Students of art history inevitably study the three great David statues of Renaissance Florence. Donatello’s bronze David, the first free-standing nude male sculpture made since antiquity, was cast around the 1440s, depicting an androgynous boy too small for the great sword he bears. And in the early 1500s came Michelangelo’s great marble David, an Apollonian warrior staring down his foe with calm determination, a colossus of masculine energy.

In between was Andrea del Verrocchio’s “David With the Head of Goliath,” cast in bronze around 1465. It is not nearly so grand as Michelangelo’s nor as voluptuous as Donatello’s, and it is the smallest of the three. But it is a thrilling psychological depiction, and perhaps the only one that leaves the distinct impression that there’s a real person inside the beautiful shell of a biblical hero. Verrocchio’s David, an aristocratic adolescent with ferocious tension running through his graceful limbs, also has an enigmatic smile, which seems to say to doubters across the ages: You think I’m not a killer?

David is one of the stars of the National Gallery of Art’s landmark Verrocchio exhibition, the first comprehensive U.S. survey devoted to the artist. Curated by Andrew Butterfield, “Verrocchio: Sculptor and Painter of Renaissance Florence” includes some 50 works, including several of the major masterpieces confidently attributed to the artist (along with David is the magnificent “Putto With a Dolphin” and the marble “Lady With Flowers”) and a gallery full of paintings, many made with or by Verrocchio’s principal students, collaborators or followers.

Verrocchio was the teacher of Leonardo da Vinci, so the exhibition is particularly welcome in this 500th anniversary year of Leonardo’s death in 1519. But he also was a teacher or close associate of Domenico Ghirlandaio, Pietro Perugino and Sandro Botticelli, and through those first two artists, effectively the teacher of the teachers of Michelangelo and Raphael, respectively.

It is too easy to think of Verrocchio, however, as merely an influence on, or progenitor of, greater things to come. His workshop, a cauldron of innovation and collaboration, was a catalyst of some of the greatest works of Renaissance art, and it is often difficult to disentangle the accomplishments of his better-known followers from his own prolific invention and experimentation.

The exhibition acknowledges and explores the confusion and complexity of defining Verrocchio’s canon, and that is the great strength of a show that is small by the usual blockbuster standards but extraordinarily potent. Visitors encounter David first, a marvel of design and casting skill (Verrocchio did his own casting, which was relatively rare for Florentine sculptors of his era). His technical skill can be seen in the slight fringe at the hem of the boy’s jerkin, which is stretched taut across his frame and held together by small hooks on his left side, and in the clarity of the characters inscribed on the garment’s trim. Even more engaging are the artist’s narrative choices — the pathos of Goliath’s head, which rests at the boy’s feet, and the curious expression on David’s face, which suggests the enigma of his character and foreshadows the man he will become, the king who rapes Bathsheba and sends her husband to his death.

But the David isn’t even the best bronze in the exhibition. Even more stunning is the “Putto With a Dolphin,” a lighter-hearted work but even more impressive. The putto, a winged boy, twists on one foot, lightly touching the ground while clutching in his pudgy arms a slick, oversize fish with a curious canine expression on its face (it’s a stretch to call it a dolphin). The miracle is in the flowing drapery that clings to the boy and billows behind him. Its surface is lightly hammered to make it resemble something like a thin animal skin, and its elaborate folds seem almost to defy the possibility of its having been made from poured bronze. And yet, with the exception of the boy’s wings, the piece was apparently fashioned in a single cast.

Both the David and “Putto With a Dolphin” are securely attributed to Verrocchio, and both are mentioned in Giorgio Vasari’s “Lives of the Artists,” a problematic but indispensable source about artists of this period. Vasari, slightly condescending in his chapter on Verrocchio, tells us that the artist was experienced as “a goldsmith, a master of perspective, a sculptor, a woodcarver, a painter, and a musician” — and that he also studied geometry.

The exhibition includes fine examples of Verrocchio’s metalwork (an agate vase with silver mountings and a magnificent bronze candelabrum) and a roomful of drawings, which is an impressive assemblage given the paucity of his drawings. Among them is a spectacular “Head of a Woman With Braided Hair,” which is likely one of the “certain heads of women, beautiful in expression and in the adornment of the hair, which Leonardo da Vinci was ever imitating for their beauty,” as mentioned by Vasari.

It is a room of paintings, however, that is the most absorbing chapter of this exhibition. The National Gallery has moved, for the first time in about 30 years, its prized Leonardo, the portrait of Ginevra de’ Benci, and placed it in a free-standing case in the middle of the room. This emphasizes not just Leonardo’s relation to his teacher but also Verrocchio’s broader role as an instigator and general prod to the creative energies of late-15th-century Florence. Many of the works in this room repeat a common theme — the Madonna and Child — with some painted, others made of plaster or terra cotta and others painted with or by his acolytes or admirers.

The repetition of the theme helps highlight the particular virtues of Verrocchio’s unique contribution, especially in a work known as the Berlin Madonna and Child. Here one sees the sweetness and mystery for which Leonardo is often granted the historical patent, and the subtle shading and volume that makes Verrocchio’s figures look more fully three-dimensional than those of other painters of his time. And the finicky pursuit of detail — the attention to such things as lace and texture of cloth, and how light hits gold threads woven into a piece of fabric. It is a stunning and deeply moving painting.

The inclusion of Leonardo’s Ginevra portrait also lets visitors trace the DNA of an idea, from Verrocchio’s marble carving of a “Lady With Flowers” to Leonardo’s painted version of what seems to be the same woman or, at least, the same general idea of a woman. Moving back and forth between sculptures and paintings is infinitely rewarding, and one begins to wonder how much of Verrocchio’s painterly innovation was derived not just from studying life itself but also from studying life frozen in stone or metal. It’s tempting to think that the shadows under the chin, and the highlights on the face and neck of the Berlin Madonna, are visual discoveries made from Verrocchio’s own three-dimensional work.

And so, too, the famous “sfumato,” or haziness and shading of forms, celebrated in Leonardo’s painting. It’s not just in the Berlin Madonna but also in drawings such as the “Woman With Braided Hair.” When the geometry and surfaces of three-dimensional objects gets complicated, the mind tends to soften and resolve forms. We can’t see deeply into complex surfaces, such as the billowing folds of the Putto’s garment, so we register them in a kind of visual paraphrase. Perhaps Leonardo’s signature painterly gesture also has its origins, or was furthered by, a response to the complexity of Verrocchio’s sculpture and the curiously opaque expressions of his figures.

The exhibition also manages to give us a fleeting sense of something that has been mostly absent from Verrocchio’s reputation: a sense of his personality. There isn’t enough extant work to fully flesh out his character beyond the sparse details of his biography. But in certain grotesques (drawings of old men drinking and dancing), in a powerful painting of Saint Jerome’s face, in the Berlin Madonna and in a fanciful rendering of a proposed tomb for a notable Venetian, we see a roundedness and richness that hasn’t made it into the standard art historical accounts of the artist.

If Verrocchio is destined to be remembered primarily as Leonardo’s teacher, we can at least see that what passed from master to pupil was far more than a set of skills or techniques for rendering facsimiles of the world. There was a world view, as well, a restlessness, a surfeit of curiosity and ambition, and perhaps even a shared sense of philosophical levity that transcends mere humor.

Verrocchio: Sculptor and Painter of Renaissance Florence Through Jan. 12 at the National Gallery of Art. nga.gov.