Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics
Ronan (Mark)
This Page provides (where held) the Abstract of the above Book and those of all the Papers contained in it.
Text Colour-ConventionsDisclaimerPapers in this BookNotes Citing this Book



Amazon Book Description


Negative Amazon Customer Review
  • This is a history book about the history of research into group theory and the discovery of the "Monster", not a book about that Monster. The math has been simplified beyond recognition, and even after reading up on the subject in the Wikipedia and with a PhD in computer science, I could not make head or tail of it.
  • The first problem is that the author does not make clear what he means by "a symmetry".
  • We learn that the "zillions of symmetries" of the Rubik cube6 are "generated by 90 degree turns", which in the lines above are compared to "symmetry operators". This suggests that the 24 turns (4 on each of the 6 sides) are the operators and that the positions that can be achieved are the symmetries. But operators in a (mathematical) group have the property that the combination of two operators is again an operator in that group, so any configuration can be achieved with a single (compound) operator. So are all these operators "symmetries"? I find it confusing.
  • Symmetries are also explained as permutations, but the relationship remains vague.
  • A second problem is that the level of explanation is very uneven: the root sign is explained, but the j-function is written out without any explanation.
  • We learn a lot about the people around the Monster but next to nothing about the Monster itself, except that it is 196,884-dimensional, but that's already on the cover of the book. Does it have a geometric representation, like a cube? Or is it just a network of symbols? (Does a network of symbols have symmetries?) If it can be geometric, it must have sides. Are all sides the same length like in a cube or a dodecahedron? How big is it if the length of the shortest side is 1 unit? Answers to such questions would have made the Monster much more accessible.
  • Perhaps the subject is too complicated to allow a popularized treatment, in which case sticking to just the history is OK. But it would have been nice to see an example or two of representatives of the simpler symmetry groups. Some examples are given, but they are not assigned to groups. And it would have been nice to be told to what position in the periodic table of symmetries Rubik's cube occupies, probably the most complicated symmetric object any of us can relate to.

Positive Amazon Customer Review
  • Popularisations of mathematics are difficult to do well because you need to have a fair amount of the language of maths under your belt before you can follow the arguments. To that end, putting across the ideas in a non-technical manner needs a skill that few possess.
  • Ronan does a sparkling job here. The basic concepts of group theory7 are glossed over without going into tedious detail (and despite my affection for this particular branch of maths, I consider a lot of the detail *extremely* tedious), and once the story gets under way, the ideas are brought forward in a flowing, almost breathlessly excited, style which is infectious.
  • The author himself was involved in this stupendous quest of classification, so he knows what he's talking about.
  • One of the aspects of such a popular account is the bringing to life of the people behind the name, many of whom I'd never heard, quite a few of whom I'd already encountered in my travels through an undergrad degree in mathematics. Neither does the author shrink from confronting the political circumstances in which certain of the mathematicians were working, which adds a further dimension of interest to the tale.
  • The first thing one wants to do having read this book is to go and find out the mathematics behind it all. Be warned: it is difficult area to get to grips with. The basics are simple but the detail is diabolical.



In-Page Footnotes ("Ronan (Mark) - Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics")

Footnote 1: Footnote 2: Footnote 3: Footnote 4: Footnote 5: Footnote 6: Footnote 7:
Book Comment



Text Colour Conventions (see disclaimer)
  1. Blue: Text by me; © Theo Todman, 2024
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)



© Theo Todman, June 2007 - July 2024. Please address any comments on this page to theo@theotodman.com. File output:
Website Maintenance Dashboard
Return to Top of this Page Return to Theo Todman's Philosophy Page Return to Theo Todman's Home Page