So who is this book intended for? I would guess that students of all ages would find it invaluable. Yes, they can Google a topic instead, but that can be pot luck. Bynum offers you five or six pellucid pages that give you the boundaries of your topic.

Then there are the busy professionals. All of us are suddenly required as journalists, speakers, parents, or travellers to bone up quickly on Islamic science or Aristotle or DNA or miracle drugs or cosmology – and here’s a chapter to suit. And there is the arts contingent: I meet so many who bemoan their skewed miseducation (not only in Britain) and who want some starting point in science to make amends. The Little History, in its clear, unfussy summaries, does this admirably.

It begins in Babylon, Egypt, China, India, and Greece. In the beginning, three sciences mattered most, we’re told: ‘counting, astronomy and medicine.’ They were, and this is no surprise though it’s often forgotten, invariably infused with magic, religion, and other strongly held essences of everyday life. The ancient civilisations were also adept at favouring ‘pure’ science instead of the applied. One of my heroes, Sir Peter Medawar (not mentioned in this book), who won the Nobel Prize for medicine with our own Sir Macfarlane Burnet (also not mentioned), liked to remind us that ‘pure’ science did not mean theoretical – which is a perfectly sound and necessary branch of science – but, instead, pure was the kind you can do while sitting on a sand dune without getting your toga soiled. Pure, in other words, meant devoid of nasty, practical experimentation.

Madame du Châtelet at her desk (detail, artist unknown)A few, in classical times, such as Archimedes (not mentioned), did actually try. He leapt in and out of bath tubs. But the most influential pondered, dirt free, and pronounced, and thus gave us four elements to describe matter – earth air, fire, and water – or four humours to account for disease. They tied up human thought for millennia until some brave innovator was willing to break the precious mould of snobbery and self-deceit to create the next revolution. The anatomist Galen ruled until Vesalius swept him aside; Aristotle persisted with all sorts of hokum, revered, until modern times; and Hippocrates gave us not only his oath, but also that shamanistic interpretation of bodily functions involving yellow and black bile, phlegm, and blood.

But the beginnings of a scientific method were perceptible even then. Hippocrates, was, for example, also keen to dispel the idea that illness is a revenge of the gods; it was, he and his followers insisted, a bodily, an organic imbalance. This was progress.

Before we become too judgemental, Bynum reminds us that all science is a product of its age, of human beings facing astonishing limitations with no microscopes, telescopes, or even libraries. He notes that the first international meeting in chemistry took place about 1860: ‘In the days before telephone, emails and easy travel, scientists rarely met and they communicated mostly by letters.’ You could not dash off a note to a colleague to check a thought or compare findings and hear back by tomorrow. Imagine studying in your own chosen field with hardly anyone to talk to. Even worse, imagine the resistance to change when the only reference point is a hide-bound establishment of gruff men whose reputations depend on the dictum ‘nothing shall ever happen for the first time’.

Yes, men. There are eight women mentioned in the 256 pages of this book, a couple as wives with benefits (Madame Lavoisier and Mary Leakey). The others are Vera Rubin (astronomy), Mary Anning (fossils), Lise Meitner (nuclear physics), Rosalind Franklin (DNA), Dorothy Hodgkin (molecular biology), and both Curies, Irene and Marie. There is also Lucy – but she’s a fossil. This may be a fair commentary on the exclusion of the female mind from science until very recent times, but I am more inclined to view it as a blind spot. The work of Newton, for example, is clearly singled out as a force that transformed science outside England, but Bynum chooses to credit Voltaire with this revolution when it was in fact Voltaire’s brilliant lover who did the work and, in doing so, developed Newton’s ideas in the process. Émilie du Châtelet was every bit as significant as the philosopher.

Another omission is Australia. It’s not in the index. We do get Florey (how could we not?) as an Oxford-based genius producing penicillin in less time than it takes to get a budget through Congress, but there is no mention of Lawrence Bragg, the youngest person in history to receive a Nobel Prize for science and who invented two new fields of research; nor of Mac Burnet or his subject immunology. We do, however, have Raymond Dart, the archaeologist, who spent much of his time in South Africa, and Mike Morewood of Hobbit (or Homo floresiensis) fame, who comes from New Zealand.

But these are small points in the sweep of history. What is more surprising (other than no immunology) is the omission of Apollo and trips to the moon or space, of environmental research (ecology – Rachel Carson?) and climate science, or mention of the brain and neurology. Are they too recent to be part of ‘history’?

What we do get in this history, in the tradition of E.H. Gombrich’s Short History of the World (1936, first published in English in 2005), is every main area of discovery from continental drift to the Big Bang, from genetics to the Human Genome Project, and from atoms to Darwin, with most of the big names recurring in crossovers. We are reminded of the frustrations, blind spots, and false leads, but also of how often and how early our forebears got it right. Yes, the ancients did, already, have views about atoms and the passage of the Earth around the sun long before Rutherford or Copernicus. They were, Bynum insists, as clever as we think we are, but with few resources. They may have had distracting world views, but they nonetheless observed that world to good effect.

It was only as recently as 1833 that Samuel Taylor Coleridge thought to ask what these newly practical ‘natural philosophers’ should be called, with their soiled hands and complicated apparatus making stinks and bangs. The Reverend William Whewell, Newton’s successor as Master of Trinity College, Cambridge (where the gathering took place) offered ‘scientist’. Though half-rhyming with ‘atheist’, the appellation stuck. The ‘profession’ is remarkably recent. This book displays its formerly largely unprofessional, genteel origins with sympathy and erudition.

Did you know, by the way, that the three computer kings – Bill Gates, Steve Jobs, and Sir Tim Berners-Lee – were all born in 1955? Odd that, as Bynum notes. But he could have added that the first ‘computers’ were actually the women who once upon a time wrote down the thousands of measurements astronomers came up with; or that the first computer programmer was Ada Lovelace, Lord Byron’s daughter. Even odder!