“I have just one chance for escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.” As the great number theorist G. H. Hardy went on to conclude in A Mathematician's Apology, his work, producing nothing that was useful, had simply “added something to knowledge, and helped others to add more; and these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any other artists, great or small, who have left some kind of memorial behind them.”

Science will grab anything that it can turn to its own ends, and plenty of seemingly useless mathematics has turned out to be essential for future breakthroughs. When Hardy wrote his book in 1940, physicists hadn't discovered the possible links between the Riemann hypothesis on the distribution of prime numbers and the statistics of eigenstates of quantum systems with underlying classically chaotic behaviour. And science poses fundamental mathematical challenges of its own, such as the unsolved Navier–Stokes equations of fluid dynamics and the Yang–Mills equations derived as a geometrical account of the fundamental forces between elementary particles.

All credit, then, to the Clay Mathematics Institute for celebrating the intrinsic value of such challenges. The institute has gone beyond the Fields Medal and the Wolf Prize in singling out long-standing mathematical problems — the three above, plus four others that are less obviously applicable — and valuing each of their solutions at US$1 million (see page 383). It's an excellent way for a private foundation to recognize the eternal fascination that mathematics holds for people such as Hardy, and for the rest of us.