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17 Maths equations that changed the world

Neeraj Gangal
Neeraj Gangal
Professor Ian Stewart

Few academic subjects evoke as polarised reactions as ‘Mathematics’ does.

It is a dreary chore for most, an inescapable rite of passage that they have to endure during their growing years.  Many others relish it with aplomb, finding the subject as gripping as a suspense novel or as intriguing as life itself.

But it takes someone like Professor Ian Stewart to bridge this divide by unraveling the mysteries of a complex subject and presenting them in simplified English before millions of readers who are more excited by the recipe of a pie, than the value of Pi.

If his attire (in the picture above) reminds you of Steven Spielberg’s iconic character Indiana Jones, it’s probably no strange coincidence. If the fictional Dr Jones is a University professor and as the industry magazine Archaeology described him, a 'great diplomat for archaeology', so is Professor Stewart for Mathematics.

With more than 80 books to his credit, Professor Stewart has popularized the subject like few others. His books on Mathematics have consistently made it to the ‘bestsellers’ lists; his creations even include three comic books on the subject.

The Emeritus Professor of Mathematics at the University of Warwick is currently in the news for his latest book ‘17 Equations that Changed the World’. "Equations are the lifeblood of mathematics, science, and technology. Without them, our world would not exist in its present form," Stewart says.

According to Prof. Stewart, the following 17 equations have changed the world: Pythagoras's Theorem, Logarithms, Calculus, Newton's Law of Gravity, The Square Root of Minus One, Euler's formula for Polyhedra, Normal Distribution, Wave Equation, Fourier Transform, Navier-Stokes Equation, Maxwell's Equations, Second Law of Thermodynamics, Relativity, Schrödinger equation, Information Theory, Chaos Theory and Black Scholes Equation.

So what inspired him to write the book and are there any equations that could pull us out of the current global downturn?

Professor Stewart spoke to Yahoo! India Finance Editor, Neeraj Gangal, in an exclusive interview:

What was the trigger that pushed you to write this one dedicated to ‘equations’?

A Dutch publisher, who has translated some of my books, was talking to my English publisher at a book festival, and asked him whether he knew of a popular book on mathematical equations. Not the nuts and bolts of the mathematics, but where they came from historically, what they did for humanity, what they’re used for now, and what they mean. He replied that there are a few nice books about equations, but not one like that. The more we thought about the idea, the more potential we saw in it. It was slightly dangerous to try to tackle equations head on, because many people find them intimidating. On the other hand, that’s what science popularisation should be about: making intimidating things comprehensible and friendly. So we delayed a couple of other books that we were planning to produce, to make time for this one. Judging by the response, it was the right choice!

How many of the 17 equations influence each one of us the most in our routine life - on a daily basis?

We ‘use’ about ten of them almost every day; not consciously, but they are behind the scenes, built into our technology, influencing our lives. Engineers have to know about them, and the rest of us benefit without realising they’re present. Radio, TV, and wireless communications rely on Maxwell’s equations and the wave equation. The food we eat comes from crops that have been bred using the equations of statistics. Aircraft overhead, and our cars, involve the equations of aerodynamics. The Internet requires equations from information theory, computer chips use equations from quantum mechanics, digital cameras use the Fourier transform. I could continue for some time — design of buildings for earthquake protection, satellite navigation, communications satellites, design of bridges...

Why are most youngsters intimidated by the very mention of Mathematics?

Over the years, mathematics has acquired a negative image. It’s not ‘cool’. It’s also demanding and unforgiving --- if the answer’s wrong, then it’s wrong, and no amount of clever argument can change that. In the USA a recent study shows that the mathematical abilities of mathematics teachers have declined. Basically, if you’re good at maths then you have a huge range of jobs available, of which teaching is just one. To teach maths well, you have to be confident about your own understanding of it. But many teachers aren’t. But even the best ones are heavily constrained by the need to teach to a specific syllabus, one that focuses too strongly on technique. I find that if young people are made aware of the way maths affects our lives, of its creative aspects, of how you can tackle new problems, and generally just enjoy the subject, then their attitudes become much more positive.

Which equation, do you think, has had the greatest impact on human civilisation?

Overall, the equation(s) behind calculus, worked out by Newton and Leibniz, with some predecessors like Fermat. In Newton’s hands, calculus became the key that opened up what he called the System of the World. How the Universe works. Ironically, he didn’t use calculus in his epic Principia Mathematica, but it influenced his thoughts. The mathematical physicists of Europe turned calculus into the basis of the whole of science --- heat, light, sound, waves, gravity. Then electricity and magnetism got in on the act as well. Many of my 17 equations were made possible by calculus; for instance, Maxwell’s equations, which among other things gave us radio and TV.

In the current global financial gloom, which is the one equation that you would suggest bankers/ financial experts look at?

I’d like them to stop looking for mathematical tricks that promise huge profits but don’t adequately reflect the realities of the market or the risks involved. I’d like them to consider stability and control of the financial sector, not just runaway surges that lead to meltdown when they go wrong. The work of Robert May and the Bank of England’s Andrew Haldane, on stability equations motivated by ecosystems, would be a good starting-point. Outside the world of equations altogether, bankers need to deal with an ingrained culture of dishonesty and greed (we’ve seen half a dozen examples in recent years).

How difficult was it writing this book, considering you are as popular among readers from non-Mathematical backgrounds?

I was confident that I could make the material accessible, even to non-mathematicians, because of the historical and cultural aspects. The equations were the characters in a drama, so to speak; the main action was the drama itself. The hardest part, in some ways, was to choose the equations. Not because there were too few, but because there were too many. My first attempt listed about 40. I wanted to do a thorough job on each equation, so the most I could sensibly handle was 20, preferably fewer. So I started throwing out anything that hadn’t made a really major impact on human history, combining related equations into one chapter, and so on. Then I took a deep breath and removed three or four for which the story wasn’t as strong. After that it was surprisingly easy to write. I learned a lot about history, and areas of human activity that I’ve not worked in myself, and that meant that a lot of the material was fresh, even to me. That generally helps with the writing.

About Professor Ian Stewart

Ian Stewart was educated at Cambridge (MA) and Warwick(PhD). He has honorary doctorates from Westminster, Louvain, Kingston, and the Open University. He is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He has held visiting positions in Germany, New Zealand, Hong Kong, and the USA. His present field of research is the effects of symmetry on dynamics, with applications to pattern formation and chaos theory in areas including animal locomotion, fluid dynamics, mathematical biology, chemical reactions, electronic circuits, computer vision, quality control of wire, and intelligent control of spring coiling machines.

More information about the author and the book can be found here or here.