Their stories are the stuff of legend鈥variste Galois, the 20-year-old mathematical genius who, in a letter the night before he was killed in a duel in 1832, frenziedly scribbled down the discoveries he had made in group theory, breaking off repeatedly to scrawl 鈥淚 have not time鈥� in the margin. And Karl Schawarzschild, the astronomer who, before he died of a rare skin disease contractred in the trenches of the Eastern Front in 1916, struggled with the general theory of relativety to extract the first exact solution of Einsten鈥檚 complex field equations of gravity. To the relatively well-known names of Falois and Schwarzschild we must now add the naturalised French mathematician Wolfgang Doeblin, who did his maths on the march, racing to get his ideas down before the soldiers of the Wehrmacht closed in on his battalion.
PICTURE the scene. January 1940, Secheval in the French Ardennes. A phone box in a swirling snowstorm. Inside, in a fog of frozen breath, a man in French infantry uniform is feverishly filling a scruffy school exercise book with arcane mathematical formulae. The man鈥檚 name is Wolfgang Doeblin. He is 23 years old, one of the most gifted mathematicians of his generation. And ever since this morning, he has known he is going to die.
Doeblin is a Jew. When his family fled to France from Germany in 1936, they thought they had found a place of safety, far from Nazi persecution. But they were wrong. Doeblin is a wireless operator in the third battalion of the 291st regiment of infantry. This morning, his regiment was ordered to cease its military exercises and move up into a combat-ready position. Why this sudden, ominous change? Plans had been found on a Luftwaffe pilot captured in Belgium-plans for the imminent invasion of France.
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Doeblin has already filled more than half the 100 pages of his exercise book. It鈥檚 a flimsy affair with a cover depicting 鈥淐ities and Landscapes of France鈥�, bought for 1F50 in a village the battalion recently passed through. He comes to the end of another page and, in his haste to turn to the next one, rips the paper with his clumsy, frozen fingers. It is bitterly cold but his mind is ablaze with ideas-ideas he must get down on paper before it is too late.
Doeblin has found a path through the jungle of randomness, a way to predict the inherently unpredictable. He is high on the joy of discovery, like all mathematical explorers who stumble into uncharted territory. The difference is that for Doeblin, mathematics is more than a mere intellectual pursuit. He is a refugee. He has no country. Mathematics defines him. These pages full of equations are a distillation of his life. They are all that exists to show his 23 years on Earth have meant something.
A thud on the phone booth jerks Doeblin back to reality. Someone he cannot recognise through the curtain of snow is mouthing for him to hurry. Looking up from his equations, he can make out the ghostly shapes of his comrades trudging past. They are heading for Athienville in Meurthe-et-Moselle for their appointment with the armies of the Wehrmacht. Doeblin stumbles out into the blizzard. His head still spinning with thoughts of randomness, he joins his comrades on their march to certain death.
Fast-forward to May 2000 and a dusty room at the French Academy of Sciences in Paris. The room is stacked with hundreds of sealed envelopes, dog-eared and yellowing on the shelves. For three centuries, envelopes like these have been lodged with the Academy as a means of establishing the priority of scientific discoveries.
The Swiss mathematician Johann Bernoulli sent the first envelope in 1701. Others who have trusted their insights to the Academy include Antoine-Henri Becquerel, the discoverer of radioactivity, and Jean-Fr茅d茅ric Joliot-Curie, Marie Curie鈥檚 son-in-law. In 1940, Joliot-Curie used a sealed envelope to hide sensitive nuclear secrets from the German forces then occupying the city. The Academy has only one rule: that an envelope remains sealed for 100 years or until an agent or heir of the depositor gives their permission to open it. Today is a significant day. Envelope number 11-668, which arrived by post in February 1940, is about to be opened.
The din of the Paris traffic has faded to nothing. In the dusty room are gathered a small group of Academy members and a frail old man holding an envelope in trembling hands. The old man breaks the seal and out onto a table falls a battered exercise book, its cover depicting the 鈥淐ities and Landscapes of France鈥�. He opens the book and recognises the youthful handwriting of his brother: 鈥淥n the equation of Kolmogorov by Wolfgang Doeblin.鈥�
The Kolmogorov equation describes random phenomena such as Brownian motion, the jittery movement of tiny particles in a fluid, such as pollen grains under bombardment from water molecules. In the 1930s, mathematicians were hunting for an exact, or 鈥渁nalytical鈥� solution, which would allow them to predict the trajectory of an individual particle. Doeblin realised that the jerky, discontinuous nature of the motion precluded such a solution. Instead, he found a way to predict the averaged-out trajectory using probabilistic methods that were way ahead of their time. They would not be rediscovered until the Japanese mathematician Kiyoshi Ito stumbled on them in the 1950s. The brilliant work provided a crucial bridge between Brownian motion and the Black-Scholes equation used by City 鈥渞ocket scientists鈥� to predict the random behaviour of the stock market.
Now the final scene: 20 June 1940, Housseras in the Vosges. A barn, its roof half gone, the wooden walls reverberating ever more violently as enemy mortar fire creeps nearer. In the shadows slumps a man in French army uniform, hollow-eyed and breathing heavily. It is Wolfgang Doeblin.
The soldiers of the Wehrmacht have encircled Doeblin鈥檚 battalion. Of his retreating comrades, he is the only one to make it to this barn. A mortar shell tears overhead, bursting in the farmyard behind. The explosion rocks the barn and more of the roof falls in, filling the air with choking dust. When the sound dies away and he finally stops coughing, Doeblin hears the crunch of running boots on the gravel outside, punctuated by staccato bursts of machine-gun fire. His enemies are only seconds away. He knows what he must do.
He lifts the gun to his head and slowly, deliberately, he pulls the trigger. It is not an act of cowardice, it is an act of defiance. He will triumph over his persecutors, even in death. Long after they are forgotten, the name of Wolfgang Doeblin will live on.