I don’t know where you stand on Cézanne, but I have usually found him to be difficult and ungraspable. He’s one of those undoubted heroes of art whom I respect wholeheartedly, but whom I wouldn’t necessarily cross the room to look at. Knowing he’s there is usually enough. What’s worse, the B-word often begins muscling its way into my consciousness when I am confronted by large amounts of him. I live in a fast-cut world. Cézanne’s art seems to take place in the slowest of slo-mos. I like things to be happening. He, it seems, didn’t.

Occasionally, however, the gods of art take pity on me and shine their great big light of illumination on Cézanne. Stick me in front of him in the right setting and I get him: not in that agitated and ecstatic way you usually find with flashes of revelation, but slowly, relentlessly, immovably, in the manner of a good marriage turning into a great one, or a bottle of vintage Krug transporting you to grapey heaven in tiny sips.

The ecstasy swells gently into unstoppability. And the dutiful knowledge you came in with — that Cézanne was a very important figure in the history of modern art — turns into a grotesque underestimate that needs laughing at. This man was as great a revolutionary as there has ever been in art. He changed everything. It’s as plain as day.

Something of that order happened to me at the Courtauld Institute, where a perfect little Cézanne exhibition has been modestly arranged for us in the upstairs exhibition gallery, a tiny room that takes up about a millionth of the volume occupied by the foyer of Tate Modern, that totally amazing cavern of emptiness that everyone loves, with the, er, totally amazing sloping floor. At the Courtauld, I think I was the youngest person in the room. And the only one without grey hair. And, as we lucky oldies circled this tiny hot spot of art, getting closer and closer to Cézanne, floating higher and higher on the helium of art love, we created a rising tornado of appreciation that I imagine must have been visible from wherever it is that you live.

The Courtauld is fortunate to own the largest collection of Cézannes in Britain. This is because the gallery’s founder, the remarkably generous Samuel Courtauld, textile magnate-turned- Cézanne-worshipper, came across a Cézanne landscape in 1922 that had been rejected — predictably — by the Tate Gallery for an exhibition of “Modern Foreign Art” and had gone on show instead at the Burlington Fine Arts Club, where Courtauld saw it and experienced something like the ecstatic reaction described above. Cézanne got his claws into Courtauld. And never let go.

Courtauld duly went on a Cézanne buying spree. And now, for the first time, the entire collection of drawings, prints and letters he bought, as well as his superb selection of paintings, have been put on show at once. The resulting event has the personal air about it of a fan’s handiwork. If Cézanne’s toenail clippings had come up for sale, Courtauld, you feel, would have acquired them.

Because it was put together by a fan, rather than an art historian or a curator, the display does not unfold along the walls in the usual predictable manner favoured by art professionals, step by step. It seems to come at you in a bit of a jumble, all at once, just like a Cézanne painting. Here, there are oils. There, there are watercolours. In the middle, there are letters.

The first offering is a modest little drawing, from 1880, of Cézanne’s wife sewing. She is sitting in a chair in the bedroom, her hair scraped back in a practical bun, seemingly unaware of the artist’s presence as she concentrates fully on the tiny domestic problem in her hands. It’s a scene of traditional village effort, with a homely glow that can trace its ancestry back to Rembrandt. Except that whatever it is that Madame Cézanne is sewing is missing. Her husband has deliberately left the middle of the picture blank. The whole composition seems to zero in on something that isn’t there. It’s like a face without a nose or a whirling bicycle wheel without its hub.

We are, therefore, in the immediate presence of some kind of crazy artistic risk-taker who seems, simultaneously, to be cherishing the old ways. The next drawing, of a humble garden shed, continues this dichotomy. Most of the paper has been left untouched. It is only in small moments of suggestive colouring and shadowing that the ramshackle shape of the old shed is encouraged to emerge in a manner that seems to have more in common with sculpting than with drawing. The white of the paper is like a block of Carrara marble in which a Michelangelo-esque Cézanne has discovered his hidden form and begun the process of releasing it.

This blurring of drawing and sculpting continues in the thoroughly exciting parade of paintings that follows. What an eye Courtauld had. A pair of village card-players face each other across a table as stonily and unhurriedly as if they had been there since the Middle Ages (when, methinks, they slunk off the facade of Chartres cathedral and headed for the nearest tavern). The famous still life with the armless statue of a cherub surrounded by apples and onions is as full of bouncy roundels as the inside of the Lotto machine. That secret sense of inner sculpture that all Cézannes have is more obvious than usual when plump apples are compared with the plump cheeks of a plump cherub.

It was the landscapes, however, that moved me most. What mighty campaigns of creativity were involved in bringing each one to its conclusion. In the distant view of the Montagne Sainte-Victoire, seen through the needles of a pine, poor Cézanne sets himself the impossible task of combining the foreground, middle ground and background in one receding plane of bone-dry Provençal hotness. He doesn’t quite get there. Nobody could. Elsewhere, in those dappled peeps he loved beneath the French undergrowth, he sends his pictures on extraordinary optical journeys in and out of the vegetation as the paint tries to slant down through the leaves as nimbly as a shaft of light. It’s an impossible task. But don’t anyone tell him.

The show is small enough to make every exhibit feel like a special treasure. Cézanne’s most revolutionary insight was to realise, more fully than anyone had realised before him, that a painting is a painting, not a window. That it needs to follow its own internal logic rather than import its logic from outside. It’s an insight of such apparent obviousness that, these days, it makes us yawn. “Of course a painting is a painting, numbskull,” I hear you chorusing cockily. But wind back the clock 169 years, to Cézanne’s birthday, January 19, 1839, and this obvious thing wasn’t obvious at all.

Indeed, there are still people abroad in our world today who expect a painting to look like something they can recognise, rather than to be itself.

The Courtauld Cézannes, Courtauld Gallery, WC2, until October 5