Infinity: A Very Short Introduction [#519]
Infinity: A Very Short Introduction [#519]


  • Explains the mathematical concept of infinity and its uses in calculus, Fourier analysis, and fractals
  • Discusses the role of infinity in the physics of space, time, and matter
  • Describes philosophical aspects and debates involving infinity, and shows how current mathematical thinking can be used to illuminate some of those issues.
  • Considers the important applications of the concept of infinity to everyday reality

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.

In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.


1: Why infinity is dangerous
2: The flipside of infinity
3: Geometric infinity
4: Infinity in probability
5: Physical infinity
6: Counting infinity
7: Infinity revisited
Further Reading


Ian Stewart, Emeritus Professor of Mathematics, University of Warwick
Professor Ian Stewart of Warwick University is a well-known and highly successful writer on mathematics and its applications. He has authored over 80 books including From Here to Infinity (OUP, 1996), Does God Play Dice? (Penguin, 1997), Symmetry: A Very Short Introduction (OUP, 2013), and the bestselling series The Science of Discworld I, II, III, and IV with Terry Pratchett and Jack Cohen.

"This particular volume does exactly what it says on the tin, providing just enough background on various aspects of infinity to pique the readers interest. It is written with the same clarity and attention to detail as Professor Stewarts other books." - David Hopkins, Mathematical Gazette

"Stewart has turned what must have seemed like a daunting project into an entertaining, illuminating, and digestible read... the book has something for everyone." - Marianne Freiberger, Plus

"Even the experienced reader may have more occasion to learn something new. Some of these non-essential but nevertheless flashes of a that's-interesting-I-didn't-know-that experience will make it worthwhile reading." - Adhemar Bultheel, European Mathematical Society


ISBN : 9780198755234

Ian Stewart
160 ページ
111 x 174 mm
Very Short Introductions





Infinity: A Very Short Introduction [#519]

Infinity: A Very Short Introduction [#519]

Infinity: A Very Short Introduction [#519]