How to make mathematics popular and exciting | Interview with Dr. Keith Devlin

We met with Dr. Keith Devlin to discuss the battle between academic research and popularization, the importance of making math both fun and informative, inspiring math books, and much more. Enjoy!

How to make mathematics popular and exciting | Interview with Dr. Keith Devlin
"Either you could write, or you could do it. People say the same thing about teaching, they say, "Either you can do it or teach it." Complete nonsense. You can't teach well if you can't do it."” – Dr. Keith Devlin

Top mathematician Dr. Keith Devlin talks about his path as a student from physics to mathematics through calculus and popular math books that inspired him, and how he was able to write those books himself and become a “math expositor.” He shares about math popularizer Martin Gardner’s influence, his own decision to make math both fun and informative, and the battle between academic research and popularization. Co-founder and executive director of Stanford’s Human-Sciences and Technologies Advanced Research Institute Consulting Professor of Mathematics at Stanford University and now , Dr. Devlin talks with Dr. Jed Macosko, academic director of AcademicInfluence.com and professor of physics at Wake Forest University.

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Interview with Mathematician, Dr. Keith Devlin

Interview Transcript

(Editor’s Note: The following transcript has been lightly edited to improve clarity.)

0:00:15.0Calculus was key

Jed Macosko: Hi, this is Dr. Jed Macosko at Wake Forest University, and Academic Influence. And today we have Professor Keith Devlin from Stanford University visiting with us today, and I am excited because Professor Devlin loves to communicate the importance of science and math to the general person.

So how did you get started on that, Professor Devlin?

Keith Devlin: Oh, wow, that was basically when I was growing up in the UK in the late ’50s, early ’60s. For various reasons, I got interested in sort of... Well, I wanted to become a physicist, ’cause I grew up in the post-Sputnik era or when the Sputnik era was beginning.

So I was interested in physics, and to learn physics, you need to use, to learn mathematics. I didn’t really like it, I was moderately good at it, I was actually one of the better kids in the class, but that was at a very young age. But I knew I needed to learn it, and I put a lot of effort. And then by the time I got to be 15 or 16 and met calculus, all of a sudden my interest was aroused, because calculus was clearly incredibly powerful, it was certainly related to physics and space research, which was the original motivation, but I couldn’t make any sense of it. So I was really interested in getting under the hood and seeing how it worked.

Now, at that stage, there were not many books around from which you could learn advanced mathematics. There were textbooks, but they were the kind of books that I’ve written many of and that other people, like Ian Stewart and various other writers have written, popular math books, which there are now hundreds of them, or at least many tens of them, probably into the hundreds now.

So there were many popular... But there were very few, there were only a few, some written in the ’30s, one called Mathematics for the Million by Lancelot Hogben, Prelude to Mathematics by Warwick Sawyer, maybe seven or eight. And so I laid my...

In fact, what happened was I won the physics prize in my high school in physics, and so I didn’t win the maths prize because I hadn’t quite got that far yet, I was... But I won the physics prize.

And with the money for the physics prize, they said, "You can buy a book." And what they wanted me to buy was a very nice bound volume, but what I said was, "Here are these seven or eight popular math books, all in Penguin paperbacks.

The money you would spend on that, I’d rather get this whole set of books," and that created a bit of a furor ’cause they didn’t like the idea of handing that, but I sort of said, "Well, instead of handing me this thing, you can have this pile of books, bound round with a ribbon, and that will be even better ’cause it shows this kid wants to read seven or eight books on mathematics."

"…I worked my way through these books, and they were very inspiring, and I thought, that really changed my life."” – Dr. Keith Devlin

So I got all of these books with a nice plaque pasted in the front saying "Physics Prize" of whatever year it was from the school, and I worked my way through these books, and they were very inspiring, and I thought, that really changed my life. It gave me an insight into advanced mathematics.

I wasn’t ready to do advanced mathematics, I hadn’t graduated from high school yet, but I got a sense of what university mathematics was like. They were written to the point where they would lead you and tell you how it worked without giving you the details, or with only giving you some of the details. That really inspired me.

And so having realized how I as a teenager got turned onto mathematics by popular mathematics books... And it changed my life, and I’ve never regretted the change it led to, I thought, I can give back that way.

In fact, many, many years later I met Warwick Sawyer, who had written some of those books, when he visited my university, the University of Lancaster back in the UK then, and I sat with him and I said, "When I was a teenager, I read your books and it inspired me, and that’s why I’m now a lecturer of mathematics in a university." And he was absolutely beaming, he thought that was wonderful, and then maybe 10 years later, when my first book Mathematics: The New Golden Age, my first popular book came out, that led to young teenagers and students coming up to me and saying, "I read your book as a teenager, that’s why I’m now an assistant professor of mathematics."

You only need one or two of those in a decade to feel your life has been worthwhile, and you get more than that. So just being a part of that recycling from one generation to another, of the inspiration to do mathematics, the excitements in it, that is an exciting thing to be on the receiving end, and in many ways it’s even more exciting to be on the delivery end.

0:04:46.5Job search, teaching, and publishing books

Jed: Well, that is really interesting to hear the backstory on that.

Now, when you read those books and got excited, what was the progression of realizing, I want to be a math professor, but one who writes popular books? Was that always your goal as you looked for... Okay, so when did that crystallize in your mind that that’s what I want to do?

Keith: That, let me think. That would have been... I’d already... I spent the first few years after my PhD, I got my PhD in 1971, and went to Norway and Germany and then Manchester and Scotland, moved around a bit...

I couldn’t find a permanent job, but there was plenty of one-year positions, so I... Which in retrospect, was really good for my career. I made a lot of contacts, got a lot of inspiration.

So I moved around a bit and then... But I was engaged in pure mathematics, doing, writing, solving problems, proving theorems, writing papers, and that was my whole focus. And there was some teaching, but since I was on one-year positions, I never did a lot of teaching, so I was a researcher for several years.

Then I got my first tenure-track position, as in the United States terminology, at the University of Lancaster. That would have been in 1977, ’78, something like that.

Then I found myself having to teach classes, and so then I had to think about, how do you put together a first-year course? And this was a state university, there were some good students, but many students were not really good students, they were okay, they were just your average students, but they were not necessarily motivated in mathematics.

So in order to motivate students to learn the mathematics, I started trying to look for interesting things. You discover there’s these things called the Fibonacci numbers and various other things you can use to excite people in mathematics.

So I started peppering up my lectures with historical anecdotes, with fun bits of mathematics, with what we sometimes called recreational mathematics, fun problems in number theory and so forth, just to arouse excitement and to generate interest. And seeing how it can be effective, just led me to say, "Well, I’ve been doing all of this back-end research into the history of mathematics to be able to tell these anecdotal stories to inspire people, let me turn those into a book."

And so I decided I would end up writing this book and it became Mathematics: A New Golden Age. And it was just a compendium of some of the big moments of mathematics or so, top 10 ideas of mathematics throughout the ages sort of thing.

And I found I really enjoyed the process of doing that and I’ve never stopped doing it. I’ve written, I think, 35 books now, about a third of them have been popular books, a third of them have been research monographs, a third of them textbooks, undergraduate and graduate texts.

And increasingly, as my career progressed, the trend was away from textbooks and research books. And the more recent books have all been popular books, but in many cases, they’re quite serious-minded popular books.

I have written some what would normally be called research monographs, but I’ve written them in an accessible way that can be regarded as niche popular mathematics writing. But it’s all been part of that progression through my career of this urge to do it, the pleasure it gave me, but the origins of doing that, as I say, well, when I was... In the ’80s when I had my first... In the ’70s, late ’70s when I had my first tenure-track position, it was then when I was a teacher in the university that I was sufficiently motivated to write popular books.

And of course, the first one was actually, well, there’s no of course about it, it seems that way now because I’m looking back a long time. The first one was a big success. I actually got a letter from someone called Martin Gardner, now you will know who Martin Gardner is, and I do, younger people won’t.

But he was in some ways, the most famous mathematics expositor that has ever been. He was a great inspiration for me when he was young, ’cause he wrote a regular column in Scientific American, and I lapped up his, all of his stuff. I’ve read all of his stuff when I started waiting popular math books to look for key ideas for how you make mathematics exciting to a general reader.

"This is Martin Gardner, telling me he loved my book and thought I was a good writer. With an accolade like that for your first book, that drug is in your blood."” – Dr. Keith Devlin

And then when my first book was published, he not only wrote a two-page review of it in the New York Review of Books, not because they asked him to, because he bought the book and liked it and decided to write a book... But he wrote me a letter saying what a wonderful book it was.

Well, that’s like getting a letter from the Pope if you’re a Catholic. This is Martin Gardner, telling me he loved my book and thought I was a good writer. With an accolade like that for your first book, that drug is in your blood. You want those accolades, and it just kept inspiring me more and more and more to get even greater heights to reach out to a general population. It’s a small population.

Popular math books... A bestseller in mathematics is 100,000 copies. I think it’s even less than that now, ’cause people can get free PDFs off the web if they search around on the dark web for a while.

But the pleasure I get from doing it, and especially when I meet people who’ve read those books and have been affected by them, that’s been all the reward. You don’t get rich writing those books, you don’t do genuine bestsellers...

Actually, one or two people have. John Allen Paulos managed to do it with his first book and a couple of others have. Though typically, they only do it because they are verging on mathematics education and everyday mathematics. My popularizations have all been in relatively advanced parts of mathematics, so it’s popularization to a very narrow and niche audience.

0:10:27.4Success

Jed: Well, it does seem like you had two streams going, the stream from when you were a young boy and got those seven books and saw how powerful they were in your own life, and the other stream of trying to be a teacher and peppering your lectures with something interesting.

When did you... As you were writing the book, as a professor, as a teacher, did you... When did you look back and say, "Well, this is what I had always wanted to do." Was it as you were writing or before you started?

Keith: It was actually when I... After the first couple of books got reasonable success, I started getting invited to... The BBC would get me on the radio, occasionally the TV. And then I got to the stage where there were...

I start writing for the Manchester Guardian, I wrote a regular column for maybe a decade in the ’80s, in the days when the science... There was a big... There’s a whole Science section in the Manchester Guardian.

So I got quite a following in the UK, the Guardian, I think, reached several million readers. So within the UK at least, and to some extent at this stage, I became known as a mathematics expositor.

So there was always lots of feedback as to me doing this, but I really only sort of started rationalizing... I only learnt how to answer the question you’ve just asked me when I got to the point of doing interviews where people would regularly ask me that question.

And it’s kind of lame if you get asked a question, you say, "Well, I actually don’t really know what it is. I’ll have to think about it." I probably did answer the first day that time, but I kept getting asked that question and pretty soon I needed to... I realized I had to look back and reverse-engineer what had happened.

So I don’t think I invented that story, I simply reverse-engineered it from my own history and how it all began. And it was clear when I did that, that I realized there were the influences like Martin Gardner, there were the books by Lancelot Hogben, Warwick Sawyer, all of that stuff became a story when I had to tell that story for having found myself now in that world.

Jed: That’s fascinating. So really, the two streams didn’t come together while you were writing the book, it was much later. But that was probably an undercurrent somewhere in your subconscious that you wanted to bring that out. And of course, as you said, those were the stories that you had read as a younger person and they were coming out as you wrote your books.

Keith: When I was doing that, not only were these two threads separate, they sort of had to be, because I met the same sort of issues that Carl Sagan met, was that if you were a scientist and you had two threads, you were doing research, good research, and you were doing popularization, those will be regarded as antagonistic.

You know, the assumption was, which is crazy in retrospect, that either you could write or you could do it. People say the same thing about teaching, they say either you can do it or teach it.

Jed: Yeah.

Keith: Complete nonsense. You can’t teach well if you can’t do it. And actually, it’s very difficult to do it if you don’t know how to teach it, so those two things always were connected.

But certainly when I grew up, and I took solace from knowing that Carl Sagan met the same problem, I met quite a bit of opposition from within academia for writing for the popular press, for writing for popular science magazines, for writing popular books, that was regarded to sort of breaking the oath, it’s almost as if academia was regarded as a cabal where you had to keep it secret, almost Pythagorean in its nature, that you had these secrets of society that you had to keep a secret. Those days, thankfully, have largely gone by now, and some of the best scientists in the world write some of the best popularizations.

Jed: That is true.

"The world has changed and it's all the better for it."” – Dr. Keith Devlin

Keith: The world has changed and it’s all the better for it.

Jed: Well, and the United States is better for it, that you did face that struggle in the UK, and you decided to come to the United States and live here with us. So we appreciate that. Yeah.

Keith: Oh, yeah.

0:14:24.8Margaret Thatcher and the movement that pushed you out

Jed: And I know you think of it as a blessing in your own life that Margaret Thatcher and her regime decided that you wouldn’t be able to stay... [chuckle] Thanks for sharing that story with me.

Do you want to share just a little bit of that so that people watching this can know what’s going on behind the scenes there?

Keith: Oh, yes. So in the mid 1980s... By the way, if anyone wants to watch season four of The Crown, I’m going through the seasons of The Crown, I’m rewatching the first three and I know that in season four you see the Margaret Thatcher story.

She was very anti, an interesting person in many ways because she was a... She got a degree in chemistry, and she was a science background, but in many ways she was not unlike today’s Republican party, she was very anti-science, and there was just a thing about being anti-science and anti-universities.

There are all sorts of stories as to what made her that way, but there was certainly a depression of the university system in the UK, there was a sort of sense that they should return to the days when there was just Oxford, Cambridge, London, Edinburgh and a couple of other places, and the idea of universities for thousands and thousands of people was regarded as sort of not a good idea. So, there was this anti-intellectual, anti-science, anti-universities movement.

But the university where I was at, the University of Lancaster, was a very good one, but it was a new one, and the new ones were regarded with suspicion, in many ways because they were new, they were very socialist leaning, they had all these new-fangled things like gender studies and all of this other stuff was going on and it was becoming a modern university, it wasn’t one of the traditional universities that the UK had been world-famous for, and so there was a strong feeling that places like Lancaster were just sort of socialist leaning.

And it seems kind of weird now, but that was how it felt back then, and I think the US is going through it now, but the UK went through it in the ’80s. And so the university where I was at was forced to cut its mathematics department by a half, it was supposed to go through, down from about 30 faculty to 15 in the space of two years, and the only way they could do that was take the people who were most likely to find a position elsewhere, in the United States, Canada, New Zealand, Australia, the South Africa, that’s where most of us went, the English-speaking world.

And so they basically took the top half of the faculty in terms of the fame and research capabilities and said, "You’d better leave." I wasn’t fired because I had tenure, but the pressure was on, "Life is not going to be very nice for you anymore if you stay here."

I was actually resisting until out of the blue, I got an invitation to spend a couple of years at Stanford. Well, you don’t say no to an invitation to Stanford whatever else is going on in the world, so I instantly said, "Okay, you want me gone, give me my pay-off and I’ll go to Stanford," and I’ve never looked back. It was a wonderful move, but that was the time, it was a time when there was anti-intellectual feeling, anti-academia, anti-science, and it just... It did a lot of damage and... It’s recovered, but it’s taken a long time to recover.

Jed: Do you think that... You said that the United States...

Keith: Yeah. It is a bad story, because for me there was a golden egg coming out of that thing. Namely, it brought me to the States through Stanford, and I’ve had a wonderful second career, almost, in the United States.

Jed: Well, you mentioned earlier that what you went through in the ’80s is what the United States is going through now, do you think we will recover? It looks like we have a new administration, and do you think that our recovery will be rather rapid or will it take as long as it did in the UK?

Keith: With a First Lady who’s a professional educator, I think we’re on a winning ticket there. [chuckle] I really do.

0:18:10.5Sign off

Jed: Good. That’s good. Well, that’s really encouraging. Well, thank you so much for spending some time with us today, and we just really appreciate you breaking down some of the intricacies of how you started becoming a popularizer of science and math, we really appreciate you taking time on our show today.

Keith: Oh, it was a pleasure. Thank you very much for inviting me, Jed, much appreciated.