Mathematics Weblog

Mathematical Intrigue

There’s a long and fascinating article in The New Yorker* about power, international politics and intrigue at the top level of mathematics connected with Grigory Perelman’s proof of the Poincaré Conjecture and his rejection of the Fields medal.

Basically Perelman, a reclusive mathematician, in 2002-3 had published an outline of a proof of the Poincaré Conjecture. In June 2006 a paper by Huai-Dong Cao and Xi-Ping Zhu says: “In this paper, we give a complete proof of the Poincaré and the geometrization conjectures“. The argument is over whether the latter paper just ‘filled in the gaps’ or is a proof in its own right.

If you thought that mathematicians are free from all the prejudices and scrambling for power that inflicts many human beings, then the New Yorker will quickly disabuse you of the fact. One of the earliest such squabbles was between Newton and Leibniz over who first invented differential calculus and it has always been so. The difference between mathematics and other spheres is that the arguments are about prestige rather than money.

*Thanks to Ars Mathematica for the link to this article

A Level Results Day

The Qualifications and Curriculum Authority, the body in charge of exams in the UK, is running a newspaper ad to show that A levels are not getting easier. They do this by reproducing exam questions. And which gets the greatest prominence by far? You guessed it – an A level maths question. This is because everyone “knows” that maths is hard and only the brightest people take it. Sigh!

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The question just asks you to find the x-coordinate of the minimum point of using an iterative solution of . Of course it holds your hand through the question, as is the fashion these days as I have mentioned before.

There is some good news. The BBC report Maths resurgence follows changes says that the number of students taking A level mathematics is increasing, though sadly still at a low level. The article also says: “Another encouraging feature of the figures is that girls significantly outnumber boys among the new students.” which certainly agrees with my experience as you’ll see from the photo. The results for the pictured students were excellent – congratulations to all of them.

Menger Sponge

Maths can be fun. Students at Cornell College in Iowa have built a 3-dimensional fractal called a Menger Sponge and you’ll find a video and pictures of how they did it here.

Menger sponge

Thanks to Mathforge for the link