Plus Blog

July 14, 2011

What's a particular piece of mathematics good for? It can take decades, or even centuries for an answer to this question to materialise. The power of mathematics is hidden behind a range of unforeseeable applications in the modern world that arise from mathematical discoveries of the past. In today's climate, in which scientific research is increasingly judged according to its impact, this can pose a problem for pure mathematics.

Now a group of mathematicians from the British Society for the History of Mathematics have collected some examples of the unplanned impact of maths, which are reported in the 14th July issue of the journal Nature. Peter Rowlett, who coordinated the collection, said, "Although most mathematicians know that mathematics has this surprising nature, many that I have spoken to aren't aware of more than one or two specific examples. I thought the British Society for the History of Mathematics could help by searching through history for examples that are less well known. We hope this collection will only be the start and that more mathematicians will send their favourite stories to us."

Leonhard Euler

Leonhard Euler 1707 - 1783.

The field of topology is an illustrative example. Started by Leonhard Euler and studied for 250 years as a purely theoretical discipline, it has in the last two decades found applications in areas as diverse as genetics, the study of galaxy formation and robotics. These applications rely on 250 years of pure research, but the advances would not have been made if the researchers had had to justify the planned impact before studying their mathematics.

In technology quaternions, a 19th century discovery which seemed to have no practical value, have turned out to be invaluable to the 21st century computer games industry, while work on the best way to stack oranges started by Kepler in 1611, is essential to modern telecommunications.

Einstein's theory of relativity, which seemed to come as a spark of genius from nowhere, nevertheless drew on abstract geometry developed half a century earlier. Fourier's theory of vibrating strings, via very abstract mathematics in the 20th century, has now yielded new insights into quantum physics.

Gambling on 16th century dice games led to a discovery in mathematical probability that is crucial to the insurance industry, while a recent insight into a quantum theory thought experiment has unexpectedly found applications in the outbreak of viral disease and the risks associated with stock market volatility.

To find out more, read the Nature article (behind a pay wall unfortunately) and if you've got further examples of your own, post a comment here or contact Peter Rowlett on Twitter.

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July 8, 2011

Suppose you and a friend have been arrested for a crime and you're being interviewed separately. The police offer each of you the same deal. You can either confess, incriminating your partner, or remain silent. If you confess and your partner doesn't, then you get 2 years in jail (as a reward for talking), while your partner gets 10 years. If you both confess, then you both get 8 years (reduced from 10 years because at least you talked). If you both remain silent, you both get 5 years, as the evidence is only sufficient to convict you of a lesser crime.

What should your strategy be? As a selfish and rational individual, you should talk. If your partner also talks, then your confession gets you 8 years instead of 10. If your partner doesn't talk, then it gets you 2 years instead of 5. Talking is your dominant strategy, it leaves you better off than silence, no matter what your partner does.

The trouble is that your partner, just as selfish and rational as you, will come to the same conclusion. You'll both decide to talk and get 8 years each. Paradoxically, your dominant strategy will leave both of you worse off than silence would have done.

The prisoner's dilemma is one of game theory's most famous games because it illustrates why people might refuse to cooperate when they would be better off doing so. One real-life situation that is similar to the dilemma is an arms race between two countries, in which both countries increase their military might when it would be better for both to disarm.

Read more about the prisoner's dilemma on Plus:

Adam Smith and the invisible hand

Mathematical mysteries: Survival of the nicest

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July 7, 2011

Three cheers for John Barrow, the Director of the Millennium Mathematics Project (of which Plus is a part), for winning the IMA-LMS Christopher Zeeman Medal for his work promoting maths to the wider community!

Barrow has made enormous contributions to the public understanding of mathematics, particularly in his role as Director of the MMP, based at University of Cambridge. The MMP has done a huge amount to develop mathematical interest and ability among school students and the general public with activities such as NRICH and, of course, Plus.

In a joint statement, David Youdan, Executive Director of the Institute of Mathematics and its Applications, and Professor Angus Macintyre, President of the London Mathematical Society, said: "Our two societies have a common priority of promoting mathematics both to school students and to the adult public. Society should not lose sight of the fundamental importance of mathematics, both as a foundation for much of science and engineering, and as a human endeavour aimed at understanding some of the deepest problems about the structure of our universe. Professor Barrow has been at the forefront of mathematics communication for many years and is world famous for his contributions to public understanding of one of the oldest, most beautiful, and most essential of sciences".

The medal is named in honour of Professor Sir Christopher Zeeman, FRS, one of the UK’s foremost mathematicians who spent much of his career at the University of Warwick sharing his love of mathematics with the public. In 1978, Sir Christopher was the first ever mathematician to be asked to deliver the Royal Institution’s Christmas lectures in its 125 year history. Barrow said: "As someone who was inspired by Christopher Zeeman’s compelling presentations of mathematical ideas as a school student, it is a great honour to receive this award that bears his name".

As well as promoting mathematics through his work with the MMP, Barrow is also the author of many books on mathematics and cosmology. His recent publication – One hundred essential things you didn’t know you didn’t know – shows how mathematics explains our world, in a way that is accessible to anyone with only a basic mathematical knowledge. His most recent work, The Book of Universes, shows how mathematics has enabled us to understand so much of the Universe we see around us.

A tireless champion of mathematical awareness for several decades, Barrow has won both the Royal Society’s Faraday Prize and the Kelvin Medal of the Institute of Physics. He has also engaged with the arts and in 2002 his play Infinities premiered in Milan, directed by Luca Ronconi, and won the Premi Ubu Theatre Prize and the Italgas Prize. The Italian edition of his book Cosmic Imagery, about the role of pictures in the history of science and mathematics, won the 2011 Merck-Serono Prize for Science and Literature. Barrow has also been both the Gresham Professor of Astronomy and Gresham Professor of Geometry at Gresham College, London and is a Fellow of the Royal Society.

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June 21, 2011

The strawberries are out and it's raining... so it must be Wimbledon time! If you're trying to while away the time waiting for the covers to come off the court then give Cliff Richard a break and take a look at some of the great tennis articles and puzzles here on Plus!

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Anyone for tennis (and tennis and tennis...)?
American John Isner and the Frenchman Nicolas Mahut are set for a rematch in the Wimbledon 2011 Championships — but how will it compare with their match of epic proportions from last year? Just how freaky was their titanic fifth set from 2010 and what odds might a bookmaker offer for a repeat?

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Making a racket: the science of tennis
A perfect althletic performance takes more than training, it also takes engineers working hard to produce the cutting-edge equipment. If you're a tennis player, your most important piece of equipment is your racket. Over recent decades new materials have made tennis rackets ever bigger, lighter and more powerful. So what kind of science goes into designing new rackets?

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Winning at Wimbledon
What does it take to win at Wimbledon? Can you figure out how many games the champion has to win? And how many matches are played overall?

And you can also find out if the robots have their eye on the trophy, if tennis should be in the Olympics and much, much more about maths and sport on Plus and on the MMP's Countdown to the Games.

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June 7, 2011

How big is the Universe? And how small is the smallest thing within it? This cute website developed by Cary Huang puts things into perspective. It lets you explore the entire range of scales, from the smallest length (the Planck length) all the way up to the entire Universe, via atoms, people, giant earthworms, planets, galaxies and more.

http://www.primaxstudio.com/stuff/scale_of_universe/

 

4 comments
June 7, 2011

Kneeling in the mud by a country road on a cold drizzly day, I finally appreciated the wonder that is a lever. I was trying to change a flat tyre and even jumping on the end of the wheel wrench wouldn't budge the wheel nuts. But when the AA arrived they undid them with ease, thanks to a wheel wrench that was three times the size of mine. There you have it ... size really does matter!

lever

Image by CR

A lever is a truly remarkable device that can literally give any of us the strength of ten men. You can counteract 10 men pushing down on one side of a see-saw by applying just 1/10th of their force, as long as you are 10 times further from the see-saw's centre as they are.

This is because the forces acting on a lever are proportional to the distances they are from the fulcrum. In this way a small amount of force moving a longer distance can move a large load over a smaller distance.

Levers are working hard all around us: in see-saws (where the fulcrum is between the loads), in wheel barrows (where the load is between the fulcrum and the force) and even in our very jaws (where the force is applied between the fulcrum and the load).

Archimedes was the first to mathematically describe how levers work and famously said: "Give me a place to stand, and I shall move the earth with a lever." And give me a long enough wheel wrench and I might just be able to change my next flat tyre for myself!

You can read more about levers from Wikipedia, and more about mechanics and about Archimedes on Plus

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