Journalists who rely on the cuttings library say there are 700 biographies of Hitler. The figure is old, the first mention I can find of it is in Angela Lambert's 2006 life of Eva Braun, and suspiciously round. But we can agree that we already knew a great deal about Hitler, and learned much more after Ian Kershaw's monumental biography. AN Wilson answers the question "Why do we need another one?" by producing the opposite of an exhaustive study. His biography is a short, sharp account of the life of Hitler. After histories that press down on the reader like mortuary slabs, it is a liberation.

Wilson's novels are underrated  his 2004 My Name is Legion is the only work of fiction to capture the hypocrisies of Fleet Street in the years before the Leveson inquiry. He looks at Hitler with the eye of a novelist searching for telling details. "A shilling life" does not give you "all the facts", as Auden claimed, and a part of the attraction of reading Wilson is wondering which facts he will haul out of the mass of evidence to illuminate the wider picture.

Wilson emphasises Hitler's un-Germanic laziness. The author of Mein Kampf never struggled. He ended up in doss houses because his sense of entitlement did not allow him to get out of bed in the mornings and go to work. Nor were his accounts of his bravery in the first world war true. Nonetheless, his downward mobility and service in a defeated army had the advantage of allowing him to appeal to the resentments of a Germany humiliated by Versailles and destroyed by the Great Depression.

His indolence meant that he was physically as well as mentally incapable of running Germany. Even before he drove the world to war, Hitler was afflicted by hypochondriacal paranoia, and eczema on his feet and legs so sore that he was often unable to pull on his boots. He also "suffered acutely from meteorism", although, as Wilson notes, "perhaps he did not suffer so acutely as those around him, since meteorism is uncontrolled farting, a condition exacerbated by Hitler's strictly vegetarian diet".

Wilson refuses to play the "parlour game" of counterfactual history and ask what if Britain and France had found the strength to stop the Nazis in 1936. The historian should only study what happened, he says. No one can know what might have happened. He is also superb at putting himself in the shoes of others and sketching the mood of a time with a few strokes of the pen. Even the diaries of anti-Nazis record that Germans, who were not themselves sinister, were happy that Hitler had come to power and found work for the unemployed. "Happy" was not a word anyone associated with Stalin's Soviet Union. He raises the ghost of Sir Horace Wilson, who negotiated with Hitler on Chamberlain's behalf to make the point that the only concern the rest of the world had about the fate of Germany's Jews was that they should not flee to their countries. Sir Horace told the journalist Colin Cross in 1968  that is, 23 years after the liberation of Auschwitz  that he understood Hitler's feelings about the Jews. "Have you ever met a Jew you liked?" he asked Cross.

All the sadder then, that this good, short book might have been shorter and better if Wilson had resisted the temptation to add his "final verdict" in the concluding chapter. In "some strange way, national socialism was the natural consequence of the Enlightenment", Wilson opines. "Hitler believed in a crude Darwinism as do nearly all scientists today." In no way, "strange" or otherwise, was nazism a consequence of the Enlightenment. You can blame Jacobinism and by extension communism on Rousseau if you want. But nazism was a movement rooted in the counter-Enlightenment, the furious reaction against liberalism, democracy and the American and French revolutions. More to the point, the Nazis knew it. "The year 1789 is hereby erased from history," said Goebbels a few months after Hitler took power and began to destroy the Enlightenment ideals of democracy, socialism and individualism.

As for modern scientists, if Wilson does not know that none believes in racial hierarchy and most doubt that the concept of race has any validity, then someone ought to tell him. He believes that nazism was possible because foolish Europeans had shaken off traditional religion. If this were true, we should see more totalitarian cults today because Europeans are less religious than we were in the 1930s. Instead, we see a moderate continent sitting in a world filled with fanatics who have clung to traditional religion all too tightly.

A biography that reads so well thus ends with witterings that are so asinine Thought for the Day could broadcast them.