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Reaching for the Extreme: How the Quest for the Biggest, Fewest and Weirdest Makes Maths
FROM THE BESTSELLING AUTHOR OF PROFESSOR STEWART'S CABINET OF MATHEMATICAL CURIOSITIES
'Britain's most brilliant and prolific populariser of maths' ALEX BELLOS
What is the maximum land you can enclose inside a given border?
What is the minimum number of colours you can use to colour in a map so that no region shares a shade?
And how do you calculate the shortest route between two cities?
These questions may not sound related, but they have this in they all explore extremes: shortest lines, greatest areas, fewest colours. They have also given rise to some of the most important areas of mathematical study and have resulted in a myriad of applications - from the legend of Dido's founding of the city of Carthage to contemporary satellite navigation systems.
From soap bubbles to the cosmos, Britain's most beloved mathematician tells the fascinating stories of the people and ideas pushing the very bounds of mathematics - and the discoveries that have changed our lives.
'Britain's most brilliant and prolific populariser of maths' ALEX BELLOS
What is the maximum land you can enclose inside a given border?
What is the minimum number of colours you can use to colour in a map so that no region shares a shade?
And how do you calculate the shortest route between two cities?
These questions may not sound related, but they have this in they all explore extremes: shortest lines, greatest areas, fewest colours. They have also given rise to some of the most important areas of mathematical study and have resulted in a myriad of applications - from the legend of Dido's founding of the city of Carthage to contemporary satellite navigation systems.
From soap bubbles to the cosmos, Britain's most beloved mathematician tells the fascinating stories of the people and ideas pushing the very bounds of mathematics - and the discoveries that have changed our lives.
- GenresMathematics
352 pages, Kindle Edition
First published February 12, 2026
15 people are currently reading
92 people want to read
About the author
Ian Stewart
274 books762 followersIan Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
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Displaying 1 of 1 review
February 12, 2026
Ian Stewart is arguably the UK's best raconteur of mathematics - here he takes on some of the extremes of the mathematical world, and in doing so gives us some real insights into what makes mathematicians tick.
There's a good mix here of the flashy fun aspects of maths - think, for instance of the wonders of infinity or the monster group - and the solid everyday that nonetheless can turn up surprises. The book is littered with little insights. For example, if we think it's easy to work out the area of a rectangle by dividing it up into unit squares, what do you do with one that measures square root of two by pi?
You'll find yourself jumping around from what lies beneath calculus to game theory (rock, paper, scissors anyone? - I hadn't realised a version of this game dates back around 2,000 years). One minute you'll be considering colouring maps and the next finding the shortest distance between two points on a curved surface.
Some of the mathematics here has everyday applications, some can be used in fairly abstruse corners of science and some is pure mathematical puzzle solving with no obvious application ever. You pays your money and you takes your choice.
There were a few points where Stewart lost me. Some of these were simply due to going on too far. I enjoyed the tiling chapter to begin with, but as we got onto more and more obscure aperiodic tiles there was a bit of a feeling of 'we get the point, move on'. In other cases, Stewart had the problem of dealing with mathematics that is well beyond the grasp of a general reader like me. He is clearly aware of this, but rather than avoid it, makes the discussion so vague that it's difficult to feel you are getting anywhere.
This was particularly the case in the 'weirdest symmetry' chapter, which brings in the aforementioned monster group. There's some nice material on what groups are, but when we get onto that monster, the 'largest sporadic simple group', it's way beyond comprehension, when we're dealing with something it's was difficult even to prove whether or not it existed. It doesn't really help that Stewart then ties this into string theory, an aspect of physics that many believe is more mathematical play than anything connected to physical reality, which has been notably described as 'not even wrong'.
There's a lot to like, though, in this generous meander through eighteen chapters of different mathematical pondering. It'll certainly stretch your mind - and if occasional it leaves us mere mortals behind, that's not always a bad thing.
There's a good mix here of the flashy fun aspects of maths - think, for instance of the wonders of infinity or the monster group - and the solid everyday that nonetheless can turn up surprises. The book is littered with little insights. For example, if we think it's easy to work out the area of a rectangle by dividing it up into unit squares, what do you do with one that measures square root of two by pi?
You'll find yourself jumping around from what lies beneath calculus to game theory (rock, paper, scissors anyone? - I hadn't realised a version of this game dates back around 2,000 years). One minute you'll be considering colouring maps and the next finding the shortest distance between two points on a curved surface.
Some of the mathematics here has everyday applications, some can be used in fairly abstruse corners of science and some is pure mathematical puzzle solving with no obvious application ever. You pays your money and you takes your choice.
There were a few points where Stewart lost me. Some of these were simply due to going on too far. I enjoyed the tiling chapter to begin with, but as we got onto more and more obscure aperiodic tiles there was a bit of a feeling of 'we get the point, move on'. In other cases, Stewart had the problem of dealing with mathematics that is well beyond the grasp of a general reader like me. He is clearly aware of this, but rather than avoid it, makes the discussion so vague that it's difficult to feel you are getting anywhere.
This was particularly the case in the 'weirdest symmetry' chapter, which brings in the aforementioned monster group. There's some nice material on what groups are, but when we get onto that monster, the 'largest sporadic simple group', it's way beyond comprehension, when we're dealing with something it's was difficult even to prove whether or not it existed. It doesn't really help that Stewart then ties this into string theory, an aspect of physics that many believe is more mathematical play than anything connected to physical reality, which has been notably described as 'not even wrong'.
There's a lot to like, though, in this generous meander through eighteen chapters of different mathematical pondering. It'll certainly stretch your mind - and if occasional it leaves us mere mortals behind, that's not always a bad thing.
Displaying 1 of 1 review