Pity the poor curators of major exhibitions struggling to find fresh takes on famous masters. The curators of Tate Modern’s new Cezanne blockbuster have begun by dropping the acute accent from his surname, apparently a Parisian affectation not in use on the artist’s home turf. Anticipating grumbles about another major exhibition devoted to a dead white male artist, they have emphasised Cezanne’s outsider status by painting him as a provincial from Provence. It was a role the artist liked to play in Paris, once famously excusing himself from shaking Manet’s hand on the grounds that he hadn’t washed in a week.

With or without his accent, Cezanne remains French. He was in fact the only full- blooded Frenchman among the three great pioneers of post-impressionism, Van Gogh being Dutch and Gauguin boasting Peruvian descent. He was also, coincidentally, the only one of the three to emulate the masterworks in the Louvre. Not content with hitching a ride on the impressionist bandwagon, the artist from Aix ‘wanted to make of impressionism something solid and enduring like the art of museums’. In the process, paradoxically, he set in motion the modernist revolution that led to cubism: Picasso acknowledged him as a ‘father’ and kept a chunk of Mont Sainte-Victoire as a relic.

Cezanne is what is known as ‘an artist’s artist’. That doesn’t mean he’s difficult, it means he’s good. If you want to find the best artists in any generation don’t ask the critics, ask their peers. Cezanne’s peers put their money where their mouths were, creating an artists’ market for his work long before his breakout exhibition with Vollard in 1895. Gauguin owned six Cezannes by 1883; the ‘Still Life with Fruit Dish’ (1879-80) in the exhibition was his prize possession. Monet’s total of 14 oils and one watercolour was beaten by Pissarro’s 19 oils, three watercolours and 12 drawings. Even Degas, initially sniffy about Cezanne’s inclusion in the Third Impressionist Exhibition of 1877, became a convert, making ‘an orgy of purchases’ from the Vollard exhibition and pipping Renoir to the purchase of ‘Three Pears’.

‘How does Cezanne do it?’ wondered Renoir. ‘He can’t put two strokes of colour on a canvas without it being very good.’ There are various possible answers to Renoir’s question. First, unlike his scuffling fellow artists, Cezanne wasn’t painting for the market. He could afford to thumb his nose at the Salon, submitting early works one jury member described as ‘peinture au pistolet’ because he lived on an allowance from his banker father. When he decided to put down the pistolet and focus on recording his ‘sensations’, he was able to give it as long as it took.

Second, he used his directional strokes of colour not to suggest light falling on things, like the impressionists, but to create a sense of air circulating around them, air that wafts as if stirred by draughts or breezes. Third, he went big on blue. Conservators have identified different mixes of blues – cobalt, Prussian, cerulean, ultramarine, indigo – not just in his skies and seas but in the junctures between apples, the interstices of Madame Cezanne’s interlocked fingers, the folds in tablecloths and the shadows of the fragile blooms making up his glorious ‘Grand Bouquet of Flowers’ (c.1892-95). In his watercolours strokes of blue hover round the forms, positioning them in space without stifling them. ‘Nature exists for us humans more in depth than in the surface,’ he explained to Émile Bernard in 1904. ‘Therefore, into our vibrations of light… we need to introduce sufficient blues to make one feel the air.’

What distinguished Cezanne’s art, in his own opinion, was the strength of the ‘sensations’ he was driven to record. His paintings thrum with them. At the same time, he never lost sight of the actual stuff of which nature is made. His painting of ‘Mont Sainte-Victoire Seen from the Bibémus Quarry’ (c.1895-99) is like a cutaway contrasting the physical substance of the quarry’s red sandstone with the dreamily distant white limestone peak. ‘I need to know some geology – how Sainte-Victoire’s roots work, the colours of geological soils,’ he felt. The flesh-and-blood farm labourer in ‘Man in a Blue Smock’ (c.1896-97) is sitting in front of a screen decorated with a pastoral idyll.

The same tension between the real and the ideal, the substance and the dream, animates Cezanne’s signature series of bathers, from the naturalistic ‘Bathers at Rest’ (1875-76) – actually vigorously towelling – through the Poussinesque ‘Battle of Love’ (1879-80) to the National Gallery’s ‘Grandes Baigneuses’ (c.1894-1905) with its dog and apples, a monumental mash-up of classicism and modernism, past and present.

The painting was still in his studio on his death in 1906, perhaps because he wasn’t satisfied with it. Weeks before dying he had written to his son Paul: ‘As a painter I’m becoming more clear-sighted in front of nature, but realisation of my sensations is still very laboured. I can’t achieve the intensity that builds in my senses.’ Just as well for us, or we might be blown away.