Back at math camp as a counselor, some of the other counselors were standing around our kitchen after dinner, trying to prove a certain result about finite groups. Buoyed by my success in the group theory course a few years earlier, I tried to join them. After they went down a dead end, I suggested that we try to prove or disprove it for some concrete examples. My fellow counselors disdained that approach, which would have gotten their hands dirty with computation. They preferred to go straight for the loftier goal of proving it in general.
I loved group theory, I enjoyed getting to know individual finite groups of small order, and I thought of them as my friends. Seeing where the difficulties were likely to be, I played around with groups of order 24 and 36.
Eventually I showed the other counselors a counterexample to what they were trying to prove. I was pleased that I had learned from Loomis how illuminating a counterexample can be. But for my friends, a counterexample made the problem uninteresting, and they turned up their noses and went on to something else. (Would they have been more grateful for my counterexample had I been someone they respected more? I don't know.)