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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?

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

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

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

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.

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