Piero della Francesca Annunciation of Virgin Mary, 1467 -1468 (Moulding of Saint Anthony’s polyptic) Tempera on wood, 122x194 cm Perugia, Umbria National Gallery
‘Annunciation of Virgin Mary’ (c1467-68), by Piero della Francesca © Umbria National Gallery, Perugia

A monograph show devoted to Piero della Francesca is not an everyday occurrence. The 15th-century Tuscan painter is a titan of art history. A mathematician as well as a painter, he was described by Renaissance biographer Giorgio Vasari as an “uncommon master” who was also “the greatest geometrician” of this time.

That the Hermitage in Saint Petersburg has succeeded in bringing together 11 paintings, the most ever assembled outside Italy, is in part due to its contemporary connection with Piero’s homeland, where the presence of the Hermitage Foundation — headquartered in Venice — has fostered a rich network of exchange, which also sees many works from the Russian institution’s deposit travel to exhibitions in Italy.

Nevertheless Piero’s most legendary masterpieces are absent. London’s National Gallery refused to lend its “Baptism of Christ”, for example, and the site-specific freschi for which the artist is perhaps most famous cannot be parted from their ecclesiastical walls. Still, to see this cache of paintings under one roof is a privilege.

With sensitivity and skill, curator Tatiana Kustodieva has transformed the gallery into an ecclesiastical fantasia. Each painting is set back into a chapel-like niche whose walls are covered in white gauzy material, while the floors are decorated with gold geometric designs. The overall effect is to evoke the Platonic utopia that resided within the mind’s eye of the painter himself.

The earliest work in the exhibition — the Contini-Bonacossi “Madonna and Child” from Delaware (c1435) — had yet to arrive when I visited. Next in age however is “Saint Jerome and the donor Girolamo Amadi” (1440-50), on loan from Venice’s Accademia Gallery.

Piero della Francesca Saint Jerome and the donor Girolamo Amadi, 1440 - 1450 Tempera on wood, 49x42 cm Venice, Gallerie dell'Accademia
‘Saint Jerome and the donor Girolamo Amadi’ (1440-50) © Gallerie dell’Accademia, Venice

It’s hard to say exactly how old Piero was when he executed it, as details of his life are sketchy. Kustodieva estimates his birth to have been in 1412. Others put it later, around 1415-20. The painting’s own potential date spans a decade.

The composition is still tainted by Gothic fiddliness: the saint and his Venetian donor loom over a backdrop busy with a crucifixion, an imposing tree and a cluster of sentry-straight towers. But there is nothing fiddly about the evanescent tones and immaculate shadows that bind figures and landscape into a single unity to create a spellbound stillness that suggests an encounter with the spirit of God.

Given that no painter before or since has ever got close to conjuring the remote, idealised realms that were Piero’s kingdom, it’s fair to say his genius was as much nature as nurture. Nevertheless, there were earthly reasons why he was able to paint as if Plato, who believed that geometry was a gateway to the divine, was whispering into his ear.

Born in Borgo San Sepolcro in eastern Tuscany into a family of merchants, Piero learnt arithmetic, or so Vasari tells us, before deciding to become a painter at the age of 15. By 1439, he was in Florence assisting Domenico Veneziano, a painter renowned for his diaphanous light and uncluttered compositions, and just one of numerous painters in the city whose vision was transformed by the rediscovery of classicism at the time.

A provincial artist such as Piero must have been fascinated by the solid, uncompromising figures and spatial depth of freschi by Masaccio, for example, in the Brancacci Chapel in the Church of Santa Maria del Carmine. Equally inspiring would have been the architecture of Filippo Brunelleschi, who had remodelled various Florentine squares and churches according to spare, rational, Vitruvian principles.

Probably his most explicit influence was Leon Battista Alberti. A true Renaissance man, the artist, architect and writer was responsible for De Pictura (c1436), a treatise that set out the mathematical principles essential to painting in classical perspective. Armed with these tools and his knowledge of arithmetic, Piero was able to bestow his pictures with the depth, equilibrium and clarity of a view seen through a window.

Paradoxically, however, Piero’s most ingenious stroke was to quit Florence and head back into the campagna. It was here that he found bold, ambitious patrons — tough, clever men, as hungry for intellectual and cultural dominance as they were for military power. Bent on challenging the Medici as the quattrocento’s most innovative connoisseurs, they gave Piero the liberty to push his art beyond the bounds of anything seen in the Florentine hothouse.

Piero della Francesca Portrait of Sigismondo Malatesta, 1451 c. Oil on canvas, 44,5x34,5 cm Paris, Musée du Louvre
‘Portrait of Sigismondo Malatesta’ (1451) © Musée du Louvre

These patrons demanded portraits, still a fledgling genre, to mark their moment of glory. In St Petersburg, Piero’s 1451 picture of Sigismondo Malatesta, reveals the lord of Rimini as a prince of darkness, his cruel, hooded gaze testifying to the steely will that saw him rise from condottiere to ruler of a hub of Renaissance culture.

Sigismondo is painted in half-profile, in keeping with the medals that were a popular feature of International Gothic art. Yet Piero uses the new-found medium of oil paint to create a sense of depth through satin-toned contrasts between Sigismondo’s sculptural jawline and the black background in which he is suspended.

By the mid-1450s, Piero was in Arezzo where, in the Basilica of San Francesco, he painted his greatest masterpiece: the cycle of frescoes that narrate the Legend of the True Cross. A digital projection in the Hermitage can’t convey the awesome presence of the original, which plunges its cast of flawless, ivory-pale saints, soldiers and royals into a melodrama that canters from the Garden of Eden to the 7th-century battle between the Roman and Persian empires.

But another fresco fragment on show here does hint at the Arezzo cycle’s majesty. An image of Saint Julian, painted around 1451-54 for the Church of Saint Augustine in Borgo San Sepolcro, it shows the rapt, wheaten-haired saint crowned by the wafer-thin gold disc that is etched against the astral blackness like a satellite floating in the cosmos.

If Piero succeeded in emulating the hand of the divine geometer it’s because he had the guidance of classical mathematicians. In the late 1450s, he illustrated an Italian translation of Archimedes, whose mathematical research saw him arrive at groundbreaking inventions, including the lever. (A facsimile copy of Piero’s manuscript is on show here.)

Only a meticulous understanding of space, measurement and proportion could have allowed Piero to create the painting that is in itself sufficient cause to visit this show. Painted between 1467-68, this Annunciation scene — normally in Perugia — sets Mary and the Angel either side of a corridor bordered by blinding white Corinthian columns. As they burrow towards the marbled, sky-blue panel at the far end, each vertical casts a graphic shadow on the floor. So convincing is the impression of depth you long to stretch out a hand to check that the artist hasn’t carved a three-dimensional tunnel through the canvas.

Above this vortex hovers the dove as he shoots his haze of golden rays towards Mary’s head. The bird’s presence heightens our awareness that it is in the limbo between the two figures that Christ’s conception occurs.

Piero della Francesca Madonna di Senigallia, 1470-1485 Oil and tempera on wood, 61x53,5 cm Urbino, Marche National Gallery
‘Madonna of Senigallia’ (c1470-85) © Marche National Gallery

Is Piero telling us that mathematics can work miracles? If so, the Euclidean precision of the other great masterpiece on show, the “Madonna of Senigallia” (c1470-85), boosts his case. Probably painted when Piero was in the employ of his last and most important patron, Federico da Montefeltro, the Duke of Urbino, it shows Mary as a 15th-century Tuscan maid flanked by two angels. The painting is a synthesis of austere geometric order — the figures are framed by crisp, angular spartan grey walls and an open doorway — lifted to transcendence by a single crystalline beam of light which falls obliquely through the window behind them: a simple, irresistible statement of unswerving faith in the hereafter.

Unable to paint by the 1480s due to blindness, Piero gave himself over to mathematics, writing treatises on geometric solids, on abacus and on the use of perspective in painting — 15th-century paper codices of the latter two are on show — which became influential for both mathematicians and artists.

If this show has a flaw it is that the connections between science and art in Piero’s oeuvre could have been teased out more fully. Nevertheless to experience the Tuscan’s unparalleled gift for uniting these two spheres is both educational and entrancing.

To March 3, hermitagemuseum.org

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