The Joy of Mathematics - A Conversation with Ian Stewart

Howard Burton

• Éditeur: Ideas Roadshow
• Année: 2021
• ISBN:
  9781771700955
• Sujet: Matemáticas
• Sous-sujet: Matemática aplicada

This book is based on an in-depth conversation between Howard Burton and Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick and bestselling science and science fiction writer. For Ian Stewart, mathematics is far more than dreary arithmetic, while mathematical thinking is one of the most important—and overlooked—aspects of contemporary society. This wide-ranging conversation explores what mathematics is and why it's worth doing, symmetry, networks and patterns, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, linking mathematical oscillations to animal gaits, how to deal with the peculiarities of the mathematical community, and much more.This carefully-edited book includes an introduction, Counting Sheep, and questions for discussion at the end of each chapter: I. Fear and Loathing - Mathematics and the wider worldII. Doing Mathematics - An insider's viewIII. Teaching Mathematics - How to get unstuck and other valuable lessonsIV. Mathematics and Gender - Portuguese mysteriesV. Mathematics Everywhere - And widely underappreciatedAbout Ideas Roadshow Conversations: This book is part of a series of 100 Ideas Roadshow Conversations. Presented in an accessible, conversational format, Ideas Roadshow books not only explore frontline academic research featuring world-leading researchers but also reveal the inspirations and personal journeys behind the research.

Ideas Roadshow conversations present a wealth of candid insights from some of the world’s leading experts, generated through a focused yet informal setting. They are explicitly designed to give non-specialists a uniquely accessible window into frontline research and scholarship that wouldn’t otherwise be encountered through standard lectures and textbooks.

Over 100 Ideas Roadshow conversations have been held since our debut in 2012, covering a wide array of topics across the arts and sciences.

See www.ideas-on-film.com/ideasroadshow for a full listing.

Copyright ©2013, 2021 Open Agenda Publishing. All rights reserved.

ISBN: 978-1-77170-095-5

Edited with an introduction by Howard Burton.

All Ideas Roadshow Conversations use Canadian spelling.

Contents

A Note on the Text

Introduction

The Conversation

I. Fear and Loathing

II. Doing Mathematics

III. Teaching Mathematics

IV. Mathematics and Gender

V. Mathematics Everywhere

Continuing the Conversation

A Note on the Text

The contents of this book are based upon a filmed conversation between Howard Burton and Ian Stewart in Coventry, England, on March 18, 2013.

Ian Stewart is Emeritus Professor of Mathematics at the University of Warwick and a bestselling science and science fiction writer.

Howard Burton is the creator and host of Ideas Roadshow and was Founding Executive Director of Perimeter Institute for Theoretical Physics.

Introduction

Counting Sheep

An engineer, a physicist and a mathematician are on a train that has just crossed into Scotland when outside of their window they see a black sheep standing in a field.

“How odd,” says the engineer. “All the sheep in Scotland are black.”

“No, no!” counters the physicist indignantly. “You can’t just generalize like that. All we can say is that only some Scottish sheep are black.”

“You idiots,” sighs the mathematician, exasperated. “Always jumping to conclusions. The only thing we can say with any certainty is that there is at least one sheep in Scotland which is black on one side.”

This joke might surprise you for two reasons.

For starters, you may be shocked to discover that there is such a thing as “mathematical humour” at all. It’s not the sort of thing that most people are even aware of.

But more significantly, it might make you suspect that what mathematicians are—what they do, how they think and what motivates them—is very, very different from what any long buried tussles with long division might have naively led you to believe.

Of course, we frequently have a pretty superficial image of other professions. Policemen do more than chase bad guys, while doctors do more than dispense medicine. On the other hand, policemen do chase bad guys and doctors do dispense medicine. Mathematicians, on the other hand, typically spend no more time doing long division than the rest of us. And most aren’t any better at it—or any more excited at the prospect of doing it—than anyone else.

So what do they do all day?

According to Ian Stewart, Professor of Mathematics at the University of Warwick and a highly acclaimed writer of both popular math books and science fiction, real mathematics is far removed from arithmetic.

“It’s about form and structure and logical connections. If certain things happen, if a problem is set up in a particular way, it has certain ingredients. What does that tell you? How can you answer it? It’s about problem solving, but it’s also about seeing the kind of elegant structure that opens up a better understanding of whatever it is you’re working on.”

If all that seems a little too abstract and highfalutin, jarring a bit too harshly with your own school day experiences, Professor Stewart will happily detail his mathematical motivations further.

“I like to work in areas, which, essentially, combine symmetry with the real world. Symmetries give you a built-in, beautiful, mathematical structure even before you start. It’s got to be nice, because symmetries are always nice. And then I find some connection to the real world. Combining the two, that’s where I feel happiest.”

Still too abstract?

Well, consider this. One of Stewart’s most significant achievements came from applying mathematical symmetry to animal movement. And it happened, as so often tends to be the case in the world of basic research, quite by accident.

At the time he was an expert on the mathematical symmetry principles of linked oscillators (think of springs or pendulums that are connected in some way). But then one day a popular science magazine asked him to review a book on how engineers take inspiration from nature, which serendipitously drove him in quite another direction entirely—at least at first.

“There were chapters on vision and robots, but it had a chapter with a whole series of papers on animal movement. One of the things they talked about was symmetric gaits, a gait being a pattern. And as soon as I saw ‘symmetric’ I thought, ‘Oh! That’s interesting!’

“I looked at the patterns and they were just like our oscillator systems. So in my review, I put in a throw-away sentence saying, ‘These patterns look like things I’ve seen in coupled oscillators. I wonder if anyone would want to fund that sort of research?’ I think I said, ‘Could anyone fund a robot cat?’

“About two days later I got a phone call from Jim Collins, who’s a biomechanical engineer now at Boston. Jim was in Oxford at the time, and he phoned up and said, ‘I can’t fund a robot cat but I know some people who can. Can I come and talk to you?’

“He knew the biology, the physiology of animal movement, and I knew the mathematics of coupled oscillators. We talked to each other and we put together a series of papers explaining how we thought this connection went. And that’s how it started.

“The beautiful patterns you see when an animal moves—think of a trotting horse, one diagonal pair of legs hits the ground and then the other diagonal pair—it’s absolutely perfect rhythm and it’s this beautifully symmetric movement. That’s one of the standard patterns you expect to see in a network of nerve cells, which is presumably what is controlling the movement.”

So now, suddenly, we’ve gone from networks of coupled oscillators to neurophysiology.

And that sort of leap, that rapid interplay between mathematical structure and the world around us, happens all the time, every moment.

“Math is in everything we use, everything we do. If you’re aware of this, from the moment you get up in the morning you start to see it. I look at the clock: it’s one of these modern clocks that sets its own time by radio. Without radio, that clock would not work in that way. Well, radio works because of a whole pile of mathematics. The engineers have to know the math. We don’t need to know it to read the clock, but in order to manufacture the clock somebody there has to know a certain amount about that. And that’s just one example.

“It’s absolutely everywhere. I often feel t...