One Two Three... Infinity

One Two Three... Infinity: Facts and Speculations of Science is a popular science book by theoretical physicist George Gamow, first published in 1947, but still (as of 2020) available in print and electronic formats. The book explores a wide range of fundamental concepts in mathematics and science, written at a level understandable by middle school students up through "intelligent layman" adults.[1] The book includes many handmade illustrations by Gamow.

One Two Three... Infinity
One Two Three... Infinity (cover).jpg
First edition
AuthorGeorge Gamow
IllustratorGeorge Gamow
CountryUnited States
SubjectsScience, mathematics
Published1947 (Viking Press)
Media typePrint
LC ClassQ162.G23


Beginning with an exploration of elementary numbers, the book opens with a description of 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 then explores number theory, topology, four-dimensional space, spacetime, relativity, atomic chemistry, nuclear physics, entropy, genetics, and cosmology. The book is known for a quirky sense of humor and for memorable metaphors, such as a visualization of the periodic table of elements on a spiraling cylindrical strip.[1]: 136–137


Science writer Willy Ley praised Gamow's book, describing it as an "admittedly rare ... book which entertains by way of instruction".[2] Kirkus Reviews declared it "a stimulating and provocative book for the science-minded layman".[3] Theoretical physicist Sean M. Carroll credited One Two Three... Infinity with setting the trajectory of his professional life.[4] Cognitive scientist Steven Pinker read the book as a child, and has cited it as contributing to his interest in popular science writing.[5] Astrophysicist and science popularizer Neil deGrasse Tyson identified One Two Three... Infinity as one of two books which had the greatest impact on him, the other being Edward Kasner and James Newman's Mathematics and the Imagination.[6]

In 1956, Gamow was awarded the Kalinga Prize by UNESCO for his work in popularizing science, including his book One, Two, Three... Infinity, as well as other works.[7]


  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.
  3. ^ "One Two Three...Infinity by George Gamow". Kirkus Reviews. Retrieved 6 January 2015.
  4. ^ Carroll, Sean M. (April 16, 2008). "Life-changing books: One, Two, Three... Infinity". New Scientist. Retrieved 6 January 2015.
  5. ^ "Up Front". The New York Times. May 27, 2007. Retrieved 6 January 2015.
  6. ^ "Neil deGrasse Tyson: By the Book". The New York Times. December 19, 2013. Retrieved 6 January 2015.
  7. ^ "Kalinga 1956". United Nations Educational, Scientific and Cultural Organization. Retrieved 2020-05-16.