When John Donne in the 17th century wrote, “I am a little world made cunningly,” he was echoing a theme which had intrigued philosophers and poets since ancient times. This was the notion that the human form mirrored the larger world in which we live. The human being was a microcosm, a universe in miniature. Our bones were like the rocks that support the earth, our veins were like the rivers. The comparisons were far-fetched but a deeper perception lay beneath them. The world displays a surprising symmetry: Not only are we ourselves symmetrical creatures with our paired and matching limbs and organs, but between us and other beings there exist secret symmetries. And these are governed not by mystic forces but by numbers. The underlying patterns of the world are mathematical.

In “Symmetry: A Journey into the Patterns of Nature” (Harper-Collins, 384 pages, $25.95), Marcus du Sautoy, professor of mathematics at Oxford University, explores the age-old quest to discover and define these symmetries. He begins with Pythagoras and Plato and ends with the publication, in 1985, of the monumental “Atlas of Finite Groups.” This atlas, a kind of scripture of symmetries, was a collective effort, though the brilliant and flamboyant John H. Conway, an English mathematician now at Princeton, was its guiding spirit. Mr. du Sautoy’s account is really a history of the development of that branch of higher mathematics known as Group Theory. This may sound impossibly dry, but he enlivens his abstractions with dramatic and quite candid portraits of the scientists involved, many of whom he knows well and has worked with in his own research. If the puzzles Mr. du Sautoy describes are weird — and they are sometimes surpassingly so — the mathematicians who work on them are often weirder still. One of Mr. Conway’s favorite pastimes involves staring fixedly at brick walls; he loves to discover the patterns hidden in things.

This sounds eccentric, but it isn’t really. We may not stare long and hard at bare walls but we all look for symmetry in everything we see, even if we don’t think much about it. Symmetry is important to us; measure and proportion please and reassure us, whether in a stately façade or in a beautiful face. And it is in the contemplation of symmetries, as Mr. du Sautoy makes plain, that the world and our consciousness coincide. Sometimes survival too depends upon it, and not only for us.

“Symmetry tastes sweet,” Mr. du Sautoy says, and he means it literally. Bees identify flowers by their geometric shapes. They like “the pentagonal symmetry of honeysuckle, the hexagonal shape of the clematis, and the highly radial symmetry of the daisy.” Plants which can construct such patterns succeed; they have that something extra which attracts pollinators. Symmetry gives our limbs mobility; it even plays a part in our choice of a mate: We shy away from the lopsided.

Mathematicians like Mr. du Sautoy and his colleagues go far beyond such obvious aspects of symmetry, however. For them symmetry means “what you can do to an object to leave it essentially looking like it did before you touched it.” Depending on how it is spun or rotated, an equilateral triangle has six possible symmetries; at the farthest extreme of the conceivable, the ultimate symmetry, appropriately dubbed “the Monster” and possible only in a multidimensional realm, possesses more symmetries than there are atoms in the sun (the number alone would take up two lines here).

Though Mr. du Sautoy does his best to avoid equations and technical jargon — and though he includes many excellent diagrams and figures — this isn’t an easy book. It compels you to think in new and unaccustomed ways; it introduces you into strange mind-bending dimensions where numbers alone are meaningful. Mr. du Sautoy is entranced with numbers and he’s very good at conveying their hidden logic. When he discusses Fibonacci numbers — that sequence which progresses in accord with the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, 21…) — he notes that the sequence corresponds exactly with the growth rate of certain natural forms. The shell of a snail, for example, grows this way; new chambers added are precisely twice the size of the two chambers of its last growth spurt. Even a snail is a microcosm governed by mathematical symmetries.

At the same time, this is a deeply personal book. Mr. du Sautoy began it when he was turning 40, the age at which mathematicians are supposed to burn out, and he structures it according to each month of that year, a sequence which is itself a symmetry. He quotes Paul Erdds, one of the pioneers of Group Theory, who quipped that “a mathematician is a machine for turning coffee into theorems.” This is witty — and probably true — but there’s nothing mechanical about Mr. du Sautoy’s narrative. In even his most abstract flights an unusual freshness comes through, perhaps not surprisingly; after all, numbers are inexhaustible and they never grow old.

eormsby@nysun.com