Cézanne demands of us. Like no one else's, his paintings push and pull at our vision. His mountains seen through trees and his tabletops of apples upset our notions of "here" and of "there", of light, matter and distance: what constitutes a feeling and what an object get radically spun about. Cézanne's art is giddying and heady, a charge of magnetic energy sent through shapes and colours to regroup them in strange new harmonies: the world looks different as you walk away. Allen Ginsberg, quoted in Alex Danchev's new biography, Cezanne: A Life (Profile, £30), described its effects as "eyeball kicks". Although this painter was a school of one, resembling no one else, few painters could work the same way again after taking in what he had been doing. Here is the man who more than any other set 20th-century painting on its course.

And yet this messiah of modernism has always  from his youth in the 1860s, down to the present  appeared a misfit. If his way of representing things is strong, on certain levels it also seems wrong. This is not the world we normally move about in, it's some alternative plane of experience made solely possible by paint. To reach for it, so people have thought, Cézanne must have been in the grip of an obsession  some disturbance, some malfunction. Such reactions came not only from casual observers confused by his boorish manners and dismayed that he didn't draw "straight". It was Cézanne that Zola, his old school friend from Aix-en-Provence, had largely in mind when he wrote a novel about an artist doomed to failure by "heroic madness" and defective vision. In fact the cues for this could have come from Cézanne himself. "I am a primitive, I have a lazy eye," he would protest in his later years. He was afflicted by "brain trouble" and was "no longer my own master".

Danchev's new life  original, engaging and highly persuasive  brushes aside that line in pathos, likewise refusing the "profitless psychoanalysis" that many a distinguished interpreter has applied to the artist. The problems of Cézanne, Danchev argues, were of his own conscious choosing. An ambitious and well read young Provençal, coming to Paris just as a new art scene was coalescing around Manet, began pretty early to stake out his own independent path. "In the mid-1860s, at the age of about 25, Cézanne set about becoming Cézanne." Socially, that involved developing a sardonic, forbidding crust, posing as a querulous hick from the sticks. (On being introduced to the dapper maestro of modern painting: "I won't offer you my hand, Monsieur Manet, I haven't washed for a week.")

Intellectually, it meant taking seriously France's leading philosopher of the day, Hippolyte Taine, who wrote that real art came about through "sensation" driving the brain "to rethink and transform the object, sometimes to illuminate and elevate, sometimes to twist and distort." What was this "sensation"? Perhaps it meant the impulses of lust and violence Cézanne's early paintings often featured; perhaps it was the rhythmic intuition about two dimensional relationships that literally distorts the dinner-plates and the Monts-Sainte-Victoire in his later work. "I have very strong sensations," Cézanne would remark. In Danchev's account, that becomes a boast that the painter requires himself to live up to, a persona to inhabit: "Performing Cézanne became one of his best turns." The tale is largely of how the role expanded and deepened, spurring him on to prod at strange new faultlines in the field of vision and, in the decade before his death in 1906, to act as guru to a select few listeners come to seek him out in his Provençal lair. Also, of how he "immatured with age", as Danchev puts it, letting his self-appointed wildness take over the reins. We hear of a neighbour covertly watching him as he puzzled over a Mont-Sainte-Victoire: "He seemed to be all out of sorts ... Do you know what he did? He picked up a big rock and threw it right through the middle of the canvas!"

The tale largely turns on these considerations because, outwardly, it is far from incident-packed. Cézanne pursuing his 19th-century research project more resembles a gentleman scientist such as Darwin than struggling contemporaries such as Monet, in that his father, a leading banker in Aix, ensured he was never dependent on sales. He could thus could face down a critical indifference that lasted until his late 50s. Old Louis Cézanne, it is true, halved the allowance when he found out that up in Paris, the nearly 40-year-old Paul had long been keeping a common-law wife and their child. But this Hortense Fiquet is almost the only amatory interest in the artist's career, and although Danchev valiantly tries to see her in three dimensions, the evidence is just too slight to gain purchase  especially as she never looks the same from one depiction by her husband to the next. (As Danchev nicely puts it, "A Cézanne portrait is more a thereness than a likeness.")

During Cézanne's financial contretemps with his father, it was Zola, the schoolfellow turned literary celeb, who stepped in with loans. It's long been assumed that this friendship of Cézanne's  surely "the main axis of his emotional life"  was betrayed and decisively broken when Zola published his melodrama about an artist doomed by "heroic madness". But again Danchev is intent to read the evidence more subtly. He portrays a more gradual divergence, ending with in one corner a political loudmouth, hosting suppers in his flash mansion outside Paris, while in the other a no less proud recluse shunts canvases in and out of a self-designed studio on the outskirts of Aix, keeping his distance even from his own wife and son.

With relatively little to work with dramatically, Danchev creates his Cézanne by a method that in less capable hands would seem outrageous. He assembles him out of emotions gathered from other people's lives. How did Cézanne feel about his father? Let's read what Kafka had to say about his own. For Cézanne's sense of self-worth, go to Valéry writing about Stendhal. A Beckett short story gives us an angle on the eventual marriage to Hortense; while Flaubert can voice whatever disdain the artist felt for critics, the bourgeois and his fellow Provençals. Equally, the paintings come to life as they have lived in others' eyes. Ginsberg's poetic witness is joined by Heaney, Walcott and Rilke, whose letters about a 1907 Cézanne retrospective remain more vivid than anything written about the paintings since. Stan Brakhage, Giacometti and Heidegger all put in a word. In fact, Danchev seems to report back from some cultural meta-space in which high artistic achievements in every medium and from every era interconnect.

Why should we trust him to do so? First, because his own prose is so witty, mobile and sensitive: second, because to a lay reader it seems grounded in long and thoughtful study of the primary sources; third, because that study brings out how committed a reader Cézanne himself was, a devotee of poetry from Virgil to Baudelaire. This feeds Danchev's argument that the imagination of this alleged obsessive was "richer than is generally realised, and rather less strange". Confident of his material, Danchev paces around the chronology fairly freely, pursuing whatever line of thought engages him, genially holding the stage.

Trying to close in on Cézanne's landscapes and still lives from the years before his death at 67, the approach does hit a limit. In the face of those uniquely momentous arguments between eyesight and the world, one instinct tells Danchev to pile up appreciations and circumstantial data  his peroration expires in a scattershot of lists  and another, more wisely, to submit to silence. Seeing beyond the outward man, the supposed fractured sociopath, he would like to relay the substance of the painter who undertook to deliver "truth" in his art: "Cézanne's truth may be more important than Cézanne's doubt." But that truth is for showing, not telling. These pages reach their highpoint with a photo of an old man in a hat and tatty jacket, standing between a country wall and a tripod easel, brush poised before the canvas, eyes staring out. Transfixed, Danchev's happy eloquence for once stutters to a stop. "He is painting. This is it.".