This is the second installment describing my experiences teaching at a math camp for high-schoolers. More about the computers class later, right now I just wanted to mention an evening talk that I gave to the entire camp. It was on the Eternity Puzzle and its solution by a pair of mathematicians. Here is a link to a good article describing the weaknesses accidentally built into the puzzle by the designer (because he didn’t do the math!) and how two Cambridge mathematicians were able to successfully attack it (because they did do the math!).
Take home message is: Do the math!
I also have in mind a slightly more philosophical message. Though, we all know that math is fun and beautiful–We all know that, right?–it is also useful. For instance, given some problem in the real world, it is often productive to model it mathematically. The hope is that, even though the model is not perfect, working with it will give insight into the real problem. What may come as a surprise is that this also works for problems in the mathematical world. That is, given some mathematical problem, it may be productive to model it with a simpler mathematical problem. The simpler problem will not model the more complicated one perfectly. However, working with the simpler model may give useful insights to the original problem. This sort of paradigm plays out for the solution of the Eternity Puzzle. I will forbear giving further details and instead recommend that you read the article linked previously, as well as this more detailed article, and if those leave you wanting more a few additional details can be found at this third article.
One final thing: it turns out that I also gave this talk in Portuguese to some camp students from Mozambique. Do I speak Portuguese? Well, I did 13 years ago. This was my first attempt at giving a technical talk in Portuguese. It was exhausting, but an experience I’m glad I had. A reminder that I really should keep current with my Portuguese skills…