Very early one Saturday morning in the fall of 1979 I woke to my alarm and looked out the window at the pouring rain. Should I cycle to Alan Baker's transcendental number theory course, which met on Tuesday, Thursday, and Saturday mornings?
I was enrolled in the cryptically-named one-year program "Part III of the Mathematical Tripos" at the University of Cambridge. I lived in Churchill College, which was far from the Pure and Applied Mathematics Departments; those departments hadn't yet moved out of the city centre to just across the street from Churchill College.
I had managed to buy an old rusty bicycle from some astronomer. I was urged to buy fenders for it, being in rainy England and all, but I hadn't gotten around to it. The thought of arriving in Baker's class soaking wet wasn't appealing. The first thing the British students did upon arriving in the classroom was open the windows, even on the coldest days.
I rolled over and went back to sleep, and decided not to bother with Baker's course any more.
The other students told me that many professors taught from the same notes every year. The British students generally didn't ask questions, so class time meant just writing down what the professor wrote on the blackboard. I figured I could just copy some other student's notes for Baker's course and learn the material on my own. (Perhaps I was taking a page from my Lolita story.)
I was surprised to find that it wasn't so easy to copy anyone's notes. One student explained that my classmates didn't want to lend out their notes since we're all competing with each other. (Not to mention that we didn't have ready access to a photocopy machine, so I would have ended up writing out the notes by hand.)
At some point, the Part III students had to state which exams we were going to take at the end of the academic year, where each exam was associated with a course.
The year before, when I was a senior in college, Harvard postdoc Andrew Wiles gave me advice about the University of Cambridge. He suggested that I not even bother to take the Part III exams. They were a pointless exercise in memorization and regurgitation. After that year in Cambridge I was going straight to Princeton's PhD program, where no one would care about the Cambridge exams. The exams are crucial for British students, but not for me.
Leaving my options open as to whether or not to sit the exams, I filled out the form. Hoping that I could change my list later, and having given up on Baker's course, I used John Thompson's course on finite simple groups as a placeholder, and promptly forgot all about it until near the end of the academic year.
When the exam schedule came out, I learned that I was scheduled to take an exam each day of a five-day exam week, with Thompson's exam on the second day. Should I take Wiles' advice and not bother to show up for the exams? If I took them, I'd throw away an opportunity to run off to Paris with my boyfriend that week.
I liked tests because I did well on them, and I was curious about the Cambridge exams. A week or so before exam week, I decided on a compromise---take the exams, but don't study for them.
Thompson's course was considered to be unexaminable. It was an advanced topics course, a large part of which consisted of Thompson carefully going through a small fraction of a long preprint by Aschbacher that Thompson was refereeing --- a very technical step in the classification of finite simple groups. Thompson would put a lemma on the board, start presenting its proof from Aschbacher's preprint, and occasionally decide there was an error. At the next class, he'd show us an idea he had for how to fix the problem, or how to improve Aschbacher's proof. Watching Thompson scratch his head and ponder was educational for the students --- we learned that even famous mathematicians struggled but persevered --- but it didn't leave Thompson with many options for exam problems.
I had dutifully taken notes at the introductory meeting for Part III students where we were told about the courses; about Thompson's course I wrote: "VERY hard --- don't use it for exam."
Barely a handful of people attended the course, and that included advanced graduate students who weren't doing Part III. I was undoubtedly the only student who had signed up for that exam.
It was too late for me to substitute Baker's exam for Thompson's, even if I could have coerced someone into giving me their notes. I was stuck with finite simple groups. It made sense to just skip that exam, and give myself an extra day to enjoy Cambridge and relax before my later exams.
I felt quite bad about making Thompson write an exam I might not take, just for me. For several days I went to morning coffee in hopes of finding Thompson to tell him I probably wouldn't take the exam. Perhaps he hadn't written it yet, and he wouldn't have to bother.
Eventually I heard that Thompson had returned to the U.S. and wouldn't be back until the fall. My sources didn't know whether the department would send him the exam or get someone else to grade it. In any case, Thompson must have already written it.
I also worried that if I skipped one exam, the other exams might not count. Would they throw away my scores because I hadn't sat the required number of exams? I wanted to at least get credit for taking the exams.
I decided to go to the exam room, and leave right away. I'd write my name on the exam along with a note to Thompson telling him why I'm not taking the exam, that he shouldn't worry about failing me, and that I enjoyed his course.
To my surprise, when I tried to leave the exam room, the proctor refused to let me go. I was required to stay for the first half of the three hour exam.
Annoyed, I went back to my seat. What was I going to do for all that time? I tried to think about my upcoming exams, but that was hard without my notes.
I thought to myself, "Is it ruder to hand in a blank exam or make someone spend time grading a poor one? I might as well at least have a look at the exam. It would be embarrassing to hand in a blank exam if Thompson knew I had sat there for an hour and a half."
It turned out that Thompson had managed to find some examinable questions from the beginning of term, before the refereeing began. I was able to solve some of the problems after all.
As soon as the hour and a half were up, I went to the front of the room and tried to turn in my exam. The proctor seemed upset, and called over a superior. The two of them anxiously tried to convince me to stay.
It finally dawned on me that they were worried that I was distraught about the exam and planned to kill myself.
I told them not to worry. "Oh, Andrew Wiles told me not to take the exams seriously. I've already been accepted to Princeton, which doesn't care whether I take these tests. The exams aren't at all important to me," I prattled merrily. But this was 1980 and they of course had never heard of Andrew Wiles. They got even more worried about my mental state.
They couldn't imagine a world in which these exams were unimportant.
I eventually promised not to kill myself, or at least not to hold them responsible if I did, and they reluctantly let me go. I suppose it's both funny and sad that anyone would take the exams so seriously.