The World of Mathematics Four Volume Set

The World of Mathematics
by James R. Newman

Simon & Schuster
2480pp. (4 Volumes)


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In 1940 James R. Newman, a lawyer and writer who had trained as a mathematician, began to assemble a popular historical anthology of mathematical writings. He reckoned it might take him two years. Fifteen years later he delivered the million-word manuscript to his publisher: 133 entries, each with a brief introduction and biography of its author. The World of Mathematics finally appeared, in four volumes, in 1956. It was immediately successful--a classic of mathematical popularization. Now Tempus Books has reissued it, still in four volumes but this time in paperback as well as hardback form. How does it read in 1989?

The coverage, eclectic from the first, is beginning in parts to date. The broad historical background of mathematics is still excellent; the sections dealing with mathematics in the physical and social worlds, and with the bases of statistics, stand up for the most part remarkably well. But many of the entries concerned with pure mathematics and its cultural relevance would certainly have been reconsidered by Newman today. The intellectual level remains demanding but not intimidating: appropriate for the enquiring non-mathematician, or the mathematician off-duty. About 20 percent of the entries are drawn from the research literature, or at least the primary presentation of original work; 30 percent are educational or polemical pieces; 40 percent are popularizations of established mathematics; and 10 percent are stories or whimsical or discursive essays.

The charm of a good historical anthology is the variety of outlooks and challenges it presents. Here is Francis Galton in 1869 discussing hereditary genius, blandly contravening all the principles of social justice by proving that some people are inherently many times brighter than others. Here is Malthus's famous essay of 1798 on population, condemning most of mankind for most of time to unavoidable misery--and where's the flaw in his argument? Here is Alan Turing in 1950 on whether a machine might think, an amazingly modern essay which still reads cogently after nearly 40 years of massive developments in computing. Newman was clearly a connoisseur of good literary style. Each of his selections can be read purely for pleasure, even without bothering to follow its argument. Anybody who reads the scientific literature should enjoy the book for this alone; anyone who writes it will probably blush for shame.

The whole huge compilation is far too big to take in at a sitting. It is a book for extended browsing, or a rather eccentric work of reference. I like best the entries dealing with mathematics in the real world. Lanchester on the mathematics of warfare, showing how Nelson's brilliant strategy at Trafalgar closely approached a theoretical optimum; Moseley's account of the X-ray identification of atomic number, probably his last paper before his tragic and pointless death at Gallipoli; Bernard Shaw on gambling and insurance--a departure from his usual concerns, but characteristically spirited and surprisingly sensible; John von Neumann on the workings of the neuron, and the analogy between the brain and the digital computer.

This new edition has not been reprinted. A copy of the 1956 Simon and Schuster publication has been optically scanned and digitally reset (the stupefying intellectual triviality of the tasks that occupy most modern computers would have saddened Turing and von Neumann). The index has been slightly modified; I have spotted just two words of additional text. The publishers have thus missed the opportunity to remedy the most infuriating omission of the first edition: the lack of bibliographical references to the entries. Some can be placed from Newman's commentaries but many are quite free-floating. It is quite impossible to stand in proper relationship to a piece of writing if you don't know in what context, or crucially when, it was written. The annoying detective work needed to pin down each entry from Newman's introduction to it, or from other sources, is almost the only unpleasing feature of this marvelous book.

--Reviewed by David E.H. Jones in Nature, 337 (February 2 1989), p. 420.