Symmetry, Algebra and the Monster | Hacker News Reader

Symmetry, Algebra and the Monster

quantamagazine.org

66 pointsnature2411 comments

Since I first heard of the monster group I have found the idea very Lovecraftian: a higher dimensional object that is so incredibly symmetric as to be incomprehensible.

Is there a sequel to TFA? It has nothing about the promised "Monster".

It feels like the preamble to a longer article that never materialises.

He also gets the terminology wrong. "Pre-image" and "image" refer to sets, not individual objects.

There was more info on the monster group and monstrous moonshine in this linked article: https://www.quantamagazine.org/mathematicians-chase-moonshin...

I've come to expect better than clickbait from Quanta. The article's not interesting at all, just a very basic exposé about groups of symmetries.

That's a pretty great explanation and I would read a book from him on symmetries if he wanted to keep going.

I started reading a book with an eerily similar title to this article[1] and it's quite a good read so far, similarly discussing symmetry, as well as the history behind the development of this theory.

[1] https://www.amazon.com/Symmetry-Monster-Greatest-Quests-Math...

"Fearless symmetry" by Ash and Gross is one of the most readable books on symmetry and group theory I've come across. They break with the pop science tradition of not using equations, and actually get into the nitty-gritty of the maths, while managing not to read like a maths textbook.

I've got that and read it (well tried to read it) multiple times. The first few chapters I agree are readable and a nice introduction but it rapidly descends into very technical and IMO quite opaque writing. I would've preferred a book twice the length that had aspects of a maths textbook. As it stands I think the authors of that work assume far too much for the latter half of the book.

It's also terribly typeset on Kindle. I only mention because I also recommended this book a month or so ago on the post about the quintic [1]. I gave this a 3/5 on Amazon UK. Here's my review [2]:

> This review relates to the (shockingly expensive) kindle edition. At almost £20 you would expect the publishers to have proofed this a lot more. There are references throughout to pages and theorems that have no link (and are therefore difficult to follow on an e-reader), some footnotes are instead displayed inline which is confusing, in other places there are errors in the rendered formulas that force you to stop and re-read it to work out what bit was printed wrong.

> The material itself is certainly interesting but the authors are I think deluding themselves if they believe this a book accessible to someone with just a knowledge of calculus. I've studied group theory formally and this book is heavy going. Part 1 is reasonable but beyond that, it quickly becomes dense and terse and far too short. I had high hopes for this book but it, unfortunately, falls short of the mark. I wish it was twice the length and with more care to the proofing during the ebook creation.

On the topic of the Monster group, there was a very much pop-math book about it that I read called "Symmetry and the Monster". It's at the total opposite end of the spectrum compared to Fearless Symmetry (which deals with Galois theory). It's a good casual read [3] but don't expect deep insight. I would really love if there was an author like Paul Nahin [4] writing books on abstract mathematics in a similar style. If you are into just generally "advanced" books that are very readable he is an absolute joy.

[1] https://news.ycombinator.com/item?id=14687242

[2] https://www.amazon.co.uk/review/R187P6WQO86SRB/ref=cm_cr_rdp...

[3] https://www.amazon.co.uk/Symmetry-Monster-Greatest-Quests-Ma...

[4] https://www.amazon.com/Paul-J.-Nahin/e/B001HCS1XI

> They break with the pop science tradition of not using equations, and actually get into the nitty-gritty of the maths, while managing not to read like a maths textbook

I've come to love math books like this in recent years. Far too few of them in my opinion, or at least they got lost in the endless barrage of bad math books that come out constantly.

Thanks for the recommendation.

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