Mathematics

Where is science bred? Is it where the physical circumstances are right – clear skies for astronomy, for example? Where raw materials are abundant – coal for organic chemistry? Where minds freely meet? Where the enlightened patron rules? Violet Moller’s first book, The Map of Knowledge, examined the spread through the centuries of the ideas of Galen, Euclid and Ptolemy by focusing on seven, mainly Mediterranean cities, from Alexandria to Venice, where scientific knowledge was gathered, augmented and promulgated anew, ensuring the survival of classical learning into the modern period. But why these men and these cities? Are people or places the drivers? Is geography a reliable guide, a storytelling

If both players in a game of draughts stick to their optimal moves, the game will always end in a draw. You or I might have guessed that anecdotally. But being a mathematician, Marcus du Sautoy knows it for sure. The calculations that proved it took 200 desktop computers 18 years to perform. The Prussian High Command used a game called Kriegsspiel to test the abilities of aspiring officers When such a simple game produces such numerical complexity, imagine the fun a mathematician can have with something like Go, the Chinese institution whose number of possible games contains an estimated 300 digits. (The number of atoms in the observable universe

The 20th-century Austrian mathematician Kurt Gödel did his level best to live in the world as his philosophical hero Gottfried Wilhelm Leibniz imagined it: a place of pre-established harmony, whose patterns are accessible to reason. It’s an optimistic world, and a theological one: a universe presided over by a God who does not play dice. It’s most decidedly not a 20th-century world, but ‘in any case’, as Gödel himself once commented, ‘there is no reason to trust blindly in the spirit of the time’. His fellow mathematician Paul Erdös was appalled: ‘You became a mathematician so that people should study you,’ he complained, ‘not that you should study Leibnitz.’ But

Some books elucidate their subject, mapping and sharpening its boundaries. The Clock Mirage, by the mathematician Joseph Mazur, is not one of them. Mazur is out to muddy time’s waters, dismantling the easy opposition between clock time and mental time, between physics and philosophy, between science and feeling. That split made little sense even in 1922, when the philosopher Henri Bergson and the young physicist Albert Einstein (much against his better judgment) went head-to-head at the Société française de philosophie in Paris to discuss the meaning of relativity. (Or that was the idea. Actually they talked at complete cross-purposes.) Einstein won. At the time, there was more novel insight to

In 1886 the British mathematician and schoolmaster Charles Howard Hinton presented himself to the police at Bow Street, London to confess to bigamy. A theorist of the fourth dimension, he had looked destined to forge a career that would align him with the most renowned academic figures of the age. Now, with a conviction, a brief imprisonment, and ‘illegitimate’ twin sons attached to his name, his reputation was ruined. Unable to find employment, he fled with his first family to Japan. Mark Blacklock’s novel tells us what happened next. We initially encounter Hinton at Yokohama harbour where, with his four sons and his first wife, Mary, he is about to