening. Another round of applause please
for June. There are of course opportunities
here at the OU to study the curriculum related
to June’s topic. There are some relevant
courses listed on the slide displaying now.
This is just one of the many topics that The
Open University engages with. Our next Inaugural
is ‘Making new ways of organising out of
the old’ by Professor Richard Holti who
is Professor of Professional Learning at the
OU’s Faculty of Business and Law. Details
are on the OU Research website homepage. Thank
you very much all of you for joining us here
and at home or wherever you happen to be this
evening. Please join us for those of you who
are here downstairs for a drink and a safe
journey home afterwards. Thank you very much.
