If you want to be mystified, awed, undone by an art show this summer, “Cézanne Drawing” at New York’s Museum of Modern Art should do the trick. I saw it earlier this month and still can’t quite believe it.

The show, through Sept. 25, is an aesthetic and spiritual windfall. It brings together more than 250 drawings (light-sensitive and therefore rarely exhibited), extending from fascinating study sheets and sketches to fully worked-up watercolors. The sense you get of being almost behind Cézanne’s eyes — or at least, bearing intimate witness as he observes, adjusts, solves and resolves, all at an astonishing level of intuitive intelligence — is exhilarating.

How Paul Cézanne transformed himself from a hypersensitive, grudge-bearing brute of an artist into one of France’s great classicists — the Raphael or Poussin of modernism — is one of the great mysteries. I like to think of him as the Bjorn Borg of modern art. His inner life verged on chaos. “I paint as I see, as I feel,” he famously said — “and I have very strong sensations.” Dreading intimacy, he safeguarded his freedom by cultivating his own brand of anti-charisma.

But just as the great Swedish tennis player channeled his rage, fear and panic into sublime tennis, Cézanne — in attempting to bring the intensity of his feelings under control — pushed himself to such extremes of focused attention that, almost by accident, he invented modern art.

I don’t think people sufficiently appreciate Cézanne’s weirdness. His status in textbooks is so canonical, his influence so pervasive, that he has become a norm. “The greatest of us all,” said Claude Monet. “My one and only master,” said Picasso. “If Cézanne is right, I am right,” chimed in Matisse. “There is hardly one modern artist of importance to whom Cézanne is not father or grandfather,” wrote the art critic Clive Bell.

The trouble with labeling Cézanne as everyone’s grandfather is the implication that he is just there, a bearded patriarch, an aesthetic Mount Rushmore. It kills off our curiosity about what he was actually up to. “Cézanne Drawing” restores it.

Cézanne liked to draw in the afternoons, to prepare himself for the next morning’s painting campaign. His single-minded focus on art oscillated between the vocational and the spiritual. (The word “calling” nicely describes it.) As he matured, he went out of his way to approach art in a scientific spirit. “Would you believe,” he wrote to the archaeologist Jules Borély, “I have almost completed formulating principles and a method for my profession?”

Cézanne spoke of his “researches” and “studies,” of his desire “to stand firmly on the ground of observation” and “see beneath the veil of interpretation.” There is a sense in which, as Kiko Aebi points out in the exhibition catalogue, he treated his favorite subjects (Madame Cézanne, Mont Saint-Victoire, tables strewn with fruit) as scientific controls.

But the veneer of patient, disinterested inquiry cannot disguise Cézanne’s diabolical oddity. Because we know he painted and drew before the motif, and because there are so many stories about him getting annoyed whenever a sitter failed to remain absolutely still, we tend to accept the idea that he was merely trying to render faithfully what he saw. But don’t be misled. He was less empirical than we assume.

You realize this when you look at his drawings and try to imagine what he thought he was up to. It registers only subtly at first. You might see how, in a view of a street in Aix, the sloping roof lines are parallel to the perspective lines, and that both rhyme with Cézanne’s characteristic diagonal hatching, giving the whole image a distinctive rhythm. Elsewhere, you might notice how Cézanne distills a pleasant landscape into a prismatic field of subtly overlapping lozenges of color, taming nature’s teeming abundance into an organized patchwork of vibrating diagonals.

In a study for “The Eternal Feminine” — a work inspired by Delacroix’s “The Death of Sardanapalus” — you may see how Cézanne reduces an orgy of dynamic, twisting bodies to an almost abstract pattern of disconnected, semicircular curves. And in a drawing after Puget’s sculpture of Milo of Crotona, you may notice that the voluminous head of the lion is constructed from the same pattern of separated, arcing lines as the twisting musculature of the man it’s attacking.

After a while, you pick up on a tendency: the weirder and more perverse-seeming the drawing, the more fully realized are the relationships among its separate parts and between those parts and the whole.

We tend to assume Cézanne left the volatility and strangeness of his youthful efforts behind. But even in his later works, wrote the curator and critic Terence Maloon, the “grotesquerie is sometimes redoubled and the perversity of his handling can be astounding.”

Cézanne wasn’t trying to be an expressionist. He was deliberately distorting the proportions of his figures in obedience to what Maloon calls “a ‘higher’ logic of composition.” Cézanne used the word “logic” himself when he told the artist Émile Bernard that art required two things: “the eye for the vision of nature and the brain for the logic of organized sensations.”

What does this mean? It’s a notion that might not make sense if you didn’t have a Cézanne in mind when you thought about it. The art historian T.J. Clark thought Cézanne was trying to re-create the structure of experience out of the units of that experience, which sounds right to me. But if that’s too abstract, it might help to think of it as Cézanne’s personal critique of Impressionism.

Impressionist pictures, he’d come to believe, captured sensations (colored light hitting the eye) that had not yet been organized. The resulting pictures had no bones, no structure. Constructed without lines, only with discrete dabs of color, they were always threatening to dissolve into formlessness.

In a sense, you could say, Impressionist pictures were too much about transience and too literal. “One should not be too scrupulous, too sincere, nor too submissive to nature,” opined Cézanne. Art, he believed, had to aspire to something more permanent. So, to Monet’s “eye,” he wanted to bring an organizing mind.

The reasoning is sound. But what’s also clear is that organization was something Cézanne needed, by temperament. His early works were curdled with chaotic passions. A cluster of drawings here depict rape, orgies and murder, and Cézanne’s rough and frenetic mark-making matches the subjects.

But as he digested and then went beyond Impressionism, he increasingly sought out rhythms, structure, stability. Repetition became key. If the wavy line of a woman’s hair could be stabilized with another wavy line defining the contours of her torso he would add it, even if it meant her torso no longer resembled that of any actual woman. If the amputated upper arm of an antique sculpture looked like a circle from one angle, he would build up the rest of the figure with circles and semicircles. Likewise, in a rendering of foliage, he would look for echoes of diamond-like shapes not only in other leaves but in the spaces between leaves, turning the composition almost into a prototype M.C. Escher.

Cézanne’s willingness to transform objective reality into something stratified, ordered and apparently impersonal led the way into cubism and the highly ordered abstraction of Mondrian. But just as Borg only appeared ice-cool as he battled his way through those epic matches with John McEnroe, Cézanne’s art only appears impersonal. It trembles with powerfully contained emotion.

The artist he most profoundly influenced — Henri Matisse — was indebted to Cézanne’s investigations into how color and rhythm could provide stability, order and a controlled intensification of expression, even at the cost of physical distortion. But the affinity was as much psychological as methodical.

Prone to episodes of deep frustration, chronic insomnia, palpitations, drumming in the ears, cramps and spontaneous nosebleeds, Matisse hoped above all that his pictures would inspire calm and repose. He succeeded, of course — magnificently. But his success was underwritten by torment. Having discovered painting, Matisse once said, he threw himself into it “like a beast that plunges towards the thing it loves.”

It may be less helpful to think of Cézanne as Matisse’s father or grandfather than as what he assuredly was: the same species of beast.