By Eric Kvaalen AS ONE of the editors of the Annals of Mathematics, Peter Sarnak sees his fair share of mathematical proofs. Yet there is one unsolved problem for which proofs keep on turning up in his mailbox. These are from people claiming to have cracked a long-standing conundrum known as the Riemann hypothesis. “At any given moment we probably have 10 claimed proofs submitted,” says Sarnak, a mathematician at Princeton University. Perhaps that is not so surprising. First put forward in 1859 by German mathematician Bernhard Riemann, the hypothesis is one of mathematics’s most beguiling problems. Its allure lies in the fact that it holds the key to the primes, those numbers that underpin so much of today’s mathematics. The Clay Mathematics Institute in Cambridge, Massachusetts, has deemed the problem so important that it is offering a $1 million prize to anyone who proves the hypothesis is true. Despite mathematicians’ best efforts, however, no one has yet published a proof of Riemann’s hypothesis in a peer-reviewed journal. That might be about to change. One respected mathematician claims to have cracked the problem, and has posted the proof on his website for others to scrutinise. If Louis de Branges of Purdue University in West Lafayette, Indiana, succeeds in getting his proof published in a journal, mathematicians will finally be able to sleep easier at night. “There are probably thousands of theorems in the literature which start, ‘assume Riemann, then…’, followed by some spectacular conclusion,” says Sarnak. At first glance,