One of Napoleon’s more reckless gambles — there were many — was his ill-fated invasion of Egypt in 1798. Determined to cut off Britain’s trading routes with India, the petit general crossed the Mediterranean with some 50,000 soldiers and sailors, looking to drive the English from the Orient. But this was a military mission with an intellectual bent. Napoleon, intoxicated by the example of Alexander the Great, another conqueror with big ideas, had a grand vision: He wanted to modernize Egypt — even if he had to do it at the point of a gun — and explore the glories of the Egyptian past.

To accomplish this task, Napoleon enlisted a corps of France’s brightest thinkers, known as the savants. In their three-year stay, the savants would endure hardship, death, and disease as they excavated ruins and fathomed the mysteries of the Pyramids. (They unearthed the famed Rosetta Stone, the key to translating hieroglyphics, on one such expedition.) The savants mapped Cairo, as engineers tried to bring the unruly Nile under control and naturalists cataloged Egypt’s teeming wildlife. Some learned Arabic (one French general took a Muslim wife, converted to Islam, and called himself Abdullah), while others lost their health — and their minds — in the harsh Egyptian clime.

Their findings were published between 1809 and 1828 in a 23-volume collection called “The Description of Egypt,” itself a landmark of modern scholarship, unrivaled in the annals of 19th-century intellectual life for its staggering collation of sources and its exhaustive depiction of ancient and modern Egyptian cultures. Though the savants helped establish Egyptology as a field of inquiry, the judgment of posterity has been mixed. Edward Said sneered at the enterprise, which he called “engulfment of Egypt by the Western instruments of knowledge and power.” Nina Burleigh takes a more measured tack in “Mirage” (HarperCollins, 286 pages, $25.95). For her, the savants were disinterested researchers who “tried to approach the land, the people, the relics not as tourists or literary travelers, or even colonizers, but from within their fields of scholarship.” Still, her account is flawed by its avoidance of the issues about colonialism and scholarship, which are mentioned only in passing.

Ms. Burleigh is more interested in the savants themselves. Building her narrative around the lives of about a dozen of these men, she tells a lively story. Led by the tall, reserved but grandly named chemist Comte Claude Louis Berthollet, who recruited the best minds of Paris, and Gaspard Monge, a brash mathematician who sported a hip flask on his side, the corps de savants did not have an auspicious debut. While troops crashed ashore at Alexandria, a ship carrying scientific equipment sank in rough seas. And the city, once an ancient center of learning, proved disappointing. “We were looking for the Ptolemies, the library, the seat of human knowledge,” lamented an architect. “And instead we found ruins, barbarism, poverty, and degradation.”

But the French force had more pressing concerns, like the Mamelukes, the ferocious warriors who ruled Egypt on behalf of the Ottomans. A victory at the Battle of the Pyramids encouraged Napoleon, but the French Navy was not so lucky. In August of 1798, Lord Nelson annihilated the fleet in Aboukir Bay; the loss of important supplies — medicine, food, clothing — was nearly devastating. But, as Ms. Burleigh stresses throughout, the savants relied on ingenuity and pluck to get themselves through. When Napoleon groused that so much equipment now lay at the bottom of the sea, the inventor and chemist Nicolas-Jacques Conte replied, “Well, we will make the tools.” It was not for nothing that he was dubbed “the column of the expedition and the soul of the colony.”

In Cairo, Napoleon established the Institute of Egypt, where the savants gathered. Ideas tended to be mooted willy-nilly — during one meeting, Napoleon asked his thinkers to ponder how beer could be made without hops in Egypt. Cairo proved stimulating, if bewildering in its vastness. For the eccentric naturalist Geoffroy Saint-Hilaire, one of the most interesting figures on Ms. Burleigh’s pages, it was a foyer des lumières (“home of enlightenment”). The savants traded notes on lunar cycles, Egyptian music, and the properties of dissected mummies, publishing their findings regularly in a journal. The physicist Joseph Fourier, whose influential theorems on waves are still taught, set up Egypt’s first newspaper.

But the restless Napoleon was not content to sit around and talk shop, and in 1799 he embarked on the most disastrous phase of his Egyptian campaign, an invasion of the Holy Land. Stalked by the bubonic plague, Napoleon’s troops were turned back at Acre by ferocious resistance of the Turks. In retreat, he scampered back to France, taking a handful of leading savants, including Berthollet and Monge, with him. The remnant was baffled, outraged, and fearful: The Turks, aided by the English, were bearing down on Cairo, and the Arab populace was in revolt.

With Fourier taking over the Institute, the remaining scholars had orders to explore the ruins in the south of Egypt. They sailed down the Nile to Thebes and Karnak, where they excavated and made careful drawings. Astronomers and geologists worked up precise figures. It was a glorious intellectual moment, Ms. Burleigh writes, but the French were in a desperate situation. In her closing chapters, she vividly describes the nightmare that had befallen the occupiers. Devastated by plague, the French fitfully retreated in late 1801, as the English plundered the savants’ finds. Holed up in a besieged Alexandria, a bedraggled, emaciated Saint-Hilaire deliriously contemplated a unifying theory of life, “a principle so gigantic it unified all the sciences,” as he dissected an electric fish. Writing with manic energy as bombs exploded outside, Saint-Hilaire mused on “the imponderable fluids” of light, electricity, and heat as he tried to pinpoint a link to “all the phenomena of the material world.” It is a stunning image, and a fitting metaphor for the overreaching ambition that drove the savants in their quest.

Mr. Price is a contributor to Bookforum and other publications.