Formidable figures take over the world - for better or for ill

Not everything that counts can be counted, and not everything that can be counted counts." Much good would be done if that statement of Einstein's were brought to the attention of managers and accountants who exert so much deleterious influence through their unending quest to quantify the unquantifiable.

Charles Dickens mocked such bean-counters in Hard Times , especially through the character of Thomas Gradgrind, a teacher who refers to his students as numbers. He always has a ruler in his pocket, always ready "to measure any parcel of human nature, and tell you exactly what it comes to".

In The Triumph of Numbers , the final book by I. Bernard Cohen, the distinguished American historian of science who died in 2003, there is almost an entire chapter devoted to Dickens's loathing of statistical thinking. In the next chapter, Cohen lucidly reviews Florence Nightingale's pioneering use of statistics in discussions of public health and social reform, notably in the Crimean War. While Gradgrind was terrorising the children of Cokeville, Nightingale was arguing her case for more resources in the Crimean War using quantitative arguments that would have deeply impressed Dickens's monster. Yet Cohen makes nothing of the link.

This exemplifies the central weakness of this slight but enjoyable book, which describes for a non-specialist audience how numbers entered the understanding of nature and public life. The account is episodic and so selective that it sometimes reads more like a series of disconnected essays. We are, nonetheless, fortunate to have this book, which Cohen prepared during his final years when he was unwell and almost blind. It is only through the kindness of some friends and colleagues that the book has appeared, and with some semblance of unity.

The material in this work will be familiar to historians of science, but most of the stories are worth retelling. Cohen reminds us that Isaac Newton and his fellow 18th-century pioneers introduced numbers into the study of science and society at a time when traditional numerology and mystical philosophy flourished. Among the dozens of anecdotes here, I especially enjoyed Cohen's presentation of the equation devised by the Scottish philosopher Francis Hutcheson to relate virtue to public interest, private interest and natural ability. Gradgrind would have loved it.

For the most part, Cohen focuses on the growth of numerical tradition among the founding fathers of the US, notably Thomas Jefferson and Benjamin Franklin, and in Western Europe. By no means are all Cohen's protagonists widely known, and he usefully highlights the importance of the French physician Pierre Charles Alexandre Louis, one of the underrated pioneers of medical statistics.

The Triumph of Numbers is not one of Cohen's classics; it is best regarded as a draft outline of what could be a great and important popular book. Let us hope that someone, perhaps among the thousands of people Cohen influenced during his career, develops the idea into a full-blown classic.

It would be wonderful required reading for every bean-counter.

Graham Farmelo is senior research fellow, Science Museum, London.