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Eugenia Cheng - Pure maths: university and YouTube
As early as I can remember, I loved maths. At kindergarten when we measured things
using our hands, I realised immediately that sometimes I used just half or a third
of a hand, and that there must be other fractions in between. I was fascinated
by patterns and I loved doing logic puzzles. My mother is mathematical, and she
showed me interesting bits of maths. So although school maths was terribly boring,
my interest remained.I got a scholarship to go to an all-girls school, and did double maths, physics
and music for A level. Being in an all female environment helped me grow up uninhibited
by gender stereotypes, but my family background was also important as my parents
did not conform to typical gender roles -- my mother commuted to work in the City
each day, while my father, a child psychiatrist, worked near home and spent more
time with us children during the week. Plenty of girls did science subjects at
my school – though it was certainly more "cool" to be good at sports.
I was always longing to specialise in Pure Maths. I went on to Cambridge where I studied Maths and then did a PhD in Category Theory, the most abstract part of mathematics, looking at the underlying principles
and structures. Women were in a tiny minority in Pure Maths (less than ten per
cent of undergraduates, and no Lecturers). Maths is still very male dominated,
but I don't feel I suffer from that, because of my upbringing, my education, and
my personality.
You are expected to move country a lot now if you want an academic career in
Maths. Some people say that this is hard on women who have family commitments,
but I think it’s inhuman for anybody who cares about family and social life. I
was devastated when I left Cambridge after ten years there. Then I had two amazing
years working in Chicago followed one in Nice, and each time I felt horribly uprooted
when the job ended and my personal life was destroyed. I now have a permanent
job with the Department of Pure Mathematics at the University of Sheffield so I won't have to move again until I choose to.
I continue to be obsessed with research in Category Theory, but at the same time,
I am very committed to teaching and outreach. I’ve been using YouTube to explain Category Theory – it’s not really taught to undergraduates, but almost all maths PhD students
need to know about it. My short videos (with my colleague Simon Willerton) have
had 200,000 hits so far, and last year we won a prize from the University. Also,
when I had to miss an undergraduate lecture, I delivered it by YouTube. And I
put together YouTube pieces that give feedback on the students' work – the students
love all this.
I have also started a YouTube outreach project for sixth formers to help bridge the gap between school and university maths. The other voluntary
work I do is with a local primary school. I am passionate about education as the
key to social justice. I believe that if you have knowledge it’s your responsibility
to share it. So many people seem to be afraid of maths; I hope to enable more
young people to understand and love maths instead.Eugenia Cheng is Senior Lecturer in the Department of Mathematics, University of Sheffield. There are links to her publications and YouTube lectures on her university web page.
Comments:
Ruth Wilson (UKRC moderator)
Hi Eugenia,
Welcome to the blog - you are our first pure mathematician!
How wonderful that your earliest memories include loving maths. Do you see any gender difference in the way women and men approach maths, or use it? And who are the great women mathematicians of our day?
Welcome to the blog - you are our first pure mathematician!
How wonderful that your earliest memories include loving maths. Do you see any gender difference in the way women and men approach maths, or use it? And who are the great women mathematicians of our day?
Pat Morton
Great stuff Eugenia. I wonder if you have heard of the Maths Careers website (www.mathscareers.org.uk ) ? The website is hosted by the Institute of Maths and its Applications on behalf of maths and stats community. They are looking for more female maths profiles for the site to help encourage more girls to study maths - and they would also be interested in the Mathsters project you have on youtube - you could link up with them. I have been involved in the recent redesign of the website (I manage the STEM careers project on behalf of government)- the site aims to be more inclusive and to attract more young people from all backgrounds towards maths - it would be good to know what you think.
Hi Eugenia - I spent 5 years at Sheffield University and loved every minute. I now live 15 mins away and visit Sheffield regularly and still really enjoy the city and its people (and the pubs at Kelham Island!). I also had 2 weeks at the University of Illinois which I enjoyed enormously. However I do remember one of my contact lenses 'flipping out' whilst delivering a seminar. Fortunately I retrieved it at the end of the session and all was well.
Is there any way of explaining Category Theory to the lay person? Why is it important and what if any are the applications of it?
I notice that you studied music at A level. I've heard it said many times that there are well established links between maths and music. Do you agree and if so how would you summarise them?
I really enjoyed your blog and very much look forward to your responses.
Malc
Is there any way of explaining Category Theory to the lay person? Why is it important and what if any are the applications of it?
I notice that you studied music at A level. I've heard it said many times that there are well established links between maths and music. Do you agree and if so how would you summarise them?
I really enjoyed your blog and very much look forward to your responses.
Malc
Eugenia Cheng
Hello everyone and thanks for your interest and responses. Those are some very interesting and far-reaching questions so I'll answer them gradually!
As regards explaining Category Theory to the lay person, I have a few articles on my webpage aiming to do that, so do have a look if you're interested. One of them is notes from a talk I once gave in Cambridge, in which I explained Category Theory to non-specialists by comparing it with Lego!
Another thing I like to say is that "Category Theory is to Mathematics as Mathematics is to Science". I'd be interested to know what impression this gives you of Category Theory without me explaining any further... I often like to explain things by analogy! Actually, some people say that Category Theory is a theory of analogies.
Eugenia
As regards explaining Category Theory to the lay person, I have a few articles on my webpage aiming to do that, so do have a look if you're interested. One of them is notes from a talk I once gave in Cambridge, in which I explained Category Theory to non-specialists by comparing it with Lego!
Another thing I like to say is that "Category Theory is to Mathematics as Mathematics is to Science". I'd be interested to know what impression this gives you of Category Theory without me explaining any further... I often like to explain things by analogy! Actually, some people say that Category Theory is a theory of analogies.
Eugenia
Hi Eugenia,
I think what you are doing for 6th formers and those interested in math but have not been taught it well is terrific. I watched your presentation on youtube and feel to are a natural. I like your jokes. I have two queries, however.
I have a substantive question about the nature of category theory. And one about your monoid presentation. They are related. Let me take the second first.
I think I would have been more persuaded about how category theory relates to other areas of mathematics had you reformulated, say, a couple of the axioms of Peano arithmetic or of standard set theory in category theoretic terms.
I still have the feeling that category theory is little more than another language that might make more explicit what mathematicians do rather than a substantive development.
Given that, how does category theory illuminate the relationship among the propositional and predicate calculi and set theory, where the former are considered to be foundations of the latter? Where does category theory fit into all this?
Larry
I think what you are doing for 6th formers and those interested in math but have not been taught it well is terrific. I watched your presentation on youtube and feel to are a natural. I like your jokes. I have two queries, however.
I have a substantive question about the nature of category theory. And one about your monoid presentation. They are related. Let me take the second first.
I think I would have been more persuaded about how category theory relates to other areas of mathematics had you reformulated, say, a couple of the axioms of Peano arithmetic or of standard set theory in category theoretic terms.
I still have the feeling that category theory is little more than another language that might make more explicit what mathematicians do rather than a substantive development.
Given that, how does category theory illuminate the relationship among the propositional and predicate calculi and set theory, where the former are considered to be foundations of the latter? Where does category theory fit into all this?
Larry
Eugenia,
May I make a suggestion about your use of the blackboard? Rather than a blackboard, what about clever software? If you have a moment, you might wish to have a look at khanacademy.org/ and the "lectures" by Salmon Khan and his use of clever software in his demonstrations in mathematics, finance, and physics. I think he may make the software available to educators free of charge, but of this I am uncertain.
May I make a suggestion about your use of the blackboard? Rather than a blackboard, what about clever software? If you have a moment, you might wish to have a look at khanacademy.org/ and the "lectures" by Salmon Khan and his use of clever software in his demonstrations in mathematics, finance, and physics. I think he may make the software available to educators free of charge, but of this I am uncertain.
Malcolm Davies
Hi Eugenia - just watched your videos - fantastic. I wish you'd been my A level teacher.
Also I've read your Cambridge 'talk notes' and I understand the lego analogy. Fantastic.
However I would think that my 'understanding' of Category Theory is on a completely different level to that of Larry (above)!
Keep up the great work.
Malc
Also I've read your Cambridge 'talk notes' and I understand the lego analogy. Fantastic.
However I would think that my 'understanding' of Category Theory is on a completely different level to that of Larry (above)!
Keep up the great work.
Malc
Eugenia Cheng
Thanks for your comments everyone. I will continue trying to respond gradually!
Regarding the links between maths and music, I hear this comment a lot when people find out that I'm a musician and a mathematician (I still give concerts regularly). However for me the two are entirely complementary and almost the exact opposites of each other. Perhaps that is itself a form of link, but I don't think it's the kind of link people are usually thinking about. For me, music is about love, emotion, and human expression and communication. It's an important way for me to balance out the unwaveringly cerebral nature of mathematics. Not that I don't find mathematics exciting of course, but I sometimes worry about becoming like that javelin thrower in "The Twelve Tasks of Asterix", who had an enormous right arm and a puny, shrivelled left arm.
Regarding the links between maths and music, I hear this comment a lot when people find out that I'm a musician and a mathematician (I still give concerts regularly). However for me the two are entirely complementary and almost the exact opposites of each other. Perhaps that is itself a form of link, but I don't think it's the kind of link people are usually thinking about. For me, music is about love, emotion, and human expression and communication. It's an important way for me to balance out the unwaveringly cerebral nature of mathematics. Not that I don't find mathematics exciting of course, but I sometimes worry about becoming like that javelin thrower in "The Twelve Tasks of Asterix", who had an enormous right arm and a puny, shrivelled left arm.
Eugenia Cheng
Regarding the importance of Category Theory:
Category Theory has become an language for use in many areas of mathematics, physics and computer science. As it\'s a branch of pure mathematics, most of the applications are inevitably still a bit far away from \"every day life\". I\'m not sure if there will ever be direct applications affecting the general public, but then, people used to think that about Number Theory, because a hundred years ago nobody could ever have foreseen the applications to internet security!
As to whether it\'s \"little more\" than a language and whether it\'s a \"substantive\" development, I would say that it doesn\'t just make explicit what mathematicians do anyway, but rather, it enables them to do more things that they would not otherwise be able to do, just as mathematics enables us to do things we otherwise couldn\'t do, although at a basic level (eg solving linear equations) it \"merely\" makes precise what we could do intuitively in our heads. This is probably not the right forum for this discussion though. What is your background Larry? Have you read any of the writings of John Baez? if you have a mathematical background then the introduction to Tom Leinster\'s book (available from his webpage) might interest you, as might the post he wrote on the n-category cafe this week.
Category Theory has become an language for use in many areas of mathematics, physics and computer science. As it\'s a branch of pure mathematics, most of the applications are inevitably still a bit far away from \"every day life\". I\'m not sure if there will ever be direct applications affecting the general public, but then, people used to think that about Number Theory, because a hundred years ago nobody could ever have foreseen the applications to internet security!
As to whether it\'s \"little more\" than a language and whether it\'s a \"substantive\" development, I would say that it doesn\'t just make explicit what mathematicians do anyway, but rather, it enables them to do more things that they would not otherwise be able to do, just as mathematics enables us to do things we otherwise couldn\'t do, although at a basic level (eg solving linear equations) it \"merely\" makes precise what we could do intuitively in our heads. This is probably not the right forum for this discussion though. What is your background Larry? Have you read any of the writings of John Baez? if you have a mathematical background then the introduction to Tom Leinster\'s book (available from his webpage) might interest you, as might the post he wrote on the n-category cafe this week.
Eugenia Cheng
Regarding expressing the axioms of set theory using Category Theory: I appreciate your comments. The body of videos is not at all well-planned as we knew that if we tried to do things in a planned way we would fizzle out quickly and stop. So instead we just make videos on whatever we feel like doing that day. We haven't really taken a dogmatic viewpoint on what "ought" to be done - we just did our favourite things!
I think teaching turns out much better if you can teach just whatever you feel like at any given moment, because then your heart will really be in that piece of exposition. Of course, this is not practical for ordinary lectures/classes that need to go in a sensible order. This is one advantage of video lectures!
I think teaching turns out much better if you can teach just whatever you feel like at any given moment, because then your heart will really be in that piece of exposition. Of course, this is not practical for ordinary lectures/classes that need to go in a sensible order. This is one advantage of video lectures!
Eugenia Cheng
Regarding the use of "clever software":
Thanks for sending me that link to the Khan Academy. I am always interested by "clever technology" but at the moment I still prefer blackboards and video cameras as I like the physicality of it. I like to be able to show the human aspect of doing maths, rather than having disembodied symbols that float across the screen. I want to show my facial expressions, body language and so on - like chatting to friends using a webcam rather than just a phone. I have tried using "clever software" in lectures but it makes me feel extremely static and glued to the spot. I like to feel free and relaxed when I'm teaching!
Thanks for sending me that link to the Khan Academy. I am always interested by "clever technology" but at the moment I still prefer blackboards and video cameras as I like the physicality of it. I like to be able to show the human aspect of doing maths, rather than having disembodied symbols that float across the screen. I want to show my facial expressions, body language and so on - like chatting to friends using a webcam rather than just a phone. I have tried using "clever software" in lectures but it makes me feel extremely static and glued to the spot. I like to feel free and relaxed when I'm teaching!
Eugenia Cheng
Regarding the Maths Careers Website:
Thanks for sending me that link, Pat! It looks like a really fantastic resource and I feel a bit silly for not knowing about it before. I would be happy to see if I can link up with them in any way, to be profiled, or for something to do with the Mathsters. Would you be able to put me in touch with someone?
Thanks for sending me that link, Pat! It looks like a really fantastic resource and I feel a bit silly for not knowing about it before. I would be happy to see if I can link up with them in any way, to be profiled, or for something to do with the Mathsters. Would you be able to put me in touch with someone?
Eugenia Cheng
Regarding gender differences in the way people do maths:
I tend to find that gender differences are completely subsumed in general human differences. That is, I certainly notice that different people do maths in very different ways, but I don't see any link with gender at all, apart from the basic fact that more men do maths at all (professionally, I mean). In terms of students again it's more of a human thing. I've never yet had a female student who overestimated her abilities, but there are always a few male students who do that. I find it more important to respond to each individual I teach as an individual. Some people say female maths students talk less so you should be careful to encourage them, but there are some male students who talk less as well, and they should be encouraged too! I've heard other differences mentioned, but I've never found them prominent enough that I would spontaneously notice them when I'm teaching, without being fore-warned to go round looking for them. Perhaps the differences are more obvious with younger people, before they have self-selected themselves as mathematicians/non-mathematicians?
ruth Wilson (UKRC moderator)
Thank you for all these responses, Eugenia. I suppose pure maths may truly be gender-free. The barriers to women entering maths probably lie more in our culture and society than in the maths itself. I love what you say about education being key to social justice. I hope more young women get drawn to specialising in maths!
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