News from the world of maths: Mathematical moment - Henry Whitehead

Born: 11th of November 1904 in Madras, India
Died: 8th of May 1960 in Princeton, New Jersey, USA

"He would have been more successful in mathematics if he had been less so at cricket," is what Whitehead's maths teacher wrote about him on his graduation from Eton. Once at Oxford, to which he'd nevertheless gained entry, Whitehead's distraction diversified to include squash, tennis, boxing and poker, at which he reportedly staked large sums of money. Worse, Whitehead did not even seem to want to become a mathematician at first, instead he joined a stockbrokers firm in London on completion of his degree.

But luckily, all turned out well for maths in the end. Working in the City wasn't to Whitehead's taste, and after a detour to Oxford he enrolled for a PhD at Princeton in the US. Here he began to work on two areas which benefitted greatly from his contributions: topology and differential geometry. Both differential geometry and topology deal with surfaces like the sphere or the torus, or their higher dimensional analogues. While differential geometry looks at rigid properties that depend on a metric, for example the curvature of a surface, in topology metric properties are irrelevant. Topologists regard two objects as being the same if you can deform one into the other without tearing. The famous example is that a coffee cup and a doughnut are topologically the same.

Whitehead contributed two major works to differential geometry, now considered classics. In topology he is best remembered for his work on "homotopy equivalence", a central notion when it comes to pinning down whether two objects are topologically equivalent. Notably, Whitehead spent quite some time working on the now famous Poincare conjecture and even thought that he had found a proof. However, an inconspicuous pair of interlinked circles, now known as the "Whitehead link", gave rise to a structure that Whitehead had assumed not to exist. This toppled his proof and the Poincare conjecture was to remain open for another 70 years.

Whitehead also contributed to maths in another, less theoretical way. The percecution of Jews in Nazi Germany troubled him greatly, and he helped a number of eminent mathematicians to escape, including Erwin Schroedinger, one of the founders of quantum mechanics.

Had Whitehead not died suddenly of a heart attack at only 56, he certainly would have gone on to contribute even more.

You can read more

• about Henry Whitehead on MacTutor,
• about topology in Plus,
• and see a picture of the Whitehead link on Wikipedia.