Every few weeks, photographs of old paintings arrive at Martin Kemp’s eighteenth-century house, outside Oxford, England. Many of the art works are so decayed that their once luminous colors have become washed out, their shiny coats of varnish darkened by grime and riddled with spidery cracks. Kemp scrutinizes each image with a magnifying glass, attempting to determine whether the owners have discovered what they claim to have found: a lost masterpiece by Leonardo da Vinci. Kemp, a leading scholar of Leonardo, also authenticates works of art—a rare, mysterious, and often bitterly contested skill. His opinions carry the weight of history; they can help a painting become part of the world’s cultural heritage and be exhibited in museums for centuries, or cause it to be tossed into the trash. His judgment can also transform a previously worthless object into something worth tens of millions of dollars. (His imprimatur is so valuable that he must guard against con men forging not only a work of art but also his signature.) To maintain independence, Kemp refuses to accept payment for his services. “As soon as you get entangled with any financial interest or advantage, there is a taint, like a tobacco company paying an expert to say cigarettes are not dangerous,” he says...