This is one magnificient book. If you have the knowledge of a, say, third year undergrade student in mathematics or physics (you know what a manifold or a Lie algebra is, you had some group theory and complex analysis, some Lagrangian mechanics and quantum physics), then you should be comfortable following 90 percent of the book. Sometimes, slowing down reading is required and maybe not every equation will make sense, but you will get through and always drive home the main points. Amazingly, the author nevertheless manages to guide you through a vast amount of mathematical physics where you will learn serious graduate level (and above) stuff. It is really a big whirlwind tour of the whole mathematical physics, with Monstrous Moonshine explained on the top (alone the chapters on Lie theory, modular forms and quantum field theoy are pure gold, every page packed with insight). He does all that, by emphasizing the ideas over the rigour, by being a bit more informal in his arguments than usually allowed.

Maybe some mathematicans are put off by this approach, finding it too hand-waving. But as the author states in the introduction: this is not a textbook! He goes on : "I'm trying to share with the reader my understanding (such as it is) of serval remarkable topics that fit loosely together under the motley banner of Moonshine. I hope it fills a gap in the literature, by focusing more on the ideas and less on the technical minutiae, important though they are."

And yes he fills a gap, a big gap. And I hope so much other scholars will follow his lead and will try harder translating higher level math into a less technical, more accessible form. Of course, most notably, that is what John Baez has done with his blog for over ten years now and why it is so popular. Or what in general goes on now on many blogs and internet forums. In book form, I think 'The Princeton Companion to Mathematics' is a very fine example of how far you can go in communicating advanced math to a broader educated audience.

I'm so glad Terry Gannon has now written also a book in that style. More please!

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