book reviews that the Earth’s speed of rotation was slow- describe events known to most readers, and Erdös was born in 1913 in Hungary, and ing down. He explains the problems of during which Cartwright himself had a key discovered negative numbers when he was the dissipation energy budget which has role. This was the time when, with the intro- four. He belonged to that extraordinary intrigued astronomers since Laplace. Light duction of computers, the first global cluster of scientific geniuses — which was shed on all this by the study of the partic- model of ocean tides was calculated by included John von Neumann, inventor of ular case of the Irish Sea model (1919). But a Chaim Pekeris in 1960, when ocean tidal the electronic computer and game theory, final estimate for the equilibrium energy loading was introduced in the Laplace and the Nobel prizewinners Eugene budget had to await data obtained later by equations, while in 1979 the models of Wigner, George de Hevesy and George artificial satellites and lunar laser-ranging Ernst Schwiderski described 11-diurnal, Olah — who emerged from two or three measurements. semi-diurnal and long-period tides. Dur- schools in Budapest after the First World Until the dawn of the twentieth century, ing this time also, George Platzman calcu- War. tidal research was carried out almost exclu- lated the normal modes of oscillation of the During his life, Erdös wrote more than sively by two European countries that main- ocean, and a method for analysing and pre- 1,500 papers, books and articles, more than tained large navies and regularly observed dicting tides, known as the ‘response any other mathematician ever. Some of these the effects of huge oceanic tides on their method’, was developed by Cartwright and became the great classics of our century, coasts: the United Kingdom and France Walter Munk. opening up entirely new fields of study to (“the continental writers”, as Cartwright The book ends with the more recent which generations of mathematicians have refers to them). At first astronomers played a years (one of the last references is from devoted their lives. As the mathematician fundamental role: in Britain several 1996), which see technological advances — Paul Winkler said, “If I can see a bit farther it Astronomers Royal, including Harold bottom pressure recorders and super- is because I stand on the shoulders of Hun- Spencer Jones, were involved, while Laplace conducting gravimeters, for example, but in garians”. dominated the French scene (assisted by the particular satellite altimetry, which, with the Schechter is particularly concerned to astronomer Alexis Bouvard, as Cartwright US/French TOPEX/Poseidon satellite, has clarify a few of the basic ideas underlying this subtly notes). attained the incredible accuracy of ±3 astonishing production, such as the sieve of The development of celestial mechanics centimetres in measuring the distance Eratosthenes, Cantor’s infinities and Euler’s and “théories de la Lune” led to the theory of between the satellite antenna and the sea curious problem (the foundation of graph the tides and the Laplace tidal equations, surface. theory) about whether a man could walk which represented the first mathematical I really enjoyed this book, and consider it across all seven bridges of Königsberg with- mastery of oceanic phenomena. Lord Kelvin a masterpiece. I was delighted to find, among out crossing the same bridge twice. It is and George Darwin extended these equa- its many high-quality illustrations, George inspiring reading, because Schechter, fol- tions to describe the harmonic expansion of Darwin’s ingenious drawing of the evolution lowing in the spirit of Erdös, makes clear that the tides. And even at that time, it was possi- of the Earth–Moon system, as I used to set much good mathematics can come from ble to use the amplitude of tidal waves to this as an exercise for my students. whimsical speculation and the clever use of make a preliminary evaluation of the mass of Obviously, the book is primarily written simple ideas. If popular writing about the Moon. for astronomers, geophysicists and all those mathematics remains of this quality, there is New horizons opened with the advent known as ‘tidalists’, who will surely enjoy it. still enough unused material for a shelf-full of the American Rollin Harris’s Manual But I also recommend it to physicists and of Erdös biographies. of Tides in 1901 and his construction of pure mathematicians. In other respects, Hoffman’s book is ‘cotidal lines’ which covered the world’s Paul Melchior is at the Observatoire Royale slightly longer and better on anecdotes, but oceans. Although George Darwin was Belgique, 3 Avenue Circulaire, B-1180 Bruxelles, Schechter’s, while not so lively, is less harshly critical of this work, the great math- Belgium. inclined to get distracted from its subject. ematician Henri Poincaré gave it generous Although you would never guess it from the support. Again Cartwright reminds us how acknowledgements, both writers once Harris’s intuitiveness led him to propose the worked for Discover magazine. Erdös’s existence of an underwater ridge in the PGOML DA DL DCD famous love of creative cooperation has Arctic Ocean; this major oceanic feature was My Brain is Open: The Mathematical apparently not spilt over into the world of originally called the Harris ridge, but is now Journeys of Paul Erdös mathematical biographies. known as the Lomonosov ridge. by Bruce Schechter From his teenage years, when he could In subsequent chapters covering the Oxford University Press/Simon & Schuster: instantly square a four-digit number and twentieth century, we find oceanographers 1998. 224 pp. £22.50/$25 knew 37 proofs of Pythagoras’s theorem, and geophysicists taking the lead from the Alexander Masters Erdös called himself old and decrepit. A astronomers in the field of tidal discovery. few years before his 60th birthday he We hear about the famous Liverpool Tidal When Paul Erdös “left” (as he called it) in appended the letters PGOM to his name, Institute, which was important, both obser- 1996, even The New York Times took notice, which stood for Poor Great Old Man, then vationally and theoretically, in providing and printed a front-page obituary calling added further initials every few years. By the tidal analysis and predictions so well perfect- him “a wayfarer in math’s vanguard”. Two time he was 75 he was PGOMLDADLDCD ed by Arthur Doodson that they delayed the years later, Paul Hoffman published an (Poor Great Old Man, Living Dead, Archae- use of computers in this area. In these same excellent biography about him called The ological Discovery, Legally Dead, Counts chapters, Cartwright approaches the diffi- Man Who Loved Only Numbers (Fourth Dead). cult aspects of pure mathematics with clarity, Estate/Hyperion, 1998; reviewed in Nature His output had slowed down a little by describing, for example, the theory devel- 394, 535–536; 1998), which reached number then. “One of my greatest regrets,” remarked oped by Joseph Proudman, George Golds- three in The Sunday Times best-seller list. one of his last collaborators, “is that I didn’t brough and Doodson to describe tides in Now Bruce Schechter has followed this up know him when he was a million times faster basins and oceans as represented by simple with a second biography, My Brain is than most people. When I knew him he was geometrical shapes. Open. In his 83 energetic years, this peculiar, only hundreds of times faster.” The last three chapters see tidal research obsessive little mathematician has built up a Alexander Masters is at 6 Hertford Street, extended over the entire world, and substantial public following. Cambridge CB4 3AG, UK. 120 © 1999 Macmillan Magazines Ltd NATURE | VOL 398 | 11 MARCH 1999 | www.nature.com.