News from the world of maths

It's a bleak time for the financial markets. We've seen financial institutions fall and governments around the world struggling to stabilise the markets. But who is to blame? According to media reports there are two suspects in the dock: the "rocket scientists" (a.k.a. the financial mathematicians) who provided the information behind the market's decisions, or the greedy bankers who only thought about quick profits and their end-of-year bonuses.

But just what role does maths have in the financial market? Most of us will have come into direct contact with financial maths when applying for a loan from a high street bank. Rather than the bank manager relying on how well they know you personally, as might have happened in the past, now loan decisions are based on statistical models. But these robust mathematical models predicting whether or not someone will be able to repay their loan did not avert the subprime mortgages in the US , the first domino to fall in the current crisis. Loans were still given to people the models predicted would default on their payments.

The failure of these high-risk loans infected the whole financial markets thanks to the use of credit derivatives to share the credit risk around. These complex financial instruments were profitable in a booming market, but are now paralysing the financial system. Did the mathematicians involved in developing these products get their sums wrong?

On the other hand, if the real culprits are the bankers, then what lead them to make such bad decisions? Could it have been down to their biochemical make up, and would the problem be solved by more diversity on the trading floor?

Read more for answers to all these questions...

Sadly, the LHC is on a compulsory break after breaking down last week, but here's something to while away the time until it's fixed:

An excellent series of nine films taking you into the fourth dimension is now freely available online and cheaply available on DVD. Using superb graphics and clear, concise, no-frills presentation, the series starts with a very basic introduction to projections, then steps from two dimensions up into three and then four, and ends up with some quite sophisticated - and very pretty - geometric objects and concepts. Everyone, from complete novice to university students, will find something interesting in this series, and at 13 minutes length each, the films are a great resource for the class room. The website contains detailed background info on each episode. Go have a look, it's well worth it!

Pierre Louis Moreau de Maupertuis
Born on the 28th of September 1698 in Saint Malo, France
Died on the 27th of July 1759 in Basel, Switzerland

For an originator of the principle of least action, Maupertuis led a surprisingly productive life, shunning neither effort nor intrigue. His early academic studies focussed on philosophy and music, were interrupted by a stint with the Musketeers, and resumed in Paris, where his interest in mathematics began to blossom. His first paper as a member of the Academie de Sciences explored the influence of a musical instrument's shape on the sounds it produces, and was followed by a range of works on mathematical curves. The entirely non-mathematical Salamander - yes, the amphibian - was the topic of another of his papers from that period.

Keen to expand his mathematical expertise, Maupertuis relocated to Basle in 1729, where he lived with and studied under none other than Johann Bernoulli. Back in Paris, papers on astronomy, mechanics and differential equations followed, and Maupertuis established himself as an eclectic mathematical talent. But it wasn't all theory. In 1736 Maupertuis set out on an expedition to Lapland, his mission to measure the length of a degree along the meridian. After enduring swarms of pesky insects, terrible cold and being shipwrecked, Maupertuis returned in 1737 with the knowledge that the Earth was oblate ... and two native Finnish girls. The latter did not further his academic standing, instead they laid him open to ridicule from his enemies.

And enemies there were many. Maupertuis, who was given to penning venomous attacks on his opponents, managed to fall out with Johann Bernoulli and later also with Voltaire with whom he had become friends after the expedition. On the upside, his academic talents inspired the interest of Frederick the Great, who in 1740 invited him to become president of the brand new Berlin Academy. After visiting Frederick in Berlin, Maupertuis ended up on the battle field on the side of the Prussians, was taken prisoner by the Austrians, but was eventually released, shaken but unharmed. In 1746, after his career had made good progress in Paris, he did take the presidency of the Berlin Academy and moved to Berlin permanently.

Maupertuis talents were indeed eclectic. He published on a range of subjects including mathematics, philosophy and astronomy. A hundred years before Darwin he almost formulated Darwin's theory of evolution. But it is probably the principle of least action that he is most remembered for now. The principle says that physical systems, in getting from state A to state B, always choose the path that minimises the effort required. This begs the question of who or what does the minimising, and the principle opened up all sorts of cans of teleological worms.

Maupertuis was extremely proud of his principle of least action, so it came as a shock when he accidentally recommended a paper for publication which stated that it wasn't him but Leibniz who first postulated it. The resulting priority dispute cast a shadow over the last years of his life and had an adverse effect on his health. In 1756 he left Berlin for good and three years later died on a journey he undertook to improve his health.

For more information on Maupertuis visit the MacTutor History of Maths site

And for more on the principle of least action read the Plus article Frugal nature.

BBC Four will launch a new three-part TV series on maths at 9pm this coming Monday the 6th of October. In The story of maths Marcus du Sautoy, Oxford mathematician and one of the UK's finest maths popularisers, describes the often surprising lives of the great mathematicians, explains the development of the key mathematical ideas and shows how — in a multitude of unusual ways — those ideas underpin the science, technology and culture that shape our world. The first episode will look at the contributions from the ancient Greeks.

To get you into the mood, have a look at du Sautoy's Plus articles The prime number lottery, The music of the primes, and Beckham in his prime number.

If you prefer the radio, then tune into BBC Radio 4's In our time on Thursday the 9th of October at 9am and again at 9.30pm. Melvyn Bragg together with experts including John D Barrow will discuss Gödel's infamous incompleteness theorem.

Alles Gute zum Geburtstag! Joyeux Anniversaire! Suk San Wan Keut! Sun Yat Fai Lok! Hartelijk gefeliciteerd! Felichan Naskightagon! And Happy Birthday to Google in the other 93-plus languages it speaks!

As the web search engine Google celebrates its 10th birthday it is hard to imagine life online without it. It has become such an indispensable tool that we don't just search for something any more, we "google" it, as recognised by the Oxford English Dictionary in 2006. What many people don't realise is that Google's rise to become one of the most successful search engines on the web today is due to the mathematical algorithm PageRank, devised by Sergey Brin and Lawrence Page, the founders of Google. This algorithm not only decides which webpages match your search criteria (which all search engines do), but also which are more important and returns these at the top of the results.

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More evidence of the intrinsic beauty of maths, this time shown in a lovely slideshow from the BBC, narrated by mathematician Lasse Rempe from the University of Liverpool.

Rempe works in the area of dynamical systems: systems that change over time and can be found everywhere from the stockmarket to the weather. In the slideshow, he explains how dynamical systems can be generated from very simple polynomials yet produce extremely complex behaviour, and how these systems can be graphically represented by such beautiful images.

As John Barrow told us in our first image-enhanced Plus podcast Cosmic Imagery, mathematical images such as these have actually been responsible for changing science and how we see the world around us . So sit back with your coffee and enjoy the shows!

You can read more about dynamical systems and mathematics and art on Plus.

...and yesterday was brought to you by the number 54, thanks to the Mathematical Association of America's NumberADay blog. Every working day they post a number and a biography of its interesting properties.

Today's number 11,185,272 is the number of decimal digits in the 46th known Mersenne prime, discovered on Sept. 6, 2008 (you can read more in Prime record broken? on Plus).

54 might seems less significant, but in fact thanks to the MAA Plus now knows that it is the smallest number that can be written as the sum of 3 squares in 3 ways, the number of colored squares on a Rubik’s cube, and is a nonadecagonal (19-gonal) number!

It's lunchtime, and I'm waiting in the cafe queue to buy a sandwich along with everyone else. What a lot of sandwiches... Imagine if everyone piled their sandwiches one on top of another... I wonder how high the mighty tower of sandwiches might be? Let's see... 60 million people in the UK, say 1 in 8 is having a sandwich right now, each sandwich might be about 3cm thick including filing, so that's... over 200km high!

You might say I'm thinking too much about sandwiches, but I'm actually exercising my number sense. Which, along with allowing me to make quick guesses about how big things are or how many there might be, also might be helping me get better at calculus and algebra. Researchers Michèle Mazzocco, Lisa Feigenson and Justin Halberda, from John Hopkins University, have shown that being good at formal mathematics is linked to having a good innate number sense. See, I'm not waiting in the sandwich queue, I'm studying!

Read more...

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As sporting glories continue in Beijing with the Paralympics taking up where the Olympics left off, many of us have marvelled at the architecture almost as much as at the sporting achievements. One of the Olympic venues, the National Aquatic Centre or Water Cube, seems to be sliced from a giant foam of bubbles, and it turns out mathematics is responsible for this amazing structure.

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