Physicists at the University of California, Los Angeles set out to design a better transistor and ended up with a discovery that may lead to a new explanation of electron spin and possibly even the nature of space.

The Rolf Schock Prize in Mathematics 2011 has this week been awarded to Michael Aschbacher "for his fundamental contributions to one of the largest mathematical projects ever, the classification of finite simple groups".

Table tennis first became an Olympic sport in 1988, but changed its scoring system in 2001 to make matches more exciting for spectators. But how does the new system compare to the old one in terms of your chances of winning?

Rising like a giant pringle from the Olympic Park construction site, the Velodrome is the first of the 2012 London Olympic venues to be completed. With its sweeping curved roof and beautiful cedar clad exterior the Velodrome is a stunning building. But what most of the athletes are excited about is the elegant wooden cycle track enclosed inside, the medals that will be won, and the records that might be broken, in the summer of 2012.

When you try to put democracy into action you quickly run into tricky maths problems. This is what happened to Andrew Duff, rapporteur for the European Constitutional Affairs Committee, who was charged with finding a fair way of allocating seats of the European Parliament to Member States. Wisely, he went to ask the experts: last year he approached mathematicians at the University of Cambridge to help come up with a solution. A committee of mathematicians from all over Europe was promptly formed and today it has published its recommendation.

To coincide with the 100th International Women's Day two new competitions to find the best young female mathematical minds in the UK and Europe have been launched.

Almost nothing tangible remains of the legendary Bletchley Park codebreaker Alan Turing. So when an extremely rare collection of papers relating to his life and work was set to go to auction last year, an ambitious campaign was launched to raise funds to purchase them for the Bletchley Park Trust and its Museum. The Trust has announced today that the collection has been saved for the nation as the National Heritage Memorial Fund (NHMF) has stepped in quickly to provide £213,437, the final piece of funding required.

Journey to distant islands to discover if topology can overcome topography and bring peace to rival towns.

It requires only a little processing power, but it's a giant leap for robotkind: engineers at the University of Southampton have developed a way of equipping spacecraft and satellites with human-like reasoning capabilities, which will enable them to make important decisions for themselves.

One of the most surprising things about mathematics is its many unsolved mysteries. Mathematics is far from "done and dusted", and Steve Humble shows us how we can come up with some mathematical mysteries of our own.

Squeamish about cuts and scrapes? Maths can help you feel better.