I started out very good at math. Mostly because my father made me memorize my multiplication tables up to 12 and then showed me how you could break larger problems down and use the facts you knew to solve them. But then I ran into algebra and trig and calculus and my brain looked at the numbers and symbols on the page and all I saw was static.
In the beginning it was all about apples and oranges. I could understand a problem of division because I could act it out in my mind and it made sense. If I had twelve apples and gave half away I would have six remaining. But if I had a quadratic equation and I used the FOIL method to solve it… well, how does this tell me how many apples I have left? But worse for me were the rules, like the aforementioned FOIL method. It just seemed arbitrary.
Then, just before I was heading overseas to begin my tour of suffering duty, a friend began raving about this very big book he was reading called Gödel, Escher, Bach. This book, which was even thicker than a Stephen King novel, was about how the concepts of math and music and art are all entwined. And if that didn’t make me want to read it, he informed me that the whole thing was about Gödel’s effort to prove the statement a = a and a <> a. Oh, and the whole thing was told as a series of parables.
I can’t remember if I bought the book later or if he gave me a copy of it but somehow I ended up with this doorstop in one hand and a lot of time on the other and so I just began reading.
There is a lot to take away from Gödel, Escher, Bach – you should probably read it every year – but the thing that I took from it, the concept that changed my life, was that calculus and algebra and such things were just systems made up of rules. These systems were like games. If you played by the rules you would win a predictable prize, the correct answer, but if you violated the rules you would get a big mess. It’s not how many apples you have left. The system itself defines what the right answer is.
This simple concept that I didn’t need to see the justification for a system’s rules in order to use the system itself allowed me to get back into math and is directly responsible for a long career as a programmer. I didn’t particularly enjoy reading it and after awhile it started to feel like a chore, especially as it got more and more into Theoretical Number Theory, but this may be the book that had biggest impact on my life.
Along with Treasure Island and Kidnapped.