Thursday, January 05, 2017

Elliptic Tales

You will probably not enjoy Elliptic Tales, by Avner Ash and Robert Gross. I enjoyed it a lot, but I suspect I’m in the minority on that. You see, Elliptic Tales is by far the most math-intense math book I’ve read. In my opinion, this is a good thing. However, the whole thing might be a bit… daunting to someone who is not actually into math.

Let me back up a bit. What is Elliptic Tales about? Well, Elliptic Tales is a book which will explain to you what exactly the Conjecture of Birch and Swinnerton-Dyer (or BSD Conjecture for short) is. This might be of interest because the BSD Conjecture is one of the six remaining unsolved Millennium Prize puzzles, meaning there is a reward of one million dollars for whoever proves it. To me it's of interest because I'm a nerd, and I want to know what kinda stuff is being worked on in math right now.

The thing is that the BSD Conjecture involves a lot of preparation, and although Ash and Gross do a wonderful job at explaining things, there are some patches in which everything is confusing for a bit. My advice for these parts is to just read on for a bit. Sometimes, Ash and Gross mention concepts that they don't actually introduce until the next paragraph, or even later than that. Trust me when I say that it mostly makes sense in the end. Also, use the glossary. It helps.

I think my favorite parts of Elliptic Tales are the ones in which they are teaching about something else. This is the first source I've found which explains projective geometry well, and some of the earlier stuff with generating series is cool enough to create a formula out of. They say you can skip Part 1, which deals with the degree of a polynomial, but I had a lot of fun reading it. Also, they reference that part later in the book, so if you haven't read it you feel a bit cheated and left out. How do I know how this feels, given that I did read Part 1? Because they also reference their previous book, Fearless Symmetry, and that's how it makes me feel.

So, I really enjoyed the book, because it taught me a lot. However, I realize that this isn't that big a selling point for most people. If you don't really like math, then stay away from Elliptic Tales, and instead read Things to Make and Do in the Fourth Dimension. If you do really like math, and are excited about learning math, then read Fearless Symmetry, so that you can later fully enjoy Elliptic Tales. And never, under any circumstances, read Bridges to Infinity. I think that about covers everything. Until next time!

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