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January 23, 2007
Tuesday, January 23, 2007

Mathematical Moments - Harald Bohr

Died 56 years ago: Harald August Bohr

Born: 22nd of April 1887 in Copenhagen, Denmark
Died: 22nd of Jan 1951 in Copenhagen, Denmark

Harald Bohr must be the only mathematician who came to fame through football: as a member of the Danish national team he won a silver medal at the 1908 Olympics in London. Although it's hard to imagine these days, back then you could still pursue a sports career in your spare time, and by the time Bohr took part in the Olympics, he had already spent four years doing a maths degree at the University of Copenhagen. His sporting success gained him celebrity status in Denmark and when he defended his doctoral thesis after the games, the audience reportedly contained more football fans than mathematicians.

Eventually, though, his interest in maths gained the upper hand and he became a professor of mathematics at the Polytechnic Institute in Copenhagen in 1915, moving on to the University of Copenhagen in 1930. He was interested mainly in the application of analysis to number theory. Together with Edmund Landau he proved some major results about the Riemann zeta function, which lies at the heart of the famous Riemann hypothesis. Although their work contributed two important steps towards its solution, no-one has yet been able to fill in the remaining details — the problem is still unsolved and bugs mathematicians to this day.

But if Bohr's name rings a bell in your brain, it's probably not because of his football stardom, or because of his own excellent contribution to maths, but because of his famous brother Niels. Niels Bohr won the 1922 Nobel Prize for physics for his insights into the structure of atoms and for his work on radiation, and was one of the founding fathers of quantum mechanics. Although Niels takes most of the posthumous limelight, Harald's contribution to maths was nonetheless remarkable, gaining him international recognition as one of the most prominent Danish mathematicians of the twentieth century.

But Harald Bohr's life wasn't all maths. His generosity towards people in need, especially those fleeing the Nazi regime in Germany, gained him just as much international acclaim as his work.

You can read more about the brothers Bohr on the MacTutor History of Mathematics Archive:

Find out more about the Riemann hypothesis in the following Plus articles:

posted by Plus @ 10:55 AM

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December 27, 2006
Wednesday, December 27, 2006

Science in School - the best in science teaching and research

The third issue of the magazine Science in School is just out, and as usual is a fascinating read about all areas of science. Plus particularly enjoyed Richard West's reminiscences of discovering a comet, and the articles on the power behind the Sun and the advances of Muslim scientists during the Dark Ages in the West.

Science in School aims to promote inspiring science teaching across Europe. It's published quarterly, and you can either subscribe to the printed edition or read it free online at http://www.scienceinschool.org.

posted by Plus @ 11:39 AM

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December 8, 2006
Friday, December 08, 2006

BETT 2007 - come and say hello to the Plus team!

Always a firm date in the educational diary, BETT 2007, 10-13 January, Olympia, London, promises to showcase a wealth of new technologies, innovative ideas and the latest advice.

The MMP's stand this year is S69 in the Grand Hall Gallery, so if you're visiting BETT, come and say hello to Plus and the rest of the staff from the MMP.

posted by Plus @ 5:50 PM

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November 30, 2006
Thursday, November 30, 2006

Stats goes independent

In the recent Queen's Speech to Parliament there was one point that went largely unnoticed, but that may drastically alter the nature of political argument: the government's plan to set up an Independent Statistics Board. The board will "reinforce the independence, integrity and quality of statistics produced in government". So why is this necessary? As always with statistics, it's not necessarily their quality that gives cause for concern, but their presentation. At the moment, the Office of National Statistics reports straight to ministers — and ministers get hold of the outcomes of statistical surveys and studies ahead of everyone else. So what reaches us when results are released is not just the numbers, but also the ministers' interpretation of them.

With the proposed Statistics Board in place, ministers would no longer get these sneak previews. Statistics would not only be produced, but also analysed and interpreted by independent experts that have no links with policy makers. Their interpretations would be understandable for the general public. Politicians, who would get the results at the same time as everyone else, would find spinning them a whole lot harder than they do now. Statistics are a critical measure of a government's performance on pretty much everything, including health, education and the economy. They are a crucial tool in political debate. So, who knows — maybe politics is just about to get more honest.

To find out more read the Treasury's press release or listen to this episode of the BBC 4 programme More or less, or, if you're very brave, read the government's consultation document.

posted by Plus @ 12:19 PM

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November 23, 2006
Thursday, November 23, 2006

Mathematical moments - Taking chances with De Moivre

Abraham De Moivre

Born on the 26th of May 1667 in Vitry-le-Francois, France
Died on the 27th of November 1754 in London, England

When De Moivre first came across Newton's famous work the "Principia" he was so struck by its depth and rigour that he immediately bought a copy and cut it into pieces - carrying just a few pages at a time was the only way he could study the work while making his rounds tutoring private students in London.

But it wasn't just dedication that gained him full marks. Since an early age he had been interested in maths, especially in games of chance, and he is today known as a pioneer of probability theory and of analytic geometry. His "Doctrines of chance" presented the broadest and most rigorous treatment of probability of its day, and he is credited with deriving the normal curve and developing the concept of standard deviation. His name is famously attached to a formula that gives geometric meaning to powers of complex numbers by expressing them in terms of trigonometry.

De Moivre's eminence as a mathematician was recognised by many of his most prominent contemporaries, including Newton, who he was friends with, and Leibniz. Interestingly, the Royal Society called upon him to referee Newton and Leibniz's dispute about who had first invented the calculus.

Sadly, though, De Moivre's genius was never rewarded professionally. As a French national who had been expelled from France (after a prison sentence) because of his protestant religion, he remained a foreigner in London. Despite the support of his prominent friends he was never employed by a university. He made a living as a private tutor and died in poverty.

Death played an important role in his mathematics. Together with Halley, who gave his name to the comet, he set about investigating mortality statistics, laying the foundations for actuary theory used by life insurances.

Most curiously, De Moivre is said to have used maths to predict his own death. He had noticed that he was sleeping 15 minutes longer every day. Analysing the arithmetic progression 15, 30, 45, .... , he calculated that on the 27th of November 1754 he would sleep through the full 24 hours. He was right - it was the day he died.

Find out more about De Moivre on the MacTutor history of maths archive, about De Moivre, death and statistics in this past Plus article, and about complex numbers and trigonometry on cut-the-knot.

posted by Plus @ 4:21 PM

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November 21, 2006
Tuesday, November 21, 2006

More or Less back for more

Plus's favourite radio show on all things mathematical is back on the air. More or Less has two series a year on BBC Radio 4, exploring maths in politics, health, avalanches, and much more. In the first shows of this season they have already covered drug testing in sport, the economics of climate change, uncovered the games behind hospital waiting times, and the perverse nature of randomness.

The show is produced in association with the Open University, which provides additional material on their site. You can hear all the past shows online at the More or Less site, and listen live every Monday at 4.30pm on BBC Radio 4.

You can read more about More or Less from presenter Andrew Dilnot in a past article on Plus.

posted by Plus @ 10:41 AM

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