Plus Blog

October 29, 2010

Immortality by Nicholas Mee and John Robinson.

SCIENAR, a European project to stimulate and develop links between science and art, has just produced a new DVD exploring three emblematic scenarios where science and art intersect. Looking at three historical ages, antiquity, the renaissance and modern times, the DVD explores a range of topics, from ancient geometry to perspective, relativity and chaos theory. You can find out more on the associated website.

Virtual Image will send free copies of the DVD to the first ten people to e-mail Nick Mee at Anyone else can obtain a DVD for £5 including postage and packing by contacting Virtual Images by email, phone or post. The contact details are:

Virtual Image Publishing Ltd
184 Reddish Road
Tel: 0161 480 1915
Fax: 0161 612 2965

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October 15, 2010
 The birth of Hiroshima, Carla Farsi, oil on canvas. Reproduced with kind permission of the artist.

The birth of Hiroshima, Carla Farsi, from the Plus article Art+Math=X.

If you're an artist who's inspired by maths and science, here's a chance to exhibit your work. Through its annual open exhibition opportunities, Orleans House Gallery in London helps artists both locally and nationally to showcase their work in group exhibitions. Each year, over 500 individual artists exhibit work in a range of open exhibitions across three galleries in London: Orleans and Stables Galleries, Twickenham and the Riverside Gallery in Richmond.

In 2010, there are further opportunities for you to submit artwork for an exhibition at Riverside Gallery, Picturing Science. Scientists use an abstract language of signs to visualise and explain the invisible forces, relationships and processes which make up our world. Artists similarly create images to transmit and analyse meaning. The theme of this exhibition is the collision, intersection and contamination of these two systems of representation. Any media (prints, photos, paintings, objects, sculptures, film) and style are considered.

The submission deadline is the 23rd of October and the exhibition will run from December to February. For more information visit the Picturing Science website.

October 5, 2010

The Maths Careers website has launched a poster competition for students aged 11 to 19. You're invited to pick a historical mathematician and design an A4 poster about them. Do a little digging and find out the things they don't teach in your maths lessons – who were these mathematicians? What were their lives like? How did they come up with their great mathematical ideas? The best three posters from readers aged 11-14, 14-16 and 16-19 will win an iPod shuffle and a £25 iTunes voucher, and your posters will also appear on the Maths Careers website for everyone to see.

For information on how to enter visit the Maths Careers website.

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October 4, 2010

Martin Gardner

In May this year Martin Gardner, who has inspired generations of mathematicians with his recreational maths, sadly passed away. He wanted no memorials, but he expressed a desire for the Gatherings for Gardner to continue - these were events held every two years in his honour, exploring all kinds of topics that would interest him, mathematics, science, art, magic, puzzles and more.

In this spirit the 21st of October 2010, which would have been Gardner's 96th birthday, will see a global Celebration of Mind in his honour. Events will take place in different locations around the world. You're invited to join this celebration party by signing up to attend an event in your area, or take the lead to organise and host a celebration party yourself. There are endless opportunities to host an event and introduce others to the wonders of an eternally curious mind. To find out about events in your area and organising one yourself, visit the Celebration of Mind website.

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October 4, 2010

Brian Cox

The physicist Brian Cox, presenter of the BBC2 series Wonders of The Solar System has teamed up with the Big Bang science fair to launch the Big Bang Lesson. Brian will visit one school somewhere in the UK and deliver a lesson based around the solar system. The class is designed to inspire pupils and generate interest in science, technology, engineering and maths. Students aged 11-18 can enter their school into the draw through Facebook or the Big Bang website. One UK school will be picked at random to receive the lesson in November.

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September 9, 2010

Bad statistics can mislead, and who'd know this better than mathematicians? It's ironic, then, that mathematics itself has fallen victim to the seductive lure of crude numbers. Mathematicians' work is being measured, ranked and judged on the basis of a single statistic: the number of times research papers are being cited by others. And mathematicians are not happy about it.

Is this good maths?

Like any other area in receipt of public money, mathematical research needs to be accountable. A reasonable way to judge the quality of research is the impact it has on future research: ground-breaking work will be heavily discussed and built upon, and mediocre work largely ignored. Traditionally, the reputations of individual researchers, institutions, or research journals have hinged on the opinions of experts in the field. The rationale behind using citation statistics is that bare numbers can overcome the inherent subjectivity of these judgments. In a competitive world it's the bottom line that should do the talking.

Bottom lines are crude, however, and summary statistics open to misuse. A whiff of scandal floated through this year's International Congress of Mathematicians, when the mathematician Douglas N. Arnold (president of the Society for Industrial and Applied Mathematics) exposed what appears like a blatant example of citation fraud. It involves the International Journal of Nonlinear Science and Numerical Simulations (IJNSNS) and a summary statistic called the impact factor.

The impact factor of a journal measures the average number of citations per article in the journal, but only taking into account citations from the current year to articles that have appeared in the previous two years. So old citations don't count and neither do citations to articles that are older than three years.

IJNSNS has topped the impact factor chart for applied maths journals for the last four years by a massive margin. In 2009 its impact factor was more than double that of the second in line, the esteemed Communications on Pure and Applied Mathematics (CPAM). A panel of experts, however, had rated IJNSNS in its second-to-last category: as having a "solid, though not outstanding reputation". In the experts' opinion IJNSNS comes at best 75th in the applied maths journal rankings, nowhere near the top.

There are some easy explanations for this mis-match between the impact factor chart and expert opinion. A closer look at citation statistics shows that 29% of the citations to IJNSNS (in 2008) came from the editor-in-chief of the journal and two colleagues who sit on its editorial board. A massive 70% of citations to IJNSNS that contributed to its impact factor came from other publications over which editors of IJNSNS had editorial influence. An example is the proceedings of a conference that had been organised by IJNSNS's editor-in-chief Ji-Huan He. He controlled the peer review process that srcutinised papers submitted to the proceedings.

Another striking statistic is that 71.5% of citations to IJNSNS just happened to cite articles that appeared in the two-year window which counts towards the impact factor (the 71.5% is out of citations from 2008 to articles that have appeared since 2000). That's compared to 16% for CPAM. If you use a five-year citation window (from 2000 to 2005) to calculate the impact factor, IJNSNS's factor drops dramatically, from 8.91 to 1.27.

The conclusions from this are obvious: cite your own journal as often as possible (with citations falling in the two-year window) and make sure that authors who fall under your editorial influence do the same, and you can propel your journal to the top of the rankings.

Libraries use impact factors to make purchasing decisions,
but mathematicians are judged by them too.

What's worrying is that impact factors are not just being used to rank journals, but also to assess the calibre of the researchers who publish in them and the institutions that employ these researchers. "I've received letters from [mathematicians] saying that their monthly salaries will depend on the impact factors of the journals they publish in. Departments and universities are being judged by impact factors," says Martin Grötschel, Secretary of the International Mathematical Union, which published a highly critical report on citation statistics in 2008.

Grötschel dismisses the blind use of impact factors as "nonsense" and not just because they are open to manipulation. For mathematics in particular, the two-year window that counts towards the impact factor is simply too short. There are examples of seminal maths papers that didn't get cited for decades. In fact, scouring 3 million recent citations in maths journals, the IMU found that roughly 90% of all citations fall outside the two-year window and therefore don't count towards the impact factor. This is in stark contrast to faster moving sciences, for example biomedicine, so using impact factors to compare disciplines presents mathematics in a truly terrible light.

Another confounding factor is that papers may get cited for all the wrong reasons. As Malcolm MacCallum, director of the Heilbronn Institute for Mathematical Research, pointed out at a round table discussion at the ICM, one way of bumping up your citation rates is to publish a result that's subtly wrong, so others expose the holes in your proof, citing your paper every time. Malicious intent aside, someone might cite a paper not because it contains a ground-breaking result, but because it gives a nice survey of existing results. If on the other hand your result is so amazing that it becomes universally known, you might lose out on citations altogether — few people bother to cite Einstein's original paper containing the equation E=mc2 as the result and its originator are now part of common knowledge.

The list of impact factor misgivings goes on (you can read more in the IMU report on citation statistics). The fact is that a single number cannot reflect a complex picture. With respect to manipulation, Arnold points to Goodhart's law: "when a measure becomes a target, it ceases to be a good measure". What's more, no one knows exactly what the impact factor is supposed to measure — what exactly does a citation mean? As a statistical quantity the impact factor is not sufficiently robust to chance variation. As the IMU report points out, there's no sound statistical model linking citation statistics to quality.

How, then, should mathematical quality be measured? Mathematicians themselves aren't entirely in agreement on how big a role, if any, citation statistics should play, or even whether things should be ranked at all. Everyone agrees, however, that human judgment is essential. "Impact factors — we cannot ignore them, but we have to interpret them with great care," says Grötschel, the IMU Secretary. The IMU, together with the International Council of Industrial and Applied Mathematics, has set up a joint committee to come up with a way of ranking journals that might involve human judgment and statistics.

With their fight against the mindless use of statistics mathematicians will do a service not just to themselves. "Some of [our work on this] has very broad applications in other sciences," says Grötschel. "It's very important that mathematicians are at the forefront of this issue."

Further reading

  • Read Douglas N. Arnold and Kristine K. Fowler's article Nefarious Numbers.
  • The use of citation statistics is explored in this IMU report.
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