If you’ve ever been fascinated by how people approach solving problems, these notes from a “Programming and Problem Solving Seminar” taught by Donald Knuth at Stanford are an extremely interesting read. Knuth selected five (unsolved) problems for the class to work on (with an eye for problems that would lead to interesting subproblems) over the course of the semester. The problems are extremely interesting in their own right, but reading the way in which people attacked the problems is actually much more interesting. One gets the impression, sometimes, that theory is about solved problems, but actually it’s more about a lot of failures. Well, maybe this is my own predjudice due to the number of times I’ve failed, but I suspect I’m not the only one.
O brave new quantum world!
Carl Caves is fond of quoting John Wheeler as saying “The job of a theoretical physicist is to make mistakes as fast as possible.” I whole-heartedly agree. If you get it right the first time, you didn’t learn anything. It’s only by making mistakes that we improve.
Of course, that said, if you can get it right the first time it’s quite possible you’ve mastered this skill already 🙂 Hey, I wouldn’t mind sitting down to work on a GUT or TOE and have the answer just pop out! But I do agree that mistake are a valuable learning tool. How does it go? “A wise man learns from his mistakes.” Of course, a wiser man learns from other people’s mistakes!