Some scientists of puritanical bent argue that visual aids to scientific understanding are treacherous purveyors of illusion. So it is a rare thing for a world-class mathematician to celebrate the visual drama of nature alongside lucid explanations and absorbing stories drawn from the chronicles of science down the centuries. From the elegant complexity of a single magnified snowflake (each specific six-arm structure precisely replicated only once in every two billion flakes), to curling Moebius strips, to the swirling splendours of the Andromeda galaxy, 2.9m light years distant, John Barrow, professor of mathematical sciences at Cambridge, has assembled a pictorial feast alongside a witty, informative narrative.

Barrow believes passionately in the image as a tool of scientific discovery and understanding. He cites the spectacular simulation of the Higgs particle, an elementary state of matter, also known as the God particle, theorised in 1964 by the British physicist Peter Higgs. The picture (a combination of imagination and computer generation) suggests what the decay of such a particle might look like if vastly magnified; yet it illustrates levels of matter that are strictly unable to be visualised.

Ever since the work of MCEscher, the Dutch graphic artist, who depicted gravity-defying architectural scenarios in the early 20th-century, there has been a minority craze among mathematicians, such as Roger Penrose, for the visualisation of the logically impossible. Yet for subatomic physicists, apparent logical impossibilities are the norm. How can they be illustrated? In 1935, Erwin Schrödinger, the Austrian physicist, explained a mind-bending quantum equation by visualising a box containing a cat, some radioactive material, a Geiger counter with a trigger and a flask of prussic acid. The equation seemed to indicate that, unobserved, the Geiger counter can be in a state of both activation and non-activation, therefore triggering and not triggering release of the poison gas. Only when the box is opened, or the subatomic “measured”, do we discover or “create” the cat's fate in the world of macro everyday reality. The cartoon (reprinted in Cosmic Imagery) of the alive-and-dead cat in its box has for 70 years provided a visual feel for Schrödinger's mathematics - impenetrable to all but the experts.

The curious connections between nature, human imagination and human artifice make delightful reading. Archimedes (c287-212BC), for example, experimented with intriguing structures known as polyhedra, patterns of many-sided panels that fit together perfectly on a plain. One such polyhedron, the icosahedron, has 32 faces and 90 edges. It turned out to be a key structure in the development of modern chemistry. A scaled-down version of the same pattern (making for both strength and a perfect sphere) is to be found in the traditional football, made up of individual pentagonal panels in black and hexagonal panels in white.

The relationship between probability and randomness is nowhere more evident than in the throwing of dice - the oldest gaming devices in history; less well known is the high-precision engineering (typically to 1/5000th of an inch) demanded to avoid bias in the making of the versions used in casinos. Ancient dice were usually made of sheep's bones: in Arabic the word for dice also means “knucklebone”.

Discovery of the structures of DNA, protein molecules and a vast array of living cells, expanded rapidly in the post-second-world-war era as a result of bold three-dimensional modelling. Irving Geis, who, in 1961, produced by hand a detailed water-colour of the 2,600 atoms in sperm whale myoglobin protein, had studied fine art and architecture before turning to molecular biology. Nowadays, scientists can buy software that makes even a rank-amateur modeller look competent.

Some models, such as the famous Watson-Crick structure of DNA, have become icons of biological and medical progress, just as Einstein's face has become a ubiquitous icon for genius. The cloud that follows a nuclear explosion, however, has become the icon of global doom. The first atomic explosion in New Mexico was photographed by the Cambridge mathematician Geoffrey Taylor. His time-lapse sequences provided Life magazine with a scoop and scientists with confirmation of the consequences of their equations.

The great pioneer of high-speed photography was Arthur Worthington, the Victorian physicist. He loved taking pictures of water splashes. But he was eventually out-photographed by the American physicist Harold Edgerton, whose strobe photography could capture 3,000 images per second. His startling image of a playing card being ripped through by a 30-calibre bullet (1970) is a classic of the genre.

Space and satellite photography have produced remarkable images of the universe and our planet, including pictures of earth at night, showing the energy-squandering regions. Barrow reminds us that “light does not necessarily trace mass - the dark regions of the earth are actually the places where the bulk of the human population resides”. The reflection leads to a commentary on the dark matter that makes up, according to cosmologists, 72% of the universe.

Cosmic Imagery is a captivating pictorial and literary journey through the history of science. It demonstrates, despite reservations in some scientific quarters, the crucial role of visual imagination in deepening our understanding of nature and the cosmos. It is a book that will repay constant visits, and Bodley Head is to be congratulated on its lavish, robust production, making it a must for every school library and - perhaps - for every home.

Cosmic Imagery: Key Images in the History of Science by John Barrow
Bodley Head £25 pp608

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