“Symmetry and the Monster:

One of the Greatest Quests of Mathematics”

by Mark Ronan

Book Review

One would think that a prestigious press

such as Oxford’s, which published “Symmetry

and the Monster,” would give a manuscript at

least a cursory reading – or at least hand it over to a

fact-checker for a couple of days. But no.

The misstatements of fact herein are appalling,

but that’s only the beginning.

For example, can it be that Newton and Leibniz

invented the calculus in the 16th Century? (p.87)

No, they were both born in the 17th.

How about this: “On most maps of the world Greenland

looks much larger than any country in Africa, whereas in

reality, Algeria, Congo, and Sudan are all larger

than Greenland”? (p.196) Not one is, in reality.

Even more insulting to anyone who has been to

elementary school is the arrival, three paragraphs

from the end, on page 227 of 229, that “[pi] is the

famous ratio of the circumference of a circle to its

diameter…” Who does this guy think would have

gotten this far in a book supposedly about advanced

group theory but who doesn’t know what pi is?

This is called tone-deafness to the reader.

But those are trifles, mere faux pas. Far more

serious and devastating is an early mathematical

error that poisons the entire work. On page 8, author

Mark Ronan makes the following murderous remark:

“A cube has a great many different symmetries – how

many? The total is 48, and they form what we call the

symmetry group of the cube.”

The problem is that any plane that intersects a cube’s

center point creates an axis of rotational symmetry.

If this is too difficult, think of a square with a line passing

through its center; if the square is rotated 180 degrees

around the line, clockwise or anti, it looks exactly as it

did originally. That’s called a symmetry. The same thing

happens to a cube when it is rotated about the plane

that passes through its center point. And these are of

boundless abundance.

That difficulty haunts us throughout the work. As a whole,

moreover, the book is a mishmash, a social history of everyone

who ever did serious work in group theory, which tries to appeal to

general readers while still making mathematical sense. What

good is it, one might ask, to know what Sophus Lie looked like

or whose sister perished at the hands of Nazis – when all one

is trying to do is understand how a finite group, albeit an

immensely large one, is the largest one?

A reader will not have such a quest satisfied here. And

many important subjects (Leibniz, Greenland, e.g.)mentioned

in the text are not in the index.

Not only is “Monster” unrecommendable; it does a painful disservice

in wasting an opportunity, a squandered chance to communicate

beauty and symmetry and one of the great wonders of math. Not

worth the trip to the recycling bin.