Sphere packing has been a hobby of mine for less than a year now, and I was drew to the subject via my interest in coding theory (error correction coding). At first glance, as I skimmed
the book at the bookstore, it seemed deceptively simple. It didn't seem to have much technical substance. I bought the book anyway, as it's really one of the only books on the subject. Thankfully, my initial reaction was wrong. The book contains alot more detail than appears. The book doesn't contain alot of math equations, in fact, it tends to gloss over even the simple theory a little too much. I found this a tad dissapointing. However, the author throws enough scraps of information to you, that if your really interested, you can pursue the matter in further detail.

The authors writing style is friendly; written definately for the laymen. Unfortunately, the author is also very sloppy in his writing style. He constantly throws out names, dates, and shifts back in forth in time spans over decades and even centuries. Sometimes you think to yourself "what century is he talking about now." Sometimes he'll throw out the name of a mathemtician, but won't even tell you when he did his research or won't give you a good frame of reference. This can be confusing if you are trying to build a mental timeline of the history of sphere packing research. If you read the book 20 times, you might be able to extrapolate through this bad writing style... but some questions are still left unaswered.

The majority of the discussion focuses on packing spheres in 1, 2 and 3 dimensions. He explains the history of this quite well over the course of several hundred pages. Occasionally, he'll
talk about higher dimensions and explain in laymens terms what you can do in higher dimensions that you can do in lower dimensions,.. and he tries to give you the gist of the idea of why mathemeticians even care about higher dimensions. I found this understandable, but dissapointing in that he didn't at least dedicate 1 chapter specifically to this topic. However, in fairness, the book is about Keplers conjecture, focusing on 3 dimensions. It's not really supposed to be about sphere packing in D > 3. As an a laymen enthusiast, I was dissapointed because I was hoping to learn more about higher dimensionality, as I really don't understand how that works.
But I think the excellent way in which the authorpresented the history has really motivated me to study this subject in more detail, so I'll seek alternative means to find out about higher dimensions.

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