Professor Q was teaching group theory to undergrads. One day, while handing back homework, as he was about to hand me mine, Professor Q excitedly announced to the class that Alice's homework contained "the most ingenious incorrect double induction proof I've ever seen."
I froze in my seat, and stopped listening. All I could hear was the word "incorrect", reverberating in my head. I might not be as inventive or creative as the next mathematician, but I prided myself on getting it right. For me, submitting an incorrect proof was one of the worst sins a mathematician could commit.
Professor Q briefly explained the proof to the class, but I was so stunned by the public humiliation that I could only half listen. I turned to a fellow student and asked if he understood what was wrong with my proof, but he hadn't followed the explanation.
I spent the rest of the class looking at my homework, attempting to understand where I'd gone wrong, while trying not to show how upset I was.
I looked at my solution again that night in my dorm room.
Still no success.
Every few years, I would take out that problem set, and try to find the flaw in my proof. I knew that to figure it out would mean that I had reached a higher level of mathematicial maturity. It was important to do that on my own. Each time, I eventually put away the page, disappointed in myself for not finding the mistake.
Grad school was a particularly depressing time. Grad students (especially female ones) were at the lowest rung of the hierarchy at Princeton, even below undergraduates and postdocs, and the early 1980s might have been a particular low point in morale for math grad students.
One night I was working very late on my PhD thesis. It was perhaps two in the morning, and I was getting more and more depressed. I didn't feel I was making fast enough progress on my thesis, I was unhappy with the way I was treated at Princeton, and I felt terribly sorry for myself.
Always the problem solver, I decided to cheer myself up by looking at the incorrect proof, and finding the mistake. I knew I had made a lot of progress and learned a lot since my sophomore year of college. I was sure this was the right time to revisit that problem set. I would feel better, and perhaps finally appreciate how ingenious my incorrect proof had been.
I dug up the dreaded problem set, and read the proof. It wasn't very well written. But putting that aside, I could still figure out the logic of the argument. And I still couldn't figure out what was wrong with it. My depression hit a new low.
There was nothing I could do in the middle of the night, so I went to bed and slept fitfully. The next day I mustered up the courage to show the proof to a quite brilliant postdoc. I told him that it was an incorrect double induction proof, and I asked him to find the mistake. He read through the proof, handed it back to me, and said, "It's not very well written, but the proof is correct."
I handed the proof back to him, and said, "There's a particularly ingenious and subtle mistake. Please read it again."
He read it again. "There's nothing wrong with this proof," he said.
I insisted. "Professor Q said it's wrong, so it's definitely wrong! Please read it again," I pleaded as I thrust the homework back at him.
He refused to look at it and handed it back. "I don't care who says it's wrong. It's a correct proof."
I was taken aback. Whom should I believe, Professor Q or a young postdoc? Q was a Harvard professor! It hadn't occurred to me that he could be wrong about something he had stated so remarkably confidently.
I confess that I'm still afraid to show that proof to anyone, lest they find the truly ingenious, embarrassing, humiliating mistake.