Professor Marcus Du Sautoy
Marcus du Sautoy OBE is the Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford and the President of the Mathematical Association. He was previously an EPSRC Senior Media Fellow and a Royal Society University Research Fellow. His academic work concerns mainly group theory and number theory. He has done vast work in popularising mathematics including hosting the television series ‘School of Hard Sums’ and writing a number of best selling books.
With our finite mind, finite process and finite logic, we can actually capture the infinite.
On falling in love with mathematics
I fell in love with mathematics rather than science. I think that mathematics is actually, I think, closer to the arts than it is to the sciences. It’s something people think won’t be very useful, it’s kind of a extra thing, but it was actually a teacher who took me aside after a lesson and I thought I was in trouble but he actually he said ‘I think you should find out what maths is really about’, so he started to open up this incredible world of mathematics for me. But mathematics is the language of science, so by understanding maths, I think that’s the way in to understanding all the other things in science.
My role model, or hero, is probably Christopher Zeeman, who was an amazing mathematician based in the University of Warwick. He solved the Poincaré conjecture about the nature of high dimensional geometric spaces but he was also somebody I went to see doing the Christmas Lectures at the Royal Institution when I was a 13 year old and he just, well, he was amazing. He just sort of made mathematics sound so exciting and I came away saying ‘I want to be him when I grow up’ and the amazing thing is I got asked to do the Royal Institution Christmas Lectures myself in 2006 so I was able to kind of inspire the next generation of mathematicians.
On the joy of mathematics
I think for me the joy of science is really about the joy of mathematics. I chose mathematics over the other sciences. And I think people talk about this connection between maths and music and for me mathematics is not about the final answer, it’s actually about the journey, how you get to that final answer. So, you know, Fermat’s Last Theorem – the fact that xn + yn = zn doesn’t have any solutions – that’s, that’s pretty, pretty boring actually, but what’s so exciting is the journey you go on to show why that doesn’t have any solutions. And I think that’s the same as a piece of music. It’s not the final chord that you end up with, it’s how you got from the things, the sort of place where you’re safe, early themes, how they mutate and change and then you arrive somewhere finally and that for me is what mathematics is about. It’s about the journey as much as proving something like Fermat’s Last Theorem is true.
On the rising popularity of science
Science is really becoming so popular at the moment but I think that’s a good thing. We shouldn’t be hiding these great discoveries. People should know about them and I think something like the rainbow, you know, people say ‘Well, if you understand how the rainbow works, it takes the poetry away from it’, but I don’t think that’s true at all, I think you just have to understand the magic of how light hits a round sphere and separates and the fact that, you know, if you’ve got two rainbows the top rainbow has the colours upside down and why’s that true, I think that’s as poetic as a poet describing something like the rainbow so I think, ah, people are getting into science because they want these big explanations of the big questions. Where do we come from? Why is there something rather than nothing? How’s it all going to end? Well, we’ve got some pretty good stories to tell about that.
Understanding science and mathematics
People start to attack things when they don’t understand it so I think we had this period when people were attacking GM crops and genetically modified stuff, you know, if they don’t understand what it is, most things are genetically modified, by nature, I mean, it’s, it’s, something stem cells, you can’t have an argument about stem cells and criticise it if you don’t understand what a stem cell is, so I think the more that people engage and understand the issues the more actually we’ll have a more intelligent debate. And, yeah, sure, people have a right to be critical but only on the basis, I think, of actual knowledge.
I think people still need to understand what science is, things like the scientific method and, um, this kind of idea where people say ‘Oh, that’s only a theory’, kind of really bugs me. Yeah, yeah, but it’s a theory with a huge amount of evidence behind it and that’s why we believe in it. I think in science, as scientists, we must always be open to reformulating our view of the world in light of new evidence. I think, you know, we have this model of what fundamental particles look like, we think we’ve seen something that looks a little bit like what we think the Higgs Boson will be but then I’ll bet you it will turn out to be not quite what the Higgs Boson is and it’ll be part of a larger picture. So I think it’s important that people understand that science is an evolutionary process. Now, mathematically, this is the interesting thing that we can prove, within an axiomatic system, there will always be truths that you cannot prove, I mean this was Gödel’s incompleteness theorems, so in some sense, you know, a lot of people talk about ‘Oh yeah, we may not be able to know about the ultimate size of the universe’, or these sorts of things. Well I think, in my subject of mathematics, I can prove to you that there are things I’ll never know! And the intriguing thing is, what exactly are those things? So we know that number theory, there might be statements, like Goldbach’s conjecture which says that every even number is the sum of two prime numbers; maybe that’s one of these things that will be true but not have a proof within the axiomatic system for number theories. So the exciting thing for me, in mathematics, is we can prove that there are things that you might have to have an item of faith, namely an axiom. I mean, axioms are items of faith, in that they’re statements of faith, I mean, I think they’re things that most people would believe in. The fact that if I add six plus seven it will come out the same as if I add seven plus six, it doesn’t matter what order I do that in but in some sense we have faith that that will work however big the numbers are, that’s how we kick off mathematics.
On the difference between science and mathematics
Now that’s where I think there’s a real difference between mathematics and science because although science is an evolutionary process of survival of the fittest theory, mathematics has a very different quality to it because, given those axioms, we can prove with one hundred percent certainty that something is true. And that’s something you can’t do necessarily in science because you can’t go through all the different possibilities. The amazing thing in maths is that excitement in seeing something with that one hundred percent certainty. So I always go back to one of the first great theorems of mathematics which is that there are infinitely many prime numbers. So prime numbers are these indivisible numbers and they’re actually the most mysterious in our subject, but two thousand years ago the ancient Greeks proved that these numbers go on forever, there’s never a largest prime, they go on to an infinity and I think the amazing thing is, you know, how does a human, a finite being, actually capture the concept of infinity but with just a line, or a few lines, of logical argument you can show why there cannot be a biggest prime so I think that’s one of the most staggering things, that, ah, with our finite mind, finite process, finite logic, we can actually capture the infinite.
On the everyday use of mathematics
One of the things people very easily go for, and I think it’s a mistake, is the utility of the subject. I mean they go on about, well, you know, prime numbers are absolutely key to every time you send credit cards across the internet so you should be interested in primes because they protect, ah, your secrets, um, but that’s actually not the reason mathematicians do mathematics. Not for the utility. We get, sort of, secondary benefit because all of these things have amazing applications but we do it for the pure love of the intellectual argument and I think there is something genuinely exciting that I would try and communicate is knowing something with that sort of certainty. What else do you know with a hundred percent certainty? We are teaching that theory that the Greeks proved two thousand years ago today. It is as true today as it was two thousand years ago and to have that kind of sense of, you know, Euclid, or maybe his, or a group of mathematicians who’s collective name was ‘Euclid,’ we’re not quite sure, they’re, they have got a bit of immortality and that’s what I’m after when I do my mathematics. When I create something new, I know that that’s going to exist forever. I mean, stars will collapse, blow up, the Earth will be swallowed by the sun, species die out, but mathematics lives forever and I think that’s something, the thing that attracted me to mathematics, the sort of thing that I would love to excite somebody else about. We’re too timid when we teach science and mathematics because we think that, I mean mathematics is built in a kind of hierarchal form where each layer depends on the previous layer and, but we’re too frightened about going right to the top of the layer and saying ‘Look what’s up there!’ because we think that people have to understand all the steps to it. Well, you know, my son, he’s 15 and he studies Othello in English. Well he doesn’t understand the whole of Othello but he gets the buzz of it and why it’s exciting. Animal Farm as well, he’s doing, you know, why aren’t we teaching the sort of Shakespeare of maths in the maths classes? It’s because we’re too frightened because we think they have to understand everything. It’s absolutely important that we give people almost an impressionistic feel for what a subject looks like and that will motivate them to do all of the technical side to get to ‘I really want to understand that proof’.
Because, for me, science is all about the things we don’t know, not the things we do know. I mean, when I prove something in mathematics or when Fermat’s Last Theorem got proved it was a bit, sort of, a bit of sadness in the mathematical world because actually we love the things we don’t know and that’s what drives you as a scientist, that kind of, trying to fill in the gaps, so I think that’s really important for people to realise that, you know, Fermat’s Last Theorem wasn’t the last theorem. We haven’t finished maths. There’s a lot more out there we don’t understand. Prime numbers, um, more equations we just don’t understand, and so that’s what drives me as a mathematician and a scientist.