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.

In the preface, the shortness of the last part is attributed to the prior coverage in Gamow's previous books The Birth and Death of the Sun and Biography of the Earth.

In its preface, Gamow says that by luck the 1947 edition was "written just after a number of important scientific advances", so that "relatively few changes and additions were necessary".

Rømer's determination of the speed of light is recounted, leading to the lightyear and the light-foot (1.1×10−9 seconds) as space-time equivalents.

Speculating on future high-velocity travel, a trip after breakfast to Sirius to land on a planet for lunch and the return to Earth for dinner is described.

Dismissing the notion, Gamow asserts that atoms are "complex mechanisms with a large number of moving parts".

The Rutherford model of the atom, an analogy to the Solar System, is supported with reference to the percentage of mass at the center: 99.87% for the Sun and 99.97% for the nucleus.

Diffraction phenomena not explicable with geometric optics necessitated the wave mechanics of Louis de Broglie and Erwin Schrödinger.

In the chapter "The Riddle of Life" the states of matter in an automobile body, engine, and radiator are also present in living systems, but homogeneity of biological tissue is of a different sort.

Dismissed are crystal accretion in a super-saturated solution, and the molecular reaction On the other hand, virus reproduction is the "missing link" between non-living and living organisms.

Extra-terrestrial distances use stellar parallax, which Gamow relates to human binocular vision working to push the end of a thread through the eye a needle.

Friedrich Bessel measured the parallax of 61 Cygni, concluding a distance of 10 light years, making him "the first man who with a yardstick stepped into interstellar space".

Cephid variables are pulsating stars that have a period-luminosity relation, exploited by Harlow Shapley to estimate distances to globular clusters.

[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 Mathematics and the Imagination by Edward Kasner and James R.