This post is advice for problem-solving beginners in math. It’s halfway between Getting to know problems and Imperative statements in geometry don’t matter, but now I got it down to three words that are easy to remember: don’t be GPT-3.

What does that mean?

Basically, I see a failure case in a lot of beginners who get fixated on some (often superficial) detail or wording in the problem statement, and then try to pattern-match it to something they read somewhere before. In doing so, they stop actually thinking, and that’s a disaster recipe.

The reason I call this “don’t be GPT-3” is in reference to this toy problem:

Prove that if $\theta$ is a real number for which $\cos \theta$ is an integer, then $\sin \theta$ is an integer.

For a good high school math …