Stewart was born in 1945 in England. While in the sixth form at school, Stewart came to the attention of the mathematics teacher. The teacher had Stewart sit mock A-level examinations without any preparation along with the upper-sixth students; Stewart placed first in the examination. This teacher arranged for Stewart to be admitted to Cambridge on a scholarship to Churchill College, where he obtained a BA in Mathematics. Stewart then went to the University of Warwick for his doctorate, on completion of which in 1969 he was offered an academic position at Warwick. He is now Professor of Mathematics at the University of Warwick. He is well known for his popular expositions of mathematics and his contributions to catastrophe theory.

While at Warwick he edited the mathematical magazine Manifold.

Stewart has held visiting academic positions in Germany (1974), New Zealand (1976), and the U.S. (University of Connecticut 1977–78, University of Houston 1983—84).

In 1995 Stewart received the Michael Faraday Medal and in 1997 he gave the Royal Institution Christmas Lectures. He was elected as a Fellow of the Royal Society in 2001.

He has collaborated with Dr Jack Cohen and Terry Pratchett on three popular science books based on Pratchett's Discworld. In 1999 Terry Pratchett made both Jack Cohen and Professor Ian Stewart "Honorary Wizards of the Unseen University" at the same ceremony at which the University of Warwick gave Terry Pratchett an honorary degree.

Stewart has published more than 140 scientific papers, including a series of influential papers co-authored with Jim Collins on coupled oscillators and the symmetry of animal gaits.

Stewart was married to his wife, Avril, in 1970. They met at a party at a house Avril was renting while she trained as a nurse. They have two sons. He lists his recreations as science fiction, painting, guitar, keeping fish, geology, Egyptology and snorkeling.

Mathematics and popular science

• Another Fine Math You've Got Me Into
• Concepts of Modern Mathematics
• Does God Play Dice? The New Mathematics of Chaos
• Game, Set and Math
• Fearful Symmetry
• Figments of Reality, with Jack Cohen
• Flatterland, ISBN 0-7382-0442-0, Perseus Books Group, April 2001. (See Flatland)
• From Here to Infinity, first published as The Problems of Mathematics
• Life's Other Secret
• Math Hysteria, ISBN 0-19-861336-9, Oxford University Press, June 2004
• Nature's Numbers
• The Collapse of Chaos, with Jack Cohen
• The Magical Maze (1998) ISBN 0-471-35065-6
• The Problems of Mathematics
• What is Mathematics? – originally by Richard Courant and Herbert Robbins, second edition revised by Ian Stewart
• The Science of Extraterrestrial Life, with Jack Cohen. Second edition published as What Does a Martian Look Like? The Science of Extraterrestrial Life
• Letters to a Young Mathematician, ISBN 0-465-08231-9, Basic Books, May 2006
• How to Cut a Cake: And Other Mathematical Conundrums (2006) ISBN 978-0199205905
• A History of Symmetry (2007) ISBN 0-46508-236-X
• Professor Stewart's Cabinet of Mathematical Curiosities (2008) ISBN 1-84668-064-6
• Professor Stewart's Hoard of Mathematical Treasures (2009) ISBN 978 1 84668 292 6
• Cows in the Maze: And Other Mathematical Explorations (2010) ISBN 978-0199562077
• Taming the infinite: The story of Mathematics from the first numbers to chaos theory (2008) ISBN 978-1847247881

Science of Discworld series

• The Science of Discworld, with Jack Cohen and Terry Pratchett
• The Globe, with Jack Cohen and Terry Pratchett
• Darwin's Watch, with Jack Cohen and Terry Pratchett

Textbooks

• Catastrophe Theory and its Applications, with Tim Poston, Pitman, 1978. ISBN 0-27301029-8.
• Algebraic number theory and Fermat's last theorem 3rd Edition, I. Stewart, D Tall. A. K. Peters (2002) ISBN 1-56881-119-5
• Galois Theory 3rd Edition, Chapman and Hall (2000) ISBN 1-58488-393-6 Galois Theory Errata

Science-fiction

• Wheelers, with Jack Cohen (fiction)
• Heaven, with Jack Cohen, ISBN 0-446-52983-4, Aspect, May 2004 (fiction)

• From What Does a Martian Look Like? The Science of Extraterrestrial Life:

:"Science is the best defense against believing what we want to."

• From Catastrophe Theory and Its Applications:

:"We may predict that ... as methods relevant to organized complexity develop in laboratory science, the social sciences will benefit in proportion. The new concepts ... fusing with, changing, and adding to present understanding ... may allow the definition and measurement of quantities more central to the health of the body politick than a 'standard of living' that includes useless packaging discarded, or a 'gross national product' that includes machines whose productivity is measured in megadeaths. ... If any mathematical methods can aid in the growth of such wisdom, then catastrophe theory will be part of them."

• From Does God Play Dice? The New Mathematics of Chaos on the concept of fungibility and how it applies to science:

:"Lawyers have a concept known as 'fungibility'. Things are fungible if substituting one for another has no legal implications. For example, cans of baked beans with the same manufacturer and the same nominal weight are fungible: you have no legal complaint if the shop substitutes a different can when the assistant notices that the one you've just bought is dented. The fact that the new can contains 1,346 beans, whereas the old one contained 1,347, is legally irrelevant.

:That's what `take as given' means, too. Explanations that climb the reductionist hierarchy are cascades of fungibilities. Such explanations are comprehensible, and thus convincing, only because each stage in the story relies only upon particular simple features of the previous stage. The complicated details a level or two down do not need to be carried upwards indefinitely. Such features are intellectual resting-points in the chain of logic. Examples include the observation that atoms can be assembled into many complex structures, making molecules possible, and the complicated but elegant geometry of the DNA double helix that permits the `encoding' of complex `instructions' for making organisms. The story can then continue with the computational abilities of DNA coding, onward and upward to goats, without getting enmeshed in the quantum wave functions of amino acids.

:What we tend to forget, when told a story with this structure, is that it could have had many different beginnings. Anything that lets us start from the molecular level would have done just as well. A totally different subatomic theory would be an equally valid starting-point for the story, provided it led to the same general feature of a replicable molecule. Subatomic particle theory is fungible when viewed from the level of goats. It has to be, or else we would never be able to keep a goat without first doing a Ph.D. in subatomic physics."