The Interview: Bookbag Talks To Ian Stewart

The Interview: Bookbag Talks To Ian Stewart

Summary: Bookbag loved Ian Stewart's Hoard of Mathematical Treasures and couldn't resist the opportunity to ask him a few questions. We're delighted we did, as his answers are fascinating!

Date: 29 September 2009

Interviewer: Keith Dudhnath

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Bookbag loved Ian Stewart's Hoard of Mathematical Treasures and couldn't resist the opportunity to ask him a few questions. We're delighted we did, as his answers are fascinating!

• Bookbag: When you close your eyes and imagine your readers, who do you see?

Ian Stewart: Me! Well, in a sense. Popular maths is different from many types of writing, and there isn't an obvious ready-made audience. If I was writing biographies of footballers, I'd be aiming at football fans. But who are the maths fans? My readers have a huge age range, the proverbial 9 to 90. At different ages, I've been the sort of person that I now write for. However, my technical knowledge of maths has grown, so I have to compensate for that - I try to make most of my books as widely accessible as possible. Anyone with a lively mind who has some interest in what mathematicians are up to, or have been; but also anyone who might be tempted to try to find out.

• BB: Which is your favourite puzzle or story in the Hoard of Mathematical Treasures?

IS: I really like the sad tale of Lilavati, daughter of the Indian mathematician Bhaskara. He was born in 1114, and among his most famous works is Lilavati, named for his daughter. Why? Well, according to the usual story, she was of marriageable age, so Bhaskara cast her horoscope to work out the most propitious wedding date. (Mathematicians of that period often made a living as astrologers.) He thought he'd come up with a terrific idea to make his forecast more dramatic. He bored a hole in a cup and floated it in a bowl of water, with everything designed so that the cup would sink when the fateful moment arrived. Unfortunately, an eager Lilavati was leaning over the bowl, hoping that the cup would sink. A pearl from her dress fell into the cup and blocked the hole. So the cup didn't sink, and poor Lilavati could never get married. To cheer his daughter up, Bhaskara wrote a mathematics textbook for her. Hey, thanks, Dad. Is the story true? I really don't know. But it wouldn't surprise me. Mathematicians are like that.

• BB: We found the Hoard to be perfectly pitched: accessible and engaging, yet unpatronising and appropriately challenging. Were there any treasures that you felt you had to leave out to achieve this balance?

IS: Lots! I have a 4-drawer filing cabinet of material, plus a dozen ringbinders, plus my original notebooks. It was really a matter of selecting a sufficiently varied range of items: long, medium, short; frivolous, serious; lightweight, deep and significant... I aimed to make my miscellany miscellaneous. However, a lot of thought has gone into the ordering of the items. Readers are told they are free to dip in anywhere, and they are, but in practice most of them read in order from front to back, so it has to make sense if you do that.

In the predecessor Professor Stewart's Cabinet of Mathematical Curiosities I used up many of the most famous big problems, like Fermat's Last Theorem. So a lot of items on the uses of maths popped up to fill the void. I prefer the quirky ones, but those can often be really important, such as medical CAT scans. I've still got a big stock of applications of maths, and even simple things like calculator curiosities aren't yet exhausted.

Mathematicians have been piling up ideas for about 4000 years, and new stuff is being produced a lot faster than I can compile books about it. However, I think we may call a halt after the third book of this type.

• BB: Which mathematician (past or present) do you admire most and why?

IS: I have boundless admiration for the French mathematician Henri Poincaré, who was born in 1854 and died in 1912. He was one of the top two or three mathematicians of the time. He founded the new subject of topology ('rubber-sheet geometry' in which shapes can be distorted continuously) and got a long way into the subject. He was the first person who really appreciated that non-random rules can lead to apparently random behaviour - Chaos Theory. He discovered this in work on the motion of the solar system. He wrote several bestselling popular science books, too: he wasn't an academic snob. And he was slightly dotty, and often a bit sloppy, though creatively so.

• BB: Is there a problem with innumeracy in this country, and if so, what can be done about it?

IS: It's the wrong word, of course. Focusing on a lack of numeracy reinforces the view that maths is only about numbers. And that makes people think that school arithmetic, plus a smattering of algebra and maybe calculus, is all there is to maths. This is like imagining that composing music is all about playing scales on a piano.

Having said which, an awful lot of people seem unable to manage even basic numeracy issues, let alone anything more advanced. But I think we probably need to separate out the specific issue of being poor at basic arithmetic from the wider one of failing to appreciate what maths is, what it's for, or what it is doing for human society.

My main focus is on the second issue: I do my best to explain the wider aspects of maths, its myriad uses, the insights it gives us into the natural world, and its deep intellectual beauty. Few people realise that every time they play a CD, take a digital photo, or use the Internet, the equipment only works because of a lot of maths, some old, some new, and all of it advanced. I accept that users don't need to know how to do this, but they do need to appreciate that it's there. Otherwise they make the standard error of thinking that the only maths anyone ever uses is what they were taught at school, and since calculators do that much better, there's no point in having mathematicians! The reality is that our society requires a large number of mathematically trained people in order for it to function.

One side effect of this is that only 5% or so of maths graduates go into teaching. No, it's not the only job they can get, quite the contrary: the range of jobs you can get with a maths degree is far broader than most subjects, and the average pay is very good too. Teaching involves many skills, and a degree in maths doesn't guarantee many of those, but it's not good for the student if the teacher is struggling to understand the material (and, sometimes, failing).

It's a difficult problem and I don't know any easy answers. But I do think that part of the problem is a cultural one: few people have any clear appreciation of what mathematicians really do. I sometimes argue that schools need to spend a bit more time on that kind of issue, and sacrifice some of the hard-core classes on how to do the sums. Integrating maths with everyday activities, like laying out the football pitch, is also worth doing. Many of the best teachers do this sort of thing already.

I also often say that the single most important change needed is to stop making teachers tick endless boxes on forms, and let them teach. In all walks of life, the bean-counters and pen-pushers are destroying talent and creativity.

• BB: What's the best way to teach times tables to children?

IS: There are many ways to do this, and which one works best depends on the child. I learnt mine from my mum (who also taught me to read). She would suddenly fire out what's 6 times 7? and insist on an immediate response rather than an attempt to buy time with sorry, what was the question? Yes, she concentrated on the hard ones, too.

Some children find the hidden patterns in the multiplication tables appealing. (Look at the 9 times table: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. The first digit goes up one at each step, the second goes down one. Reverse the table and you reverse the numbers. If you can explain why that works, you're well on the way to becoming a mathematician, but anyone can use it to make the table easier to remember.

Some are wildly unimpressed by that, but enjoy the sense of achievement they get from answering questions. Some would enjoy the topic more if they were show what it can be used for.

There's also a debate about how important it is to teach 'times tables' at all, given the existence of calculators. My feeling is that children don't understand what multiplication means unless they do something along those lines. Even if you let the calculator do the work, you have to understand the background to the calculation. Otherwise it's all a meaningless ritual.

When I was a kid, I had to learn the 10, 11, and 12 times tables. 10 is of course very easy (though I've seen shop assistants struggling to work out how much ten items at £1.50 each cost). That was mainly because of Britain's pre-decimal currency. Barring really good reasons, we can now stop at the 9 times table (probably, schools already do that - I don't know, but my granddaughters would). That saves a lot of memorising.

• BB: Why is 6 afraid of 7? What did 0 say to 8? Got any even cheesier maths jokes than ours?

IS: There's a wonderful subculture of mathematical jokes, ranging from simple arithmetic to the frontiers of research. I've put quite a few in the book (and its predecessor), mainly to show readers what mathematicians find funny.

I didn't know these two (and I may steal them for the third book in the trilogy). But now I do: seven ate nine, and nice belt.

I've worked with Terry Pratchett and Jack Cohen on the Science of Discworld books, and in Discworld the magic number is 8. The god Bel-Shamharoth is associated with the number 8, but no one dare utter it. Instead, they talk of the number between 7 and 9, and so on. Or, very daringly: I can't say which number because I might get ate. So, not for the first time, Terry has tapped into a rich mine of folklore.

There's a mathematician's joke in the book, and I'll give it away in the interests of answering your question. A piece of string went into a bar and was refused a beer because we don't serve strings. A little way up the street, he passed a stranger.
You look like you could do with a beer, said the stranger.
I tried that, but the barman refused to serve me because I'm a string.
I can fix that, said the stranger. He tied the string in a granny knot and frayed his ends. Try again. So the string went back to the bar and asked again for a beer.
Aren't you the piece of string that I just sent packing? the barman asked suspiciously. You look just like him. No, the string replied. I'm a frayed knot.

Then there's: A dog has ten legs. Two hind legs and two fore-legs. (2 4-legs, geddit? Oh well.)

Speaking of which:
One cat has one tail. No cat has eight tails. Therefore, adding the two: One cat has nine tails.

• BB: Haha and groan in equal measures! Please do steal the jokes - we'd be hugely honoured! What are you reading at the moment?

IS: Abydos by David O'Connor. It's about the ancient Egyptian site of that name, the Osiris Cult that flourished there, and the remarkable pre-dynastic remains. Avril (my wife) is keen on Egyptology, and her enthusiasm has infected me. Earlier this year we visited Abydos and because we belong to the Friends of the Petrie Museum we were given a special tour of some of the sites there, and shown some of the amazing predynastic artefacts. For instance, there are tiny ivory labels from Tomb U-j, dated to the time of the predynastic king Scorpion, which appear to have early hieroglyphs on them. So this is kind of the book of the trip, and it fills in much more of the significance of what we saw.

• BB: Which book has most influenced you, and do you still have a copy?

IS: Christopher Zeeman's Catastrophe Theory: selected papers 1972-1977 is the one that had a huge influence on my research career. I do have a copy, and it's now in about 10 pieces. I changed research field because of Zeeman's lectures in the 1970s. Catastrophe theory was quite controversial at the time - I think for silly reasons - and it changed its name, but the basic idea has established itself in some important areas of modern applied maths. It's a theory of sudden changes - discontinuities - in slowly varying systems. A rainbow is one example: there the discontinuity is a geometric one, in the intensity of the light of any fixed colour. A collapsing bridge is another.

If you want something less technical, I was greatly inspired by Douglas Hofstadter's Gödel, Escher, Bach. This is about self-referential systems, from logic to DNA. It features delightful dialogues between Achilles and the Tortoise, very much a cult book. It's one of the most original bits of writing I've ever seen. And I own two copies of that!

• BB: What's next for Ian Stewart?

IS: As I write, I'm due to retire tomorrow. However, I doubt anyone will notice, except the pension fund, Warwick University payroll department, and Avril. I don't plan to don my slippers and grow roses. The cat wouldn't let me anyway, and Avril is the gardener in the family.

I've been made an Emeritus Professor (which is usual) and a Digital Media Fellow (which is not, I'm the only one, we don't really know what it means yet - except that I get an office on campus). The idea is to give me an official link to the Communications Office at Warwick University, and make it possible for me to develop - with their able assistance - popular maths and science in new media like podcasts, iTunes, even Twitter. (I do tweet, occasionally, but only on official business.) We're currently making a series of 11 podcasts (with pictures) on Mathematical Cats. This is working so nicely that we feel we will have to do dogs as well, and then probably domestic animals in general, followed by the jungle...

We also want to film a series of short items on the great British mathematicians - where they lived, what they did.

My publisher Profile Books has just drawn up a 5-year publication schedule for me. Hoard of Mathematical Treasures heads the list, but we plan two popular science books of a more serious nature, plus a third miscellany. And there are the paperback releases to fit in, as well as the hardback. In April 2010, a new book with OUP will appear: Cows in the Maze. I'd like to write another science fiction novel or two, and there are tentative plans for another Discworld book if circumstances permit.

I'm hoping to continue the usual radio and TV stuff - I particularly enjoy taking part in In Our Time. I have some public lectures lined up. The Discworld Convention in 2010 is a must and I'm already working on some talks.

Avril and I are making serious efforts now to visit all the places on our 'to do' list. We go to Egypt most years. Last year we visited Easter Island, which was an amazing experience. This year we went to the Galapagos Islands and Peru. Maybe Cambodia and Vietnam next! Plus a return to New Zealand, a research visit to my collaborator Marty... and we have a new grandson to add to our two granddaughters.

When Avril retired she ended up doing more than she had when she was working. I can see it going the same way for me.

• BB: Thanks so much for the fascinating responses, Ian. You're retirement sounds much busier than when we're hard at work, but we're sure you'll love it nonetheless!

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