Donal O'Shea is professor of maths at Mount Holyoke College, Massachusetts, and author of 'The Poincare Conjecture: in search of the shape of the universe' (Allen Lane)
Maths teachers may wince at last summer's media frenzy when the reclusive mathematician Grigory Perelman was awarded the discipline's highest honour, the Fields Medal, for cracking the century-old Poincare conjecture, but then turned it down. Yet media phenomena that put maths in the public eye are good for the subject and offer a chance for reflection.
We should ask why the problem that Perelman solved was not better known. It pertains to possible shapes that the universe might have, and is a question that could be taken up with 10-year-olds. Fascination with numbers and geometric objects is as natural to children as language and music. And we should ask why most of the educated public had never heard of topology, which is concerned with shape and connectivity and is an area to which British mathematicians have contributed much. It informs algorithms that underpin modern telecommunications and drive internet search engines.
Maths underwrites our technology and culture. Our failure to communicate it will be devastating for the UK's ability to compete. No child, no matter how gifted, can hope to contribute to maths or science without a decent education. Perelman attended a state-funded school in St Petersburg, then Leningrad, famous for its maths and science teaching. In some UK or United States school systems he would not have had a chance.
We know that science and maths are undervalued in popular culture. Maths enrolments have dropped in the UK and the US. But in our zeal to act, we may be making things worse. Granted, most of us have had some negative experience of being humiliated or baffled by inept maths instruction, and we conclude that safeguards against bad teaching will reverse the declining enrolment.
Tragically, our safeguards have perverse results. The more we fear bad teaching, the more rigid and hierarchical the curricula we impose, and the more we turn to high-stakes testing. Students who do poorly in one maths class are told that they will not be able to do well in subsequent ones.
They abandon understanding and focus desperately on computations that become ever more meaningless. Fear sets in and we squeeze the joy out of the subject.
All students learn differently. The best teachers adapt what and how they teach for different students. Tests are tools, not ends. The tighter the curriculum and the more all-consuming the test, the less time a teacher has to talk about topology or Poincare or Perelman. Perhaps we need to lighten up. And open up.