by: Lance Fortnow
A math book! I read a math book!
While I’m a huge fan of science and can appreciate math as applied to the sciences, pure math is one of those things I find best appreciated from a distance. But I read about this book in an article or a blog post or something and I decided that it was sounded really interesting. The Golden Ticket looks at the P=NP problem, one of the big math problems (if you solve it, there’s a million dollars reward) of our age.
P=NP is basically asking if all problems whose solution can be verified by a computer can be solved by a computer. Or, basically, if all problems can be solved quickly within the realm of available computing power. (Wikipedia notes that the problems in consideration have answers that are easy to verify but not easy to find.) If so, our world will basically have no more problems. Or, at least, very different problems than what we currently have. If not, well, we’re stuck with the world we have now and some problems will have to be approximated instead of solved,
Fortnow goes into the history of P=NP (that’s read as “does P=NP?”, at least in my understanding), which was okay. It was engaging enough to keep me reading. He does a really great job of developing the kind of problems a solution to P=NP would answer and how they would change society and problem-solving as I know it. He delves much more on the theoretical side than the practical one, so even though I understood the implications and the importance of this problem, I didn’t really get a good idea of how we went from the primary problem, P=NP, to the secondary problems, like efficient travel planning or encryption codes on computers. I wish that he had spent a little more time developing the math behind everything.
This is a book best read in a shorter period of time, to keep everything together. I read it in three chunks, but they were pretty spaced apart and I had to flip back to remember what the book had explained earlier. It builds on itself, so if I forgot the first chapter, I had hard time understanding, say, the fifth one.
One thing that I really appreciated was that Fortnow used the same very simple example for as many problems as he could. It was kinda fun – an imaginary place named Friendville, where people knew upon meeting someone whether they were going to be friends or enemies. It definitely helped keep me on track, simplified the learning process, and made me chuckle a few times. Fortnow keeps things as simple and approachable as he can and while it’s not the most engaging STEM book I’ve ever read, it’s good and I certainly didn’t struggle to get through it. (In fact, thanks to my Nook and an impressively waterproof case, I read a good chunk of this while floating the river.)
If you’d like a math book heavy on the theoretical and examples and light on the mathematical explanations – a good way to get introduced to math problems without becoming overwhelmed! – or if you’re a math person interested in taking a new perspective on an old problem, I’d definitely take a look at this book. If you have trouble fully understanding things in only abstract ways – you need a solid grounding in how it works – then this book might be harder to fully comprehend and may not be the book for you.