Beyond Numeracy is in part a dictionary, in part a collection of short mathematical essays, and in part the ruminations of a numbers man. Its three to five page entries range from summaries of whole disciplines (calculus, trigonometry, topology) to biographical and historical asides (Godel, Pythagoras, non- Euclidean geometry) to bits of mathematical or quasi-mathematical folklore (infinite sets, Platonic solids, Q.E.D.) well-known to mathematicians but not to the educated layman and laywoman. Occasionally, I include less conventional pieces - a review of a non-existent book, a stream-of-mathematical-consciousness car trip, brief discussions of humor or ethics. New areas are discussed (chaos and fractals, recursion, complexity) as well as more classical ones (conic sections, mathematical induction, prime numbers.
"If you've ever wanted to recapture that sense of near-mystical rapture, there is no better place than this book, and no more humane and enthusiastic mentor than John Allen Paulos, who does for mathematics what The Joy of Sex did for the boudoir interface. ..... Paulos painstakingly presents even the most recondite ideas in concrete, easily visualizable terms. ..... But Paulos's principal genius lies in the recognition that many of those humans are "unknowing mathophiles" who "have been thinking math all their lives without realizing it." For those, for anyone, who ever sat rapt at the austere beauty of a proof and later wondered where the wonder went, it's here."
"This is a book full of details, but its real aim seems to be to convey not any specific fact so much as a style, even a spirit. A book of the spirit should be deeply personal, so Paulos has chosen his format wisely. ..... P.B. and J.S. Medawar compiled a sometimes cranky, sometimes brilliant survey of biology called Aristotle to Zoos in this format, and Beyond Numeracy, though not as magisterial, can hold its own as the mathematical equivalent. ..... this inviting book shows that those of us who aren't in touch with that realm are the poorer for it."
"His brief essays are arranged alphabetically by topic, and as with one of its precursors, Voltaire's Philosophical Dictionary, it makes for an often jolly little book. ... If there is much to take issue with in Beyond Numeracy, there is also much to be amused and enlightened by. The lore has it that when Pythagoras discovered his great theorem on right triangles, he was so transported that he sacrificed 100 head of oxen to the gods as a token of gratitude. On this scale, Mr. Paulos's book is surely worth an ox or two."
"Maybe there is a royal road to mathematics, after all. If so, Paulos is motoring on it in the driver's seat with this wide-ranging book ..... Paulos tells it like the gifted teacher he is, combining mathematical lore with asides on culture and personalities ..... And on and on in what one would like to see become an infinite series."
"Beyond Numeracy will uundoubtedly entertain and educate many people and open up for them the mysterious and closed book - the book of the universe, as Galileo had it - of mathematics."