Brian Rotman

In those heady days more than twenty years ago, a slew of foreign invaders – Tibetan prayers, the Katmandu trail, ancient Chinese manuals, Yogic trances, the sayings of Chairman Mao, Zen koans shamanism, Egyptian rituals, Warrior cults, and the dreamscape of Mexican mushrooms – burst through the Eurocentric enclosure of our upbringing, announcing the age of Aquarius. Then times changed, and we and/or history drew a line in the sand under these alien forms of discourse. Most of us were left with traces of them, though. Where Chinese things were concerned, there was Sun Tzu’s Art of War, for example. I wasn’t a Maoist, but I got a frisson from the idea that in the period of the Waning States, jobbing intellectuals like Sun Tzu were boiled, pickled, sawn in half or otherwise executed, if their manuals gave bad advice to the prince Sun Tzu’s book survived courtesy of the Chinese principle of paying the doctor only if he cures you. I wasn’t a hippy either, but I encountered the I Ching. My meeting with it wasn’t a prolonged one, and this was a pity, for it, too, is seriously in the advice business and has somehow survived from an even more remote time than Sun Tzu. Now, the repressed returns and I have to take the great classic seriously.’

Aheroic story: Andrew Wiles, a Cambridge mathematician living in the United States, emerges after seven years of self-incarceration and paranoid secrecy from his Princeton attic, clutching two hundred pages of hieroglyphics. He is triumphant. He has cracked the most famous problem in number theory: Fermat’s Last Theorem, which has eluded some of the finest efforts of mathematicians for over three hundred years. He is beside himself with anticipated glory, but holds off, maintaining secrecy until the right moment. Serendipitously, a conference on exactly the branch of number theory covering his work is to take place in Cambridge. Choosing an unrevealing title, he lectures on three consecutive days. In the final minute of the final hour, he is able to utter the magic claim that the puzzle of Fermat’s celebrated theorem is now solved. Shocked silence and then a standing ovation from his astonished international colleagues. In the ruthlessly competitive world of research mathematics, Wiles has pulled off one of the most dramatic successes anyone could hope for.

Being affectionate with numbers, endlessly wondering about them, loving them, is, though impersonal and bloodless, no more strange perhaps than being possessed by the endless ramifications of cricket or trout fishing. Being consumed by numbers to the exclusion of all else, sounds deranged. The Hungarian mathematician, Paul Erdös, number theorist and combinatorialist extraordinary, eccentric, socially dysfunctional, obsessive, childishly egocentric, helplessly dependent on fellow number freaks to feed him, transport him, put him up and put up with him, was certainly outside the normal range, but not insanely so. Like most mathematicians, Erdös had a deep need to be ordered and structured, so requiring long immersion inside mathematical abstractions. He thought numbers more interesting and comforting than anything else in this world and was able to spend most of his waking life in contact with them. When he died in 1996, at the age of 83, he had worked on more problems, made more conjectures, proved more theorems, collaborated with more people, and written and co-written more mathematical papers (over 1500) than any mathematician in history.

In 1940, Winston Churchill gave the fledgling Special Operations Executive its sabotage and resistance mission: Set Europe Ablaze – an encroachment on its turf not to the liking of the espionage establishment, which used its more powerful ministerial presence in the wartime Cabinet to work against SOE whenever it could. Born thus under sufferance, occupying a lowly level in the Signals hierarchy, run by an establishment-respectful general and composed of independent units – one for each occupied country except France, which had two, one for de Gaulle’s Free French and another for those loyal to Giraud – each recruiting and running its own partisans, SOE was an intelligence professional’s bad dream.’

The English mathematician G.H. Hardy, who worked in the purest of all mathematical fields, the theory of numbers, used to boast in his patrician way that nothing he did in mathematics would ever be useful. He must be turning in his grave at developments in the ‘science of secrecy’ over the last quarter of a century. Like so many other practices, it has been transformed into a species of applied mathematics by the digital computer, with Hardy’s beloved prime numbers playing a leading role. How this came about is the subject of Simon Singh’s The Code Book, a very readable and skilfully told history of cryptography. Singh’s method is to attach the abstract ideas involved to someone who thought of them, failed to think of them, championed them, or suffered their consequences – this last allowing him to include Mary Queen of Scots, whose unfortunate contribution to the art of secrecy was to correspond with her conspirators using an insecure cipher.’‘