The history of women and maths | 91TV
Transcript
- June Barrow-Green: Thank you very much for that lovely introduction. It's a real pleasure to be
- here. Actually, it's just wonderful to have an audience, so many people I know! So thank you
- so much for coming. I really want to thank the Royal Society for awarding me this prize. I feel
- extremely honoured for my work to be recognised in this way, and especially for it to be connected
- with the name of John Wilkins, one of the founders of the Royal Society and with that of JD Bernal
- and Peter Medawar to such distinguished scientists and brilliant communicators.
- So the motivation for my topic comes from work I've been doing on the history of the gender gap
- in mathematics. It's well-known that not enough women are attracted to mathematics, and although
- the work of many different constituencies have really helped to make the situation much better
- than it used to be, there still remains a problem. The fact that women are not going into or staying
- in mathematics at the same rate as men means that a lot of mathematical talent is going missing.
- While strenuous efforts are being made to counter this, historical
- research shows not only how deep rooted the negative image of women in mathematics is,
- but also how some of those negative images are still in evidence today. I think looking
- at these images in the context in which they were created provides us with a different way to open
- up the discussion about women in mathematics. So in my talk, I'm going to show you images of
- women mathematicians as well as descriptions of them both real
- and fictional, they'll not only be examples of how women mathematicians are being viewed by others,
- but also how women mathematicians have viewed themselves. So let me start with some numbers.
- Within mathematics in the UK, currently women account for about 40 per cent doing A-level.
- There's a bit of a drop off when you get to university, 37 per cent of undergraduates
- are women. There's a large drop off going to postgraduate study with only 21 per cent of PhD
- students and then another large drop off when you move up to professorial level, only 12 per
- cent. This data comes from an article that was published in March this year in The Times Higher
- by Ulrika Tilman, who I'm delighted is here today, who's president of the London Mathematical
- Society. Rachel Norman, President of the Edinburgh Mathematical Society, Sylvia Richardson, President
- of the Royal Statistical Society, and Alison Etheridge, Chair of the Council of Mathematical
- Sciences. It's actually remarkable that all these four positions are held by women simultaneously.
- To give you some context, I looked back into the history and those positions through history.
- Those four aside, only eight other women have ever held any one of those positions. So I think we are
- at a really, it's a good moment in that respect, but there's still a lot of work to be done.
- Of course, I should mention that internationally we have some considerable success with the
- Iranian Maryam Mirzakhani winning the Fields Medal in 2014 and the American Karen Uhlenbeck winning
- the Abel Prize in 2019. These are the two of the highest awards you can get in mathematics. As
- my running friend say to me, you've got to be in it to win it. We need more women in mathematics.
- So let me move on to some images now. my story is going to be a chronological one. I'm not going
- to give much biographical information, but just enough to what I need for the representations. So
- my first example here is Hypatia. She was a Greek mathematician, philosopher, 4th, 5th century,
- and she taught mathematics, philosophy. Her father was a mathematician. She was
- reputed to have helped him with his edition of Euclid's Elements and his commentary on
- Ptolemy's Almagest, and she also did commentaries on work of the great Hellenistic mathematicians,
- Diophantus and Apollonius. She's probably most famous for the fact that she died at the hands
- of… A brutal death at the hands of a mob of Christian monks, and thus became an icon
- for various causes, and as a consequence there is a proliferation of images of her.
- So here I've shown four images. Now they purport to be Hypatia, or at least this is what Google
- will tell you. So they're clearly not the same person. So which if any of them is Hypatia. Well,
- you won't be surprised to know that none of them are. The one on the left comes from Pompeii. So
- that's some 300 years before Hypatia lived. The next one, Raphael, this comes from his
- great fresco, The School of Athens. it's one of the figures there that has been only latterly
- identified as a Hypatia. So Raphael himself did not consider… We don't know who he thought he was
- portraying with this particular figure. Then we move to the early 20th century and that's a French
- American artist, Gaspard, illustrating a novel by Hubbard. then this very extravagant Victorian
- image on the far right is by Mitchell. That illustrates the novel by Charles Kingsley,
- probably better known to many of you as the author of the Victorian fairytale The Water-babies.
- So you might well be wondering, well, why am I showing you these images if none of them are of
- Hypatia. Well, for two reasons, I think to state an obvious one, we should be clear. I think when
- we show images what their origins are, why we want to show them, what is the purpose of showing them.
- Also because of course, it is interesting to see how non-mathematicians and particularly non female
- mathematicians portray female mathematicians. If we move on to a millennium really to the
- medieval and Renaissance period, we don't so much find images of women mathematicians,
- but rather women as muses for the mathematical arts of the quadrivium.
- Here's a medieval image showing arithmetic represented by Pythagoras, geometry by Euclid,
- music by Tubalcain, and astronomy represented by Ptolemy. The mathematicians are on the left hand
- side and the muses are on the right. Now this image is something you can again find easily
- on the internet but you can't find or I couldn't find where it comes from. So how could I be sure
- that it really was a medieval image? Also, it was rather strange that it has this black background
- and I was very fortunate. I've been looking for a long time, but a chance encounter on a train
- with a young woman who helped me secure my bike rather more safely, on a train to Oxford,
- turned out to be a medievalist, so I took my chance with her and asked her. Although
- she didn't know the answer, she said, I know the person who will. Sure enough, I found the answer.
- So it comes actually from this manuscript from 1340, which is
- a manuscript of a text that was it was originally written some hundred years earlier. It's a German
- text, has the name in English as the Italian Guest, and it's an illustration of the seven
- liberal arts. So the four arts of the quadrivium and you can see so they've been extracted out
- to make this bigger image. Then the three arts of the trivium rhetoric, grammar and logic.
- We can find plenty of images of the seven liberal arts. I've got one here which is from the workshop
- of Porcellino, and in this one rather different to the previous one. The muses are much more dominant
- and they're labelled and you can see them by their attributes with
- arithmetic, with counting boards and so on. The mathematicians, the practitioners
- are much smaller in the foreground. We also find individual images, this is quite a well-known one,
- this one Typus Arithmetica which comes from Gregory Reisch, Margarita Philosophica.
- Here we see Arithmetic in her red dress and she's presiding over a contest between
- Pythagoras looking rather glum in blue with his counting board, and then Boethius on the
- other side with the new Hindu-Arabic numerals. So this is sort of an example that shows us that
- how mathematics is developing. Actually we also need to know that this is a very anachronistic
- image because Pythagoras, if indeed he existed and that's another whole question for debate, was
- Greek and lived in around 600 BC, whereas Boethius was Roman and lived nearly a thousand years later.
- So now let me move on to. To introduce my first female mathematician, Maria Agnesi, Italian
- from Milan. She was the first woman really in the modern period to make a substantial contribution
- to mathematics by publishing this textbook in 1748 on the differential and integral calculus,
- which she wrote to help with the education of her younger brothers. and unusually it was published.
- It was written in the vernacular, so it had a wide circulation and really helped promote
- the calculus in Italy. As a result, two years after its publication, she was made a professor
- of mathematics in Bologna by the Pope. She never actually went to Bologna. She never took up the
- position. She spent her life in doing charitable works after this. There also were translations
- published one in French in 1775 and one in English in 1801. It's the French translation
- that I really want to draw attention to, rather than this actual image of her,
- which nice though it is, it doesn't tell us anything about her as a mathematician.
- When we look at what the French historian of maths, Jean-Etienne Montucla said about Agnesi
- in his history, he cites her with praise. He's very enthusiastic. He says, well, this is,
- it's a great work that she's done. It's been translated into French. he queries,
- why wasn't that done by a French woman mathematician? Then he says,
- 'It's not without astonishment that we see a person of a sex so little made to brave the
- thorns of science,' the title of my lecture, 'able to penetrate so deeply into all parts of
- mathematics.' So if we actually read this carefully, what he's saying is it's remarkable
- that she did this because she's a woman, because women weren't made to do this kind of thing.
- That somehow is she an aberration of nature or whatever? I mean, that's a bit extreme,
- but it's very much that's what's remarkable about it. It's the fact that as a woman
- not made to do mathematics or science and we'll see this coming up again.
- Of course, the French woman that he's… Lady mathematician that he mentions here,
- some of you will have guessed I'm sure is the Marquis du Chatelet. Emilie du Chatelet. this
- fantastic portrait which I just absolutely love by La Tour because we see Emilie du Chatelet
- absolutely confidently presenting herself as a mathematician with her astrolabe in
- the background, her dividers or compasses and her geometry text. We have no doubt
- that she wants us to see her as a mathematician. We also have no doubt that she comes from
- a very well-to-do background. She's minor aristocracy. She basically was self-educated,
- but she also studied with two of the leading French mathematicians of the day,
- Maupertuis. She translated Newton's Principia. I'll say more about that in a minute.
- she had this longstanding relationship with Voltaire, which was both personal and scientific.
- Indeed she was a muse for Voltaire, and that's completely evident. Voltaire himself in his book
- on Newton's work. It was a book which was to popularise and make Newton's work, some of his
- ideas available to the French public. Newton had published his Principia in 1687. It was a fiercely
- difficult work, and there was a great need for some of his ideas to be made more accessible.
- Voltaire could not have done this on his own. It was Emilie du Chatelet who was really instrumental
- in enabling Voltaire to write this book. He makes no bones about it. He dedicates the book to her,
- but this frontispiece on the right-hand side shows Newton up in the clouds. We see du Chatelet
- holding a mirror. Then down on the ground is Voltaire scribbling away, there's Emilie du
- Chatelet. She's the conduit for Newton's ideas to get to Voltaire. Then we also see there's another
- portrait of her again. She's showing herself to be a mathematician with an astrolabe and
- with her compasses. This is the work for which she's really well known as a mathematician. Her
- translation of Newton's Principia and where she we know how good she was because of the
- commentary that she writes with the translation, because it's not just a straight translation.
- Rather tragically, she died shortly after she finished it. She was heavily pregnant and she
- shortly after she gave birth, she died. It was only published posthumously
- ten years after she died. If we also there are other images of her
- and this is one which is quite different. This is Francesco Algarotti, Italian mathematician.
- He visits du Chatelet in 1735. Two years later he publishes his own work on
- Newtonianism for the Ladies. It's about Newton's optics and it's done in… He presents the material
- as a dialogue between a French chevalier and a marchioness over five days. The man is very
- definitely teaching the woman, and it's been… Everybody has agreed that this particular picture,
- which is the frontispiece, is supposed to represent Algarotti teaching du Chatelet. In fact,
- we know absolutely the opposite was the case. Algarotti was happy to make you think otherwise.
- So here we have Elisabeth Ferrand, not a mathematician, really a philosopher
- who had a salon in Paris. She entertained and she had many mathematicians who were
- associates of hers. I wanted to show this image because again, it's a beautiful portrait by La
- Tour. We have in the background very clearly what is supposed to represent Voltaire's
- edition of Newton. It's a bit bigger in the picture than it would have been in reality,
- but what I think it really confirms for us that in enlightenment France, we see women who are
- absolutely able to feel they can be confident in discussing mathematics and presenting themselves
- as mathematicians, and engaging in scientific discourse. Now, of course, they can't do that in
- places like the academies or universities. Those are those are only open to men. Nevertheless,
- this is perhaps quite surprising to see. I think both of these La Tour portraits are really,
- I find them extremely attractive and they're beautifully painted, but I think they really
- tell us something very interesting. We don't have to go much further,
- staying in France to see if we look at the work of Sophie Germain, who was
- self-taught. She read books in her father's library, wanted to learn more mathematics. What
- could she do in Paris at the turn of the 19th century, the Ecole Polytechnique was where you
- went to learn mathematics. Women could not go there, but the Ecole Polytechnique did publish
- their lectures, so she was able to read what the students were learning. She wanted more. So she
- wrote to one of the leading mathematicians there, Lagrange, but she wrote under a male pseudonym,
- Monsieur LeBlanc, a former student, and engaged in discussion with him. Actually, they then met,
- To Lagrange's credit, he wasn't put off by the fact that she was actually a woman
- and she went on to some great achievements, being the first woman to win a French Academy Prize,
- for instance. Also, her theorem, which was Sophie Germain's theorem, relates to Fermat's
- Last Theorem, the very famous theorem proved by Andrew Wiles in the 1990s and from a conjecture
- of Fermat's back in 1630, and this was in the area of mathematics of number theory.
- That's what I want to really concentrate on here because this is the real reason I want to bring
- her to our attention. This is this is a bit of the good news of my talk because this is
- Gauss. Carl Friedrich Gauss, one of the leading mathematicians of the day and actually ever
- probably ask any mathematician and Gauss would come up as kind of one of their top five. He
- was in all kinds of mathematics and astronomy and things. He was really great achievement. So
- Sophie Germain writes to him because it's number theory and he's the leading number theorist and
- she's working on her number theory and she writes to him and again she writes as Monsieur LeBlanc.
- Then Gauss discovers that she's a woman. What he says is in really quite, I think, stark contrast
- to what Montucla said because he's completely astonished and he's full of admiration because
- he says number theory is really hard. He says, 'But when a woman, because of her sex,
- our customs and prejudices, encounters infinitely more obstacles than men in familiarising herself
- with their knotty problems, yet overcomes these fetters and penetrates that which is most hidden.
- She doubtless has the most noble courage, extraordinary talent, and superior genius.'
- So what he's saying is not that she's not made to do maths, but that actually men have made it very
- difficult for women to do maths. That's what's remarkable, that she's actually able to do this
- very hard mathematics. Because she's overcome the barriers that have been put up for her by men.
- Now I'm going to move to the Royal Society. Here we have a bust of Mary Somerville,
- which is upstairs. Mary Somerville was the leading woman in science in Britain
- in the 19th century. In fact, she was so well known, she appears in Queen Victoria's journal.
- She was the second woman to have a paper published by the Royal Society.
- Her Mechanism for the Heavens, published in 1831, was her interpretation of the work of
- the French mathematician Laplace and Laplace. His mécanique céleste was really the next
- stage on from Newton's Principia. What Laplace does he throws the whole machinery of the calculus
- at the kinds of things that Newton had done in the Principia and but which he hadn't used the
- calculus for, despite being the one of the people who was responsible for creating discovering it.
- What Somerville does is she makes Laplace's work intelligible to the audience in Britain
- and is rightly celebrated for it. She also writes many works of popular science. I should
- say at this point that just about everything I know about Mary Somerville I know through my
- former student Bridget Senhouse, who I'm very delighted is here today.
- I really urge you to read her PhD thesis, which has thrown really new light on Mary Somerville.
- So let me move on to some comments about Mary Somerville. We have William Whewell, one of the
- major figures in Cambridge in the middle of the 19th century. He's a real polymath. He's physics,
- maths, philosophy, geology, ends up being master of Trinity and he's writing a review
- of one of her popular books and he says this about her. He says that, 'She's one of the
- brightest ornaments of England, only women in our own time really, who can study maths.'
- In the context of this he also says, 'Well, actually there have been very few women
- mathematicians, in fact there are really only two that are worthy of entirely honourable notice.
- Hypatia and Agnesi and both were very extraordinary. Madame du Chatelet's whole
- character and conduct have not attracted to her the interest which belongs to the other two.' So
- here we have a very different standard, I think, being applied for a woman mathematician. There is
- no doubt in my mind at least, that du Chatelet was at least equivalent to Hypatia and Agnesi.
- I now want to look at some portraits of Mary Somerville. This is one by Thomas Phillips,
- one of the leading portrait painters in Britain in the first half of the 19th century.
- We can see here we can see that she is a woman of certain substance, of a sort of upper class.
- A mathematician you would have no idea. This is not at all like the du Chatelet portrait. So why
- is this? Why? This portrait was commissioned by her publisher after the Mechanism of the Heavens,
- when by which time she was well known and being feted for her abilities. was it because this just
- was not being done in Britain? Well, I do have one slightly disingenuous example. This comes from a
- text, a textbook on astronomy by Margaret Bryan. This is the frontispiece. She was definitely
- trying to sell her book to younger readers. So one should bear that in mind. Nevertheless,
- we still have a portrait here of a woman with her scientific instruments.
- Well, perhaps Thomas Phillips just didn't like painting attributes and things. Well,
- that's not true either, because we see here these very, I think, lovely portraits of Humphry Davy
- with his Davy lamp, and Michael Faraday with his Cruickshank battery. So Mary Somerville sort
- of stands out in these three as not showing any evidence of scientific endeavour. Maybe an answer
- is here. This is a manuscript draft. It wasn't published, when she was nearly 90, Mary Somerville
- started writing her autobiography, and it gets published after her death by her daughters,
- her recollections. This is part of the manuscript draft, but this bit never gets published.
- What we see here is her saying that she was really gratified by the way she was received by great men
- of science, people like Herschel and so on. She was less elated than she might have expected.
- The reason for that was she said she was conscious she had not made no discovery herself.
- She felt she had no originality. She had perseverance, intelligence,
- no genius. 'That spark from heaven is not granted to the sex, we are of the earth, earthy,
- whether higher powers may be allotted to us in another state of existence. God knows, original
- genius in science at least is hopeless in this.' So is this a really early example of imposter
- syndrome? I think I find this rather sad really, because she really, what she achieved was
- remarkable, and just as remarkable as the other women I've already mentioned.
- Here we have another portrait of her, a self-portrait given to Somerville College
- in Oxford by one of the members of her family. I thought, oh, I'll go and look at the
- catalogue for early Victorian portraits, which was published in the 1970s. Here we see the
- description, which is a painting by an unknown artist. The donor describes it as self-portrait,
- but it appears too fluent and sophisticated to be the work of an amateur. So how can this be? Well,
- my conjecture about this is that the author just didn't do his research because as a young girl,
- Somerville attended the classes of Alexander Naismith. She talks
- about this in the recollections. These landscapes are in Somerville College.
- To me, this kind of belies the sort of attitude that was prevalent in the '70s about how could a
- woman who was known to be a scientist possibly be an artist as well? I think this thought had
- just not occurred to the author. I think this shows the kind of attitudes that were
- prevalent at the time. I have another rather more shocking example in a minute.
- So Ada Lovelace, well-known. She was mentored by Mary Somerville, daughter of Lord Byron, so
- very attractive to people to want to write about and talk about and so forth. We have a portrait
- of her here, very much a society portrait, 1835, before her famous paper that she wrote in 1843,
- which was a translation of Menabrea's work about Charles Babbage's Analytical Engine.
- What Lovelace does is, she writes, she doesn't just produce a translation,
- she writes a commentary and she shows she really understands the Analytical Engine. More than that,
- she shows what potential she thinks this engine has for the future. It is a remarkable document.
- How has she been received over history? Well, when we look at what has been said about
- her in the 19th century, perhaps not so surprising when she dies. Obituaries tend on the hagiographic
- side she's described as a genius. Twenty years later, William Farrer, the epidemiologist,
- agrees and says, great knowledge of analysis, and Menabrea, the author of the original text
- agrees and so on. So there her reputation is here, very much intact as a mathematician,
- computer scientist, we might say today. What happens in the 20th century
- is we get a bunch of people completely disputing this. This is perhaps the most extreme example,
- which is why I'm showing it! These authors felt that actually it wasn't really Lovelace
- who had written the commentary and that it was really basically Babbage
- and Collier in 1970 writes, 'It's no exaggeration to say she was a manic depressive with the most
- amazing delusions about her own talents are rather shallow understanding of Babbage
- and his engine. Mad as a hatter, contributed little more to the notes than trouble.
- Well, I guess someone has to be the most overrated figure in the history of computing.'
- So how can this be? It's completely the opposite to what we've just heard about her in the 19th
- century. Well, of course, I'm happy to say that we now have an answer to this. The
- reason we have an answer to this is through the work of Chris Hollings, Ursula Martin and Adrian
- Rice. I'm delighted that Ursula is here today. That they actually looked at the manuscripts
- really carefully. In particular they analysed the correspondence between Lovelace and Augustus
- De Morgan, and Lovelace was having almost like correspondence lessons with De Morgan
- and De Morgan was the Professor of Maths at UCL. One of the leading figures in
- British maths at the time, he goes on to become president of the London Mathematical Society.
- The first president and what they have done is they've really gone through and not only looking
- at this correspondence, but they've looked at all what other people might have considered as
- doodles and mere scribbles and things, and they've recognised it for the mathematics that it is.
- So what they what they have shown is that actually in the 20th century there was an misunderstanding
- of mathematics, but there was also a kind of bad ordering of the correspondence, which kind of led
- to a complete sort of misinterpretation of what she achieved. The fact that Lovelace actually died
- quite young. So as they say, it's the contrast between mathematics she actually wrote and her
- mathematical potential that has fuelled much of the debates regarding her mathematical ability
- and I really urge you to go and look at. It's freely available on the web
- to go and look at the correspondence, and they've even transcribed it for you so you don't have to
- battle with the handwriting, which actually isn't too bad. So you can see how we can get very
- different descriptions of women mathematicians. I'm now going to move to the latter stages of
- the 19th century and in particular to Cambridge, the sort of what I call the
- beating heart of British mathematics at the time. Before I do, I'm just going to show
- one other quote. This comes from Lord Hatherley, who'd been the Lord Chancellor, who was retired,
- and it was on the opening of the Leeds Girls' High School. This is supposed to be kind of
- getting everybody going and for girls to do fine things at school. This is what he says
- about mathematics. He says, 'Medical men said that there was not physical power and strength which
- would enable the majority of girls to compete with each other in the higher branch of mathematics.'
- Now this is not isolated. There were many men at the time who really did believe that if
- women engaged in mathematics and science, it would affect, it would physically drain them
- and drain them, perhaps to the extent that they wouldn't even be able to have children.
- This I mean, it's really quite shocking for us to see this today. It's not so long ago.
- If we move to Cambridge and we see in Cambridge in the 1870s is when Girton and Newnham
- are first founded. They are colleges, but not of the university. They don't become colleges of the
- university until after the Second World War. Women cannot get degrees at Cambridge until 1948, but
- they are allowed to sit the Mathematical Tripos exam, which is this fierce exam, the kind of
- fiercest maths exam you could possibly imagine in Britain at the time. It was fiercely competitive
- too. if you were in the first class you were a Wrangler and if you were a senior Wrangler,
- that opened the doors to you for anything you want to do, not just mathematics. Whether it
- could be medicine, law, the church and so on. It was never really thought that women would be able,
- they could sit the exam, they weren't going to be ranked with the with the men, but
- they could sit the exam and just get on with it. You can see the sorts of thoughts people had about
- women doing maths. Here we have this cartoon. This is from Punch, the satirical magazine
- Girl Graduate, single figure. So this kind of pun here about actually if you're going to do maths
- as a girl, well forget about getting married. Grant Allen, the novelist and writer says, 'Well,
- you know, if you've got 100 women, 96 of them will find husbands, but the other four, well they'll
- either go into a nunnery or they'll teach maths.' So we have you know, this maths is a masculine
- subject and this comes through in spades. Charlotte Scott was the first woman to gain
- enough marks in the Tripos to be equivalent to the eighth Wrangler. This was huge news.
- It was in the national newspapers and local newspapers, periodicals, magazines and so on.
- I'm just going to give you just one example of that. This is from The Spectator, and this is
- what they what they say. '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.'
- So again, this, and we go ten years later to Philippa Fawcett, the only child of Millicent
- and Henry Fawcett to… Who were both very strong in the women's movement. Philippa Fawcett
- does something that I think no-one ever believed would be possible. She sat the Tripos.
- Due to Charlotte Scott's success women had the right to sit the Tripos by this time,
- they didn't have to get permission, but she got more than 300 marks more than the senior Wrangler.
- She of course, couldn't be still ranked with the senior Wrangler. When you look at the list,
- the men are all here and there's the Senior Wrangler and the women are still down here. This
- creates even more news. It even makes the New York Times. Here's another illustration from Punch.
- I'm just going to show you just one example of the comments that were made. This portrait of her,
- this photograph was widely circulated at the time. in the lady's pictorial, the thing that
- they're really keen to tell you is that the gown seen, the dress was made entirely by her,
- 'Proving conclusively it's quite possible to unite in one woman practical domestic virtues
- and the highest intellectual attainment.' So after all, actually, you might just be able
- to get married if you do maths, as long as you can sew as well. It's just to our eyes
- today. I mean it's really quite, yes, anyway. Even worse I think is this, which is thoughts
- on the higher education of women by a man, a Cambridge undergraduate who says, and so
- this article is about telling women how they need to present themselves in order to be attractive
- to find a husband. 'The subjects to be avoided except in an elementary manner are mathematics,
- possibly science. Certainly, however, the former, the tendency of mathematics for women is to make
- them narrow, and creatures of only one idea. Depend upon it ladies, the judgement of the
- Cambridge undergraduate represents fairly the judgement of English manhood upon your sex,
- and if there is anything he hates and ridicules, it is a masculine unwomanly woman. His ideal
- of womanhood is a lofty one. He wants to find sympathy in his pursuits, true womanly sympathy
- a helpmate, not a lady who understands the differential and integral calculus.'
- I'm now moving into fiction. I think you might think I'm already in fiction, but so
- here I'm just glancing at some late 19th and early 20th century literature, 1889 by Jules Verne,
- The purchase of the North Pole has a really pretty biting attack on women mathematicians.
- George Bernard Shaw's Mrs Warren's Profession, written in 1893, first published in 1902.
- Again, this doesn't serve women mathematicians well. Virginia Woolf, Night and Day,
- 1919. I'm going to say a little bit about that. Before I do. I'm just going to draw attention to
- another item from Punch. This is a short story by Somerset Maugham, Lady Habart from 1900.
- This is basically about how a woman brings herself to bankruptcy because she thinks she's clever
- at maths, and she's become convinced of her own abnormal cleverness. 'She was one of those persons
- who can multiply by 13 as easily as the common herd can by two. a gift for mathematics is fatal
- to a woman.' So and brings her financial ruin. Now, of course, this is a satirical magazine,
- but nonetheless this this is a strong statement to make. Again, I can find, there are other examples.
- Virginia Woolf I find really quite troubling in a sense because of course we still read Virginia
- Woolf today and so we should. She's a wonderful writer, but in this this novel, Night and Day
- really charts the lives and romances of two young women, one of whom is Katharine Hilbery.
- In this extract we see, we learn that Katharine Hilbery is very keen about maths,
- but she's not going to tell anybody. She certainly isn't. She is going to do it in secret. She rises
- early in the morning. She sits up late at night to work at maths. 'No force on earth would make
- her confess it.' Then she goes on to say, 'Perhaps the unwomanly nature of the science
- made her instinctively wish to conceal her love of it. The more profound reason was that in her mind,
- mathematics were directly opposed to literature.' So we see we have again, we have this kind of
- masculine idea about mathematics being masculine. we have now, we have also in
- opposition to literature. So it's kind of like a double whammy really for women to be doing maths.
- My last example, I'm going to move into the 20th century and move to a wonderful book, Margot
- Lee Shetterly's book, Hidden Figures. I'm sure many of you have read it and seen the film.
- I want to just remind you of this, I'm not going to tell you anything about the women in the book,
- but I want to draw attention to what she says in the preface because I think having shown you
- all these examples of really, how tough it has been for women in the past! We need to be doing
- something positive now. As I say, I think the by discussing these examples, this is a way of
- bringing the subject up p to the fore. Role models is vitally important. I think what Lee Shetterly
- says at the end here is she says, 'As a child I knew so many African Americans working in science,
- math and engineering that I thought that's just what black folks did.' So and we see here in her
- book, so it's not just women, but it's also the intersectionality with the African American women.
- The other thing that I think is important to notice from her book is it's Hidden Figures.
- It's not just a book about a woman mathematician. It is about women mathematicians working together
- and so often we see math. If you're going to be a mathematician, you're somehow a lone genius is the
- kind of obvious portrayal somehow. The stereotype and I think this is a very good example of showing
- how actually for most of us mathematicians aren't lone geniuses. They work with other people.
- I think the other thing that I just want to say is that we need to make… As well as being visible
- as women mathematicians, but we need to show how mathematics connects to every aspect of our lives.
- This is a picture of the wonderful new Mathematics gallery designed beautifully, designed by
- Zaha Hadid in the Science Museum. In this display you see areas of just about every area of life,
- it's divided up into these different sections where mathematics plays an important role. So
- you don't see lots of equations and things. I know some mathematicians have taken exception to that,
- but I feel personally that actually for people to be exposed to the fact that all
- these areas of their lives which they can't see, the mathematics that is part of the it's hidden.
- To see it in this wonderful gallery can open up their eyes to the opportunities that there might
- be for them. Of course, there are also women mathematicians are very much represented here.
- So this really concludes my talk. As I said at the at the beginning, I want by this talk to have a
- different way, a new way to open up the discussion about women in mathematics. Just to conclude,
- I just want to say that mathematics is everywhere and it is for everyone. So thank you very much.
- M1:
- Now go and sit over on the chair. Do you want to take yours, and I'll keep mine.
- June Barrow-Green: Okay.
- M1:
- We have ten minutes or so, 12 minutes even for some questions. I will give effusive thanks
- right at the end and not to break into time for questions. Do we have questions, there's a roving
- mic in the room here? I think there's details up on the board, if you want to use Slido,
- there's the code. While you're thinking about questions, perhaps I could ask the first one.
- What was the tipping point where in a sense, you became gripped by the historical
- importance of all this, as opposed to playing with symbols on a piece of paper.
- June Barrow-Green: Well, my interest in history of maths actually came from I did an undergraduate
- degree at King's College London and we had a calculus tutorial and the tutor at the time,
- we were about a dozen of us or so were in there. He began by saying Isaac Newton,
- and Isaac Newton the calculus, and Isaac Newton the second nastiest person to come out of
- Grantham. This, of course, was the Maggie Thatcher era. I had never thought about Newton as being
- nice or nasty. It actually, it just lit up a flame for me in thinking about mathematicians as people,
- because actually it was never presented to me that way at school. It was somehow mathematics
- was always there, and it was sort of in a way that you just felt it was immutable
- and whatever. Then suddenly, I was starting to think about mathematicians as people and
- how that could affect the mathematics that we do. Then of course, the names of theorems and
- who these people were and the circumstances in which they were doing their mathematics.
- So yes, and I then decided that's what I wanted to do. I wanted to really get under
- the skin of some of these mathematicians, and of course found there weren't so many women.
- M1: Another of Mrs Thatcher's legacies! Do we have any questions? Yes. Can you get the mic there?
- M2: Sorry this is not so much a question as two points, if I may. The first which illustrates what
- you were saying. You talked before about Maria Gaetana Agnesi and she studied the curve one over
- one plus X squared. that was very important at the time because it was the first curve
- that had both the negative curvature and a positive curvature as you change decks
- and some male mathematician called it the Witch of Agnesi, which I really thought was terrible.
- The second point rather different, if I may say, because you mentioned the Cambridge not
- giving degrees to women until '48. I don't know if you know how that happened.
- A man on the council said, 'Wouldn't it be interesting to give the Queen Mother
- an honorary degree?' So they wrote to the Queen. They said, 'Of course, yes, a wonderful idea.'
- They wrote to the Queen Mother. She said, 'Yes, I'd be most honoured to have a degree.' Then
- it came to light. women weren't allowed to have degrees. So they either had to write back to
- the Queen Mother and say, 'I'm terribly sorry we made a mistake, ma'am,' or change the rule. They
- changed the rule and he did that on purpose. That was a man who knew what he was doing.
- June Barrow-Green: Thank you. Yes, yes. The Witch of Agnesi,
- that came about purely because somebody made a mistranslation from the Italian. Yes.
- M1:
- It's hard for me to see from here. Can you see other hands up?
- F1: We can go to one from the online audience.
- M1: Right. Could you read it out?
- F1: I can indeed. We've got from Debbie, which is how can maths as taught in schools
- incorporate the female voice in some of these mathematicians that you've talked about tonight?
- June Barrow-Green: So the question is how can, in schools. Yes, very, very good question. I've
- actually given some talks in schools about women mathematicians. I think that it is quite
- hard because some of the maths, the actual maths that they're doing is kind of hard from
- the point of view of teaching that kind of maths at school. I think bringing into the classroom
- examples of women who have overcome these sorts of difficulties and have still managed to achieve.
- I also think another thing that's quite important is not only to concentrate,
- which I have to a large extent here, although not exclusively on the huge success stories
- because I think, you know, that can also be off-putting if you think, well, I can only
- do it. It's only really brilliant people who are doing it. I think, there are a lot of women who
- have flown under the radar, and I could sort of give you another talk about those women.
- I think that, that is also really important that there are women who have made important
- contributions in different ways. I think so I believe that within a school environment, actually
- just talking about what women have been able to achieve in difficult circumstances and kind of
- setting the challenge for them to say, well, look, actually it is possible. This is, you can do this.
- M1: Question over here.
- F2: I was wondering if you could say a bit more about
- the hunting down of the more obscure images of the women in maths that
- you've looked at. I know the Sophie Germain photo had a bit… Oh Photos,
- ridiculous, portrait had sort of a difficult way to find out where it actually came from.
- June Barrow-Green: Yes, yes. Well yes, that was sort of something I was going to say something
- about that but then I didn't think I had time. So when I showed you that image of Sophie Germain,
- there's a better known image of her as a 14 year old girl, both done by the same person.
- If you had eagle eyes, you might have noticed that both of the images of Sophie Germain were
- dated some 50 years after she died. The woodcut, the image on the on the left comes from a book on
- the history of socialism by Benoit Malon, and all it says in that book are the name of the
- person who's done the woodcut. I've written to colleagues in France and nobody seems to
- know what the origins of these images are, so I don't even actually know if they really are
- of Sophie Germain. I mean, there is rather like I showed with the story of the seven liberal arts.
- I think the thing is, it's so easy these days just to go and grab images and think, oh yes, that'll
- do. I can kind of illustrate my talk by that. I think, you know, we need to be more careful.
- It does take a lot of time and a lot of conversations. With people who I know who
- have worked on either various bits of mathematics or on the women themselves. I mean, I profited
- hugely by talking, for instance, to Ursula about Ada Lovelace, and yes, but it's fun too. It's
- really fun, with the with the Sophie Germain one, I ordered the book from the British Library only
- to my horror to discover it was five volumes that I had to go through and there was no index and no
- list of figures. So I had to go and find them. when you when you find things, it's really fun.
- F1: We've got one last one from online if we have time. A really quick one for you. Annie has asked
- throughout your research and your work on the history of maths, is there any one person that
- has really stuck out to you as your favourite or someone that's inspired you in your work?
- June Barrow-Green: Oh gosh. That's really tough. I want to say actually, rather than as the kind
- of mathematicians I've researched, one of the people who really perhaps inspired me into this
- kind of work was my late colleague John Favell at the Open University, who was somebody who
- opened my eyes to the fact that images were really important. he also had a wonderful
- way of writing captions, and things, and bringing things out. So I think
- for me, I wouldn't say I have a kind of favourite mathematician per se, but I think
- for my inspiration I looked at John for this kind of work.
- I think in the same breath I would also like to say that I also had inspiration
- from my PhD supervisor, Jeremy Grey, who was here because he taught me to really look very
- carefully at the mathematics and to make sure that actually the people who I was researching that,
- what sort of mathematics they were doing and where it came from and so forth. So I think, actually,
- I would say it's so important your colleagues and the people you're with and that's, yes.
- M1: Unfortunately, we're reaching the end of our allotted time. I was going to say span, but
- that means something else. I have one last duty to perform this evening, and that is on behalf of the
- Royal Society. It is my great pleasure to actually make the formal presentation to June of the 2021
- Wilkins-Bernal-Medawar Medal for excellence in presenting the history of science, June.
- A scroll, and a medal.
- June Barrow-Green: Thank you.
From medieval times to the modern day, female mathematicians, real and fictional, have been represented in a variety of ways, both in pictures and in words. Do they continue to marginalise the mathematical expertise of women?
Professor June Barrow-Green is the winner of the 2021 Wilkins-Bernal Medawar Medal and lecture:
“A sex so little made to brave the thorns of science”: The historical representation of women in mathematics
Joins us to explore questions like: what effect do these moments captured in time have on modern-day viewers and readers? How did these representations shape the types of mathematical knowledge women were able to claim? Do they continue to marginalise the mathematical expertise of women? And how can they be used to encourage the participation of women in the mathematical community today?
This event is the 2021 Wilkins-Bernal-Medawar Prize Lecture, which is awarded to recognise excellence in a subject relating to the history of science, philosophy of science or the social function of science. Professor June Barrow-Green was given the award for her research in 19th and 20th century mathematics, notably on historical roots of modern computing, dynamical systems and the three-body problem. Her work places special emphasis on the under-representation of women in historical narratives and in contemporary mathematics. Her recent work includes diversifying the mathematical curriculum.
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