Of all the great intellectuals of the Renaissance, Pico della Mirandola is surely the most personally captivating. “He wins one on,” as the Victorian essayist Walter Pater put it, his life having “some touch of sweetness in it”. An Italian aristocrat who dabbled in magic and escaped from prison after eloping with the wife of a Medici lord, his books were burned on the orders of the pope. Edward Wilson-Lee’s new biography brings us the events of Pico’s short, blazing life, but also what is most strange and attractive about him: the wonder of a scholar who felt himself on the verge of being able to commune with angels.

The basic facts are straightforward. Born in northern Italy in 1463, he was a child prodigy with astonishing powers of memory. (He is said to have been able to recite the whole of Dante’s Divine Comedy backwards.) The story of Pico’s education has something of the feel of a video game, a tour through the great universities of Europe – Bologna, Ferrara, Padua, Paris – completing some branch of knowledge – law, medicine, the classical languages – before moving on to the next level.

Once he had mastered the orthodox disciplines, Pico found himself hungry for more. He sought out Jewish scholars to teach him Hebrew and Arabic, and became convinced that there were secrets in the ancient texts of the east, accessible only only to those who knew how to interpret them. Writing excitedly to a friend, he declared that the first five books of the Hebrew Bible contained “the entire knowledge of all arts and wisdom both divine and human”. Unfortunately there was a catch: “This knowledge is hidden and concealed.”

At the age of 23, Pico published his 900 Theses, a collection of propositions drawn from the eclectic breadth of his reading, which aimed to present a sort of Grand Unified Theory of mystical learning. It also contained a challenge: that should anyone wish to debate him on any part of the work, Pico would be waiting in Rome. He would even pay his challengers’ travel expenses.

The authorities were not impressed. Pope Innocent VIII intervened to cancel the debate, and a committee, convened to consider the 900 Theses, promptly found it heretical. When Pico responded by publishing a scornful takedown of his critics, he found himself on the run with the dubious honour of being the author of the first printed book ever to be banned by the church.

After a spell in prison, he was released following the intercession of his protector, Lorenzo de’ Medici. The last few years of his short life were spent quietly in Florence, but when Lorenzo died and the city fell under the spell of the extremist preacher Savonarola, he found himself in danger once again. He was 31 when he died, a victim of arsenic poisoning, on the day the French army entered Florence.

Pico poses a tougher challenge for Wilson-Lee than the subject of his previous biography, the adventurer-poet Luís de Camões. It is not that his life is not remarkable, but rather that the things that make it so are difficult for us to perceive in a secular age, necessitating the telling of an intellectual backstory that Camões’s swashbuckling never did. How to express, now that magic has fled from the world, the awe that Pico felt in what he thought he was discovering?

Wilson-Lee’s method is to focus on Pico’s interest in “enrapturing speech”. The spoken word has a power to take us out of ourselves. The connection that we feel when we lose ourselves in participation – when we sing in a choir or chant at a football match or a rally – is the intimation of mystical experience: momentarily our individuality dissolves. Speakers like Savonarola, who could whip his audience into forgetting themselves, wield a dangerous power. The Grammar of Angels watches Pico as he wonders about this kind of word-magic. Where is its power hidden? “Voices that mean nothing have more magical power than those that mean something,” he observes. If we think of the meditator’s mantra or the magic word abracadabra, we can see what he means.

Wilson-Lee is good at carnivalesque historical colour, on the lonely giraffe brought to Florence as a gift from the Egyptian Sultan, or the riotous pre-Lenten celebrations in Ferrara. And he skilfully conveys the propulsive, addictive thrill when interpretation is taken for revelation, or Pico’s “endless quest for the next lost thing” (words Freud would certainly have understood).

At times The Grammar of Angels can feel as though it, too, is under the spell of this same impulse to collect and connect. Often, Wilson-Lee pulls in analogies from times or cultures that even Pico was not familiar with, suggesting affinities in a kind of comparative sociology of incantation. In another work this might be more of a problem; in the shadow of an accretive, universalist intellect like Pico’s, however, it makes perfect sense for this impressive and scholarly book to see its subject everywhere it looks.