Further reminiscences of topologist Frank Adams

As the know-it-all American, I came up with a list of ways to make life better for the students doing Part III of the Mathematical Tripos (a year of mathematics at the University of Cambridge between undergrad and graduate studies). I decided to present my ideas to Professor Frank Adams, who was in charge of the Part III students. 

As I wrote my friend (two days after Adams' deck transformations joke), "At morning coffee today I finally got up the nerve to talk to Adams (well, I didn't really get up the nerve, but I had decided to talk to him today whether or not I did). He was pretty nice. He didn't automatically agree with all my suggestions, but said he'd think about them. He asked what courses I'm taking, and what I plan to take next term, and when I answered, he pointed out that I'm not concentrating in one area. I explained why, and also said I'm most interested in number theory. He thought it would be good for all the number theorists to know each other, and thought that they should have a party. He said that if [Alan] Baker organized it, it wouldn't turn out to be a party, so maybe some grad students should do it, or possibly [Hugh] Montgomery. I thought it was a good idea. He asked me my name, and wrote it in his little book. He was very nice."

A couple of weeks later I asked Adams at tea what he decided about my suggestions for improving the room for Part III students (a nearly-unused dismal room in the basement with a narrow window near the ceiling through which car exhaust from the car park poured in). He said he had discussed it with Cassels and they decided my ideas weren't feasible. 

He asked if I got the note that was left for me in the graduate students' pigeonholes. I had looked in the pigeonholes in the past, but had felt silly doing so because I thought that Part III students were not considered to be grad students. 

I retrieved the note from the pigeonhole labeled "Visitors M-S". It was a photocopy of a handwritten list of Part IIIers who had either expressed an interest in number theory or were taking Baker's course, giving first initial, last name, and College. Adams wrote at the bottom in red ink the suggestion that I contact the one other student in Baker's course who had expressed an interest in number theory (to form a study group? to throw a party? that wasn't clear) and pointed out it might help me "get in with the Trinity mathematical mafia."

My intention was to improve the quality of Part III for everyone, not to form a study group with one other student (whom I didn't know how to contact when neither of us had phones). But Adams meant well, and I appreciated that he was trying to be helpful.

A few years later I was invited to a party at someone's home after Adams gave a talk at Rutgers University. It turned out that Adams was brilliant at party games. One game he taught us had us starting on a table top, and then going under and around the table, arriving back on top without ever touching the floor or anything other than the table. The partygoers were mesmerized by Adams' ability to contort himself. I was so delighted that I forgot to be scared of him. I wasn't surprised that Frank Adams was sorely missed after his tragic death.

Conway Kibitzing in the Cambridge Common Room

At "morning coffee" one day in November of 1979, I taught a shy PhD student how to play backgammon. That was a daring thing to do in the University of Cambridge maths department, due to the notorious kibitzers. The PhD student was glad that I asked him to play, since no one else even had the patience to explain the rules to him. Topologist Frank Adams came over to chat with us while we played, which was a friendly thing to do. Adams was in a good mood because he was pleased with the deck transformations story he had told in class that morning, which he seemed to be especially fond of because it was an anti-American joke. We got off easy on the kibitzing that day.

A few days later, we experienced the Attack of the Kibitzers. There weren't too many people at afternoon tea (at first), so the backgammon set wasn't in use, which was a rare occurrence. To avoid one of the grad students who was hitting on me, I asked the shy PhD student if he wanted to try backgammon again. 

It started peacefully enough, until John Conway sat down and told us what moves to make, using specialized language we didn't know. He spoke much too fast for us to think it through, and he moved the pieces himself if we didn't react quickly enough.

When I pulled myself together after the initial shock, I started questioning his moves, or making different ones just for fun and to slow him down. Soon a large crowd gathered around, everyone shouting out their opinions. 

When it was all over, Conway turned to me and asked, "Now wasn't that fun?" 

Everyone laughed (including, and especially, me), because all I had done was roll the dice. I felt sorry for the PhD student since it was only the second time he'd played, but he took it well.

Next, two of the grad students played, and were met with the same treatment. But to thwart Conway, one of them decided to play a variant of the game in which he purposely went against Conway's advice, even if Conway told him the only good move, which he had already seen for himself.

After that, before I ventured to play backgammon I was careful to see who was around, and then decided whether I had the fortitude to stand up to their "suggestions".

Decked by Deck Transformations

When I spent a year as a student at the University of Cambridge, I took an Algebraic Topology course from Frank Adams.

During one class, Adams asked if any of us had learned topology from an American. I was the only student to raise a hand. 

Adams explained that the German word for "cover" is "deck", but some illiterate American topologists carried it over directly into English, talking about "deck transformations" instead of "covering transformations", without realizing their mistake. 

As I wrote to a friend back in the days of blue aerogrammes, Adams emphasized "illiterate" and "American", repeating each several times and implying that they're synonymous. He warned us severely not to perpetuate such nonsense. 

I thought it was funny, but as the only American in the room, I did slink down in my seat and tried to make myself invisible.

Roving Hands, Smoldering Cigarettes, and the White Slave Trade

On my way from Como to Rome in September of 1979, I had to change trains in Milan. From riding the New York City subway in the early 1970s, I believed I had developed radar that gave me excellent intuition about what felt safe. The Milan train station did not feel safe. I left the station, hoping that the streets outside it would be better, but turned on my heels and went back in when I saw the neighborhood outside the station. I walked around and around the station until my train arrived, since I didn't feel safe sitting in the waiting room.

The train broke down at a city somewhere between Milan and Rome. I got on line at the information booth to ask about the next train to Rome. But it wasn't really a line. It was more like a mass of aggressive Italian men who pushed ahead of me with sharp elbows. Any aggressive New York City tactics I had learned growing up were no match for this crowd. After half an hour I realized that rather than getting closer to the front of the line, I was getting farther and farther away.

A voice behind me said in a very proper English accent, "They don't know how to form a proper queue, do they?" It felt like a breath of fresh air in the cloud of Italian cigarette smoke. I started looking forward to my upcoming year in Cambridge. I turned and saw a gentleman standing behind me who looked like an officer right out of a film about the British Raj.

At a hostel I stayed at in Rome, some Italian girls told the rest of us that Italian girls and young women don't leave home without an older relative to protect them from being molested by men on the street. A young English woman claimed that, although she had once slept alone all night outside the Milan railway station, she would not be willing to walk down a street in Paris without a man by her side, because so many young women disappear in Paris's "white slave trade". I laughed to myself, and assumed she was a conspiracy theorist.

One of my more unpleasant experiences in Rome was when I walked down a sidewalk and a young man who was walking towards me reached out, grabbed my rear end, and squeezed hard, without breaking stride. In shock, I continued to walk on for a few seconds, before I stopped and turned. I was enraged, and was angry at myself for not immediately lashing out and hitting him. Then I realized that being frozen in shock was a defense mechanism that might have saved my life --- hitting him could have provoked him to attack me much more violently.

My overnight train ride from Cannes to Paris was the Train Trip from Hell. Those of us who didn't have reservations stood in the aisles packed like sardines, with many people smoking in the no-smoking cars. Fellow passengers walked over me, and piled-high luggage fell on my head. While I was sleeping propped up on someone else's luggage in a no-smoking car, someone's cigarette ashes fell on me and woke me up only after burning into the skin on the back of my hand.

To make matters worse, this was the night that France turned its clocks back an hour. To agree with the schedule, my train waited for an hour on the tracks in the middle of the night in the middle of nowhere, prolonging the torture. 

I wondered what they did in the spring when the clocks were set forward.

Needless to say, I didn't get much sleep.

I considered going straight on to London from Paris, but that would be another overnight train, and I wasn't ready for that. So I left my luggage at the station, took the Métro to the Arc de Triomphe, and walked down the Champs-Élysées to the Tuileries, a beautiful and peaceful walk in the early morning hours. 

While I waited outside the Jeu de Paumes for the museum to open, a student from Oregon who was spending the upcoming academic year in Paris on a junior year abroad program started chatting with me. She seemed quite sweet, just off the farm. She offered me an extra bed in the apartment of the wealthy woman who was giving her a room during her stay in Paris. Thinking back to the kind family in Cambridge, I accepted, and we spent the day together. 

At a lunch café, I realized that my new friend wasn't the innocent just-off-the-farm girl I had taken her for. She told me about her new shady boyfriend, who was 10 years older than us. She wanted to involve me in some questionable dealings of his. Perhaps my danger radar hadn't been as good as I thought.

Having had no sleep the night before, my thoughts ran wild. I remembered the English woman in Rome who warned me about Paris's "white slave trade". Perhaps it wasn't just a conspiracy theory after all.

If I disappeared in Paris, could my family and friends find me? After Heidelberg, the only communication I attempted to have with them was a postcard I wrote to my parents from Rome. Not knowing what Italian mailboxes looked like, I couldn't be sure that I had placed it in a mailbox rather than a trash can. (Indeed, the postcard never arrived.) They would have no idea I was in France.

Even thought I was about to go to England and didn't need any French money, I decided to cash a traveler's check, just so that my parents might have some hope of tracing me if I vanished. My new friend, who until then had acted sweet and kind, was suddenly annoyed with having to wait with me in line for currency exchange at the train station. Her unusual reaction got me even more worried.

Although I wondered if I should stay vigilant overnight at the apartment, I was so exhausted that I eventually fell fast asleep ... only to be woken up in the middle of the night by my Oregon friend's roommate, who came home unexpectedly and wasn't happy to find me in her bed.

Of course, I wasn't sold into the white slave trade. Looking back on it, it seems funny that I was worried.

I made it safely to England, where the Cambridge police confiscated my passport because when I left the UK for the Continent in early August the stamp I got at Dover said I could stay in the UK for 12 months, but didn't say when the 12 months began. The police sent my passport back to Dover to get it stamped correctly.

The Magic Word

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I had heard that Lake Como was beautiful. So after an unexpected three-week interregnum in Heidelberg so I could be the female counselor in the German incarnation of the Ross Summer Math Program, I used my Eurail Pass for an overnight train from Heidelberg to Lake Como, in September of 1979.

I arrived in Como so early that nothing would be open for several hours yet. I left my luggage in a locker at the train station and took a walk. 

It's when I'm sleep-deprived that I feel especially like Alice in Wonderland.

I came across a wrought-iron gate with hours posted. Possibly a museum? Certainly a public building. I peered in through the gate and saw a beautiful garden. I resolved to come back  when it opened in a couple of hours.

When I returned to the place with the beautiful garden, I opened the gate and went in. After I walked around the garden, I wondered what was in the unmarked building. I went up to a door and turned the doorknob. Since it was unlocked, I walked in.

As I walked down a long hallway, I heard someone shouting behind me. I turned to look, and saw an agitated man running towards me waving his arms and shouting in Italian. What made me stop in my tracks was his large gun.

Perhaps this wasn't a museum.

I guessed he was asking me why I was there. I opened my mouth to reply, but realized that, in addition to the small problem that I didn't know any Italian, there was the larger problem that I didn't have a good answer. Even if I could figure out how to say in Italian "I'm very sleep-deprived, and I think I'm Alice in Wonderland and can open doors, walk in, and have interesting and strange adventures," I didn't think that would be very convincing.

As in comic strips where a lightbulb goes on over someone's head, a word popped into my brain. I had no idea whether it was an actual Italian word, but it seemed worth a try. I smiled and exclaimed, in what I hoped was an Italian accent, "Toilette!"

The man's demeanor changed completely. He burst into a wide grin. The image in my head is of the two of us holding hands and dancing around merrily singing "Toilette! Toilette!" but perhaps my memory exaggerates.

He escorted me down the hallway to the women's room, and then escorted me out of the building with a smile. I felt as if we were friends.

I never did learn what was in that building, other than a toilet, but I suspect it was military-related.

I continued on to Rome, arriving in the evening. I phoned the number that an Italian friend of my brother had given me when I saw them four weeks earlier in Tübingen. I arrived in Rome three weeks later than she expected, due to my Heidelberg stay. The woman who answered the phone spoke only Italian, of which I understood not a word. My translation of our conversation is entirely a conjectured fabrication:

Me: "I'd like to speak to X."

Her: "Oh, she's my daughter. Alas, she left two weeks ago. Is there anything I can do to help?"

Me: An explanation of how I knew X, and how I'm sorry I missed her.

Her and me: More pleasantries, ending the call on good terms, feeling as if we completely understood each other, even though the only word we both understood was her daughter's name.

Perhaps I'm completely wrong about our conversation, and I just dialed a wrong number. But it seemed to me that I had understood everything my interlocutor wanted to convey, from her tone of voice, without even the benefit of gestures or visual cues.

After staying at hostels in Rome, I moved to a hostel in Foligno, from which I took a day trip to Assisi. 

My brother's battered copy of "Europe on $5 a day" from the early 1970s said that women in Italy were expected to dress modestly and not wear pants, so I spent most of my time in Italy in a light-weight full-length cotton skirt. 

In Assisi, as I approached the Basilica of Saint Francis, I felt a tickling on my upper thigh. I pressed my hand against the skirt, and was immediately stung by a wasp that had flown up my skirt.

Knowing that people can be allergic to such venom, I wandered into the basilica, looking for advice. I soon found a small group of female middle-aged American tourists. I explained about the wasp and asked whether they thought I should do something about it. 

They accosted a passing priest and asked if the church has a first aid kit. Each time they tried to explain, he answered in perfect, unaccented English, "Please ladies, just tell me what it is that you want." They asked for a first aid kit, they asked for a doctor, they asked for a hospital, but always the same reply. The priest didn't understand anything they said. Perhaps the one sentence he spoke was the only one he knew.

Exasperated, the women began to mime. They eventually mimed a buzzing bee landing on one's palm and stinging it, complete with sound effects. The priest's eyes lit up as if he understood. He shouted, "Stigmata! Stigmata!"

The priest bade us follow him. We arrived at a fresco depicting Saint Francis of Assisi receiving the stigmata. He thought that's what we wanted to see.

I remembered my magic word and asked, "Toilette?" The priest's eyes lit up again. At last, he actually understood something we said. "Well, why didn't you just say that in the first place?" he asked, sounding annoyed. He gestured that I would need to leave the basilica and then go downstairs.

Figuring that would both extricate myself from the situation and give me a chance to look at my leg, I left the women and priest in the basilica as they continued to argue about stigmata and wasp stings.

I found a women's room of dubious cleanliness, went to a stall, and saw that a large part of my thigh had swelled up considerably. It did look like something to worry about. 

As I left the restroom, a woman entered and then followed me out, yelling angrily at me. She ran after me, but I ran faster. My conjectural (and expurgated) translation is that she was the person who was supposed to clean the women's room, and I was supposed to have left her some coins.

She eventually gave up, and I wandered up the main street of the upper town, trying to put some distance between myself and the angry woman. Eventually I saw a sign with an "H", and I wondered if that was a symbol for hospital. (If I had known that the Italian word for hospital doesn't start with an H, I might have ignored the sign.) I continued up the block until I found a plausible building and went in.

The hospital was dark and dingy, and didn't inspire confidence. I walked up to a wall that had a small pane of glass separating me from the young men at the reception desk. 

"Do you speak English?", I asked.

No. They asked if I speak Italian.

"No. What about German?"

No. Spanish?

"No. French?"

Yes! We all spoke French!

I opened my mouth to tell them my problem, but closed it when I realized I didn't know how to say "stung", "wasp", or "bee" in French.

Taking a cue from the American women, I mimed being stung by a bee.

Luckily, the hospital had no frescos of stigmata. They understood. Then they asked where I was stung, and I pointed to my upper thigh. They looked at me, exchanged glances and whispers with each other, and giggled.

A young doctor came over. I asked why the young men were laughing at me. She talked to them, then explained that they didn't see how I could have been stung in my upper thigh while wearing a long skirt. They thought there must be a more interesting (i.e., smutty) explanation.

The nice Italian doctor had studied in Boston. I liked her, but the hospital didn't seem much cleaner than the basilica's restroom. They reluctantly acquiesced to my adamant refusal of a tetanus shot, after I agreed to sign a form releasing them from liability. The doctor put on ointment and a dressing, and gave me an illegible prescription that I never filled. My swollen leg eventually recovered. 

I learned that you should always know a few useful phrases in the language of the country you're visiting, and carry a pocket dictionary (or more modern translation apps). Failing that, equip yourself with a Magic Word.