One Two Three ... Infinity

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One Two Three ... Infinity: Facts and Speculations of Science is a book by theoretical physicist George Gamow in 1947, exploring some fundamental concepts in mathematics and science, but written at a level understandable by middle school students up through "intelligent layman" adults.[1] The book is hand-illustrated by Gamow. It remains one of the most well received ever in the popular science genre. Gamow's writing style is informal and wryly humorous, showing a gift for memorable metaphors and analogies.

Beginning with an exploration of elementary numbers, the book leads with the "Hottentots" (Khoikhoi), said to have words only for "one", "two", "three", and "many", and builds quickly to explore Georg Cantor's theory of three levels of infinity – hence the title of the book. It then describes a simple automatic printing press that can in principle (given enough paper, ink, and time) print all the English works that have ever been, or ever will be, printed (a more-systematic version of the infinite monkey theorem). The author notes that if all the atoms in the Universe, as known in Gamow's time, were such printing presses working in parallel "at the speed of atomic vibrations" since the beginning of known time, only an infinitesimal fraction of the job could have yet been completed.[1]

Gamow's explorations then wind from the mathematics of infinity, to topology, the fourth dimension, relativity, atomic chemistry, nuclear physics, entropy, DNA, evolution, cosmology, and more. For a book originally written in the first half of the twentieth century, Gamow's work remains surprisingly relevant even in the twenty-first century. Gamow focused his writing on what he knew or suspected were fundamentals unlikely to change much, even as science advanced with increasing speed. As a result, very little of his book has become obsolete, and many of the key concepts he covered are even more relevant today.


The book is dedicated to his son, Igor Gamow, with the inscription, "Who wanted to be a cowboy".[1]


Willy Ley praised Gamow's book, describing it as an "admittedly rare . . . book which entertains by way of instruction."[2]


  1. ^ a b c One, Two, Three...Infinity (1947, revised 1961), Viking Press (copyright renewed by Barbara Gamow, 1974), reprinted by Dover Publications, ISBN 978-0-486-25664-1, illustrated by the author; eBook edition, Dover, 2012 ISBN 9781306350099; other editions and translations
  2. ^ Willy Ley, "Book Review," Astounding Science Fiction, June 1948, pp.158-61.