Book Reviews Symmetry and the Monster one of Greatest Quests Mathematics Mark

“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.