"Women don't do math"

At Harvard in the 1970s, I was accustomed to seeing funding opportunities that were only open to men. It was unusual to see something open only to women. When I was a senior looking for funding for grad school, I noticed that I was eligible for the Alice Freeman Palmer Fellowship. I submitted an application to the Harvard committee responsible for sending a nomination to the national selection committee.

When I wasn't chosen as Harvard's nominee, I assumed that my file wasn't strong enough. 

Harvard encouraged students to find out why they were rejected for things, since the feedback might be helpful in the future. I was the good little girl who did what I was told, so I dutifully asked why I was rejected.

I was surprised to learn that it wasn't because my application wasn't strong enough. The reason I wasn't chosen as Harvard's nominee was that the Alice Freeman Palmer Fellowship is a scholarship for women. The committee reasoned that women don't normally do math, so the national committee would most likely choose among nominees in fields with many women, such as English or History. The Harvard committee thought there was no point in selecting me, since they assumed a mathematician wouldn't make the cut.

That afternoon, at tea in the math department common room, I ran into math grad student Lisa Mantini. I told her why I was rejected for the fellowship.

Lisa told me that an Alice Freeman Palmer Fellowship had funded her first year in grad school. The national committee had awarded her the fellowship, even though she was a mathematician.

I was used to being discriminated against for being a woman. As far as I knew, this was the first time I was discriminated against for being a mathematician. 

Postscript:
By reading background for this story, I learned that Wellesley College tried to hire Alice Freeman as a professor of mathematics in 1877 (she turned down the offer to help support her family and/or care for an ill sister). The following year, she turned down Wellesley's offer to teach Greek, but in 1879, the year her sister died, Freeman accepted their offer to head the History Department. Alice Freeman became President of Wellesley College in 1881, the youngest college president in the United States, at the age of 26.

The Quincy Adams Wigglesworth Smith Scholarship

My recollection is that when I got into Radcliffe, students who were admitted to Harvard and Radcliffe were sent a thick booklet that listed endowed scholarships for Harvard students to use during their undergraduate years. We were instructed to read the list carefully, to see which scholarships we were eligible for. The expectation seemed to be that each of us would be eligible for some of these funding possibilities.

Dutifully, I scoured the list, hoping for something lucrative. My family could scarcely afford the Harvard-Radcliffe tuition and fees, so any sort of scholarship would be very welcome. 

My parents hadn't let me apply for financial aid, because they thought that would hurt my chances of getting in. I later learned that Harvard supposedly had need-blind admissions. My parents didn't know that, but if they had, they might not have trusted that it was really the case.

My optimism that I would find a nice scholarship began to fade as I turned the pages. I haven't managed to dig up that list, so here's my best reconstruction, nearly fifty years later, of a typical entry:

The Quincy Adams Wigglesworth Smith Scholarship was founded in 1792. The recipient, who should be fluent in Greek and Latin, must have the last name Smith. He must be a Harvard man who has at least three ancestors who came to America on the Mayflower, and at least one ancestor who signed the Declaration of Independence.

I wondered if I should change my name to Smith. But there wasn't much I could do about some of the other requirements.

At first, I stopped reading an entry as soon as I realized I wasn't eligible. But eventually I read each listing in its entirety, for its comic value. The criteria seemed to get more specific and weirder as the booklet went on.

Surely there must be some scholarship for which I were eligible, however paltry? I got to the end of the list and realized there were none. 

I leafed through the booklet again, to make sure I hadn't missed something. I hadn't. It seemed a little cruel for Harvard to build up my hopes, only to dash them.

Before I arrived on campus, I wondered how many of my Harvard classmates qualified for a scholarship from the booklet. Happily, there were enough New York City public school students whose parents or grandparents were immigrants that I felt at home. (However, when I opted for the "literature" section of the obligatory Expository Writing freshman year course rather than vanilla "Expos", it was pointed out by the grad student who taught the class that he and I were the only people in the room who weren't preppies.)

"Just read the damn bio!" or: What NOT to say to someone before their presentation

"I'm so nervous! There are so many people in the audience! You must be really nervous!" said the Associate Dean who was about to introduce my Breakfast Lecture. The intended audience was donors and potential donors to the School of Physical Sciences. The Dean usually introduced the talks, but he was out of town.

I sympathized with the Associate Dean, but I wanted to spend the few remaining minutes before my talk mentally preparing myself. That usually meant clearing my mind, taking slow deep breaths, and focusing on the topic of my talk and the audience. I didn't want to be distracted.

But the flustered Associate Dean continued to tell me how nervous he was, and he seemed to want me to comfort him. 

"You'll do fine. Don't worry about it," I told him in as gentle a voice as I could muster.

"You must be even more anxious than I am. Aren't you nervous?" he asked. 

"No, not really. I've given many talks. Take deep breaths," I advised him. 

When he persisted, I pointed out that I needed to spend the remaining minutes focusing on my talk.

Surely he should have known that letting a speaker think about their talk is better than telling them how nervous both he and they were?

A few years later I traveled to give a named lecture intended for the general public. When I woke up in the hotel room on the morning of the talk, my stomach hurt. I soon realized I had food poisoning (or some other extreme gastrointestinal problem) from a restaurant meal the night before.

I wasn't sure I would be able to give my talk without running to the toilet every five minutes. This time, I really was anxious.

As we stood on the high stage in front of the large audience, the professor who was about to introduce my talk awkwardly asked me for my preferred pronouns. 

Surprised by the question, I was flustered and didn't know how to respond. I sputtered something about not being a fan of using gendered pronouns, and that I try to avoid them.

He replied that in that case, he'd just use "they" and "them" to refer to me.

Given how uncomfortable the conversation felt to me, I couldn't imagine that he'd do it in a way that would sound natural and not weird.

I hurriedly added, "My preferred pronouns are `Alice' and `Professor Silverberg'. If you need to use more than that, please say `she'." 

After I had a moment to think, I added, "Could you just read the bio I supplied?" (The bio had used "she", so if he had read it, he shouldn't have needed to ask me for my pronouns.)

No, he didn't want to just read the bio. He had gone on the Internet and was pleased that he had found some interesting tidbits that he wanted to add.

When people deviate from the bio (especially by finding random stuff on the Internet), they usually get things wrong. I then have to make the mental effort to decide what to let slide, and what I need to correct before I begin the intended talk. So much for my carefully-laid plans for how to start the talk.

The introduction to my talk took so long that toward the end of the allotted time for the talk I had to make a split-second decision on which slides to skip. I didn't get to any of the "life advice" that I had recently been including in my talks. (If I had a do-over I would include the advice and leave out some of the mathematical details. The "human interest" parts of a math talk are usually more memorable than the mathematics, and the life advice seems both more necessary and more appreciated in recent years.)

You'll be pleased to know that I managed to complete the talk without running to the restroom screaming. I did half-jokingly warn the audience that I might do so; I hope that they found my warning more amusing than disconcerting.

Suicide Watch

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.

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

Click the play button for the audio version:

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.

The Kindness of Strangers

The announcement came over the PA system at Logan Airport on the last day of July in 1979 as the planeload of people waited at the gate, where many of us sat on the floor because there weren't enough seats in the waiting area. Our departure would be many hours late; the flight eventually took off at 3 am.

This was back when people chatted with strangers on planes and waiting areas. The college students sitting on the floor started talking in small groups, and I ended up chatting with a Harvard astronomy grad student.

I would spend the next academic year at the University of Cambridge, but first I planned to travel through Europe for two months on a Eurail Pass. My luggage was a second-hand ill-fitting backpack, plus two large suitcases that I hoped to leave at my Cambridge College before I went to the Continent. The heavy suitcases didn't have wheels.

My brother-in-law was living in London and had agreed to let me stay at his flat my first night. When we landed, I tried to phone him but there was no answer. He must have given up waiting for me and left for the day.

Rather than waiting for him to return, I decided to take my chances and take a train to Cambridge. 

The astronomy grad student was on the same train, and we bonded over our love for the ice cream shop Steve's in Somerville, Massachusetts. I gave him an address to which his girlfriend could send my boyfriend the secret hot fudge recipe that some of the shop's angry employees gave out while they were on strike.

When I arrived in Cambridge, I started walking toward Churchill College, before I realized that the distance from the train station to the College was quite far.

Accosting a professionally-dressed gentleman who was walking down the street, I asked which direction was most likely to quickly lead to a phone booth. (This was of course well before cell phones.) When I accosted people on the streets of New York to ask for directions, they'd answer with neither of us breaking stride. I was surprised when the British gentleman stopped, pondered my question, then escorted me down the block until we found a phone booth. When he saw me struggling with the cumbersome suitcases, he picked them up and carried them himself. He waited outside the phone booth.

I rang up the College, and a bemused Porter said that yes, there was a closet where I could leave my suitcases if I arrived in the next few minutes; if I couldn't make it in time, I could do it tomorrow. Unfortunately, they didn't have a room for me to spend the night.

I explained the situation to the gentleman, thanked him, and bade him farewell, but he insisted on seeing it through until I was properly settled. 

That street was lined with B&Bs. The gentleman walked me from one B&B to the next, where I asked for a room and was turned down. Finally he had a chat with an owner who told him that this was the week of the Cambridge Festival, so there would be no available beds.

The gentleman decided that I should spend the night with his family. We found another phone booth, he talked to his wife, then he put me on the line so his wife could reassure me that he wasn't a Cambridge version of Jack the Ripper.

The man and I hopped on a bus and took it to their house, somewhere outside of Cambridge.

They had a lot of kids, ranging in age from early teens to late twenties. What I remember from the evening meal (in extreme jetlag that I was trying to conceal) is that someone passed me a plate heaped high with some sort of minced meat dish. It smelled wonderful, but there was much too much of it. I thought to myself, "I'll never finish this. But it would be rude to turn it down." So I ate and ate until the plate was clean. Years later, it dawned on me that perhaps the dish was intended for the entire table, and I was supposed to take a small amount and pass it on. If so, the family must have been horror-struck (not to mention hungry) by my voraciousness.

After the evening meal, we all sat in the living room and watched TV. The BBC was showing a dance performance in which the dancers were stark naked. This would have been impossible on network television in the US in 1979. I expected the children to titter the way American kids would, but everyone but me took it in their stride. Being a prudish American, my face flushed beet red in embarrassment, so I looked straight at the TV and hoped no one would notice.

It turned out that the kindly gentleman who had invited me home had recently moved his family to the Cambridge area to be near the hospital where he was undergoing transplants of multiple important organs. I felt awful for having allowed such a vulnerable patient to lug my heavy suitcases from B&B to B&B.

Since then, I've often thought of that family's generosity and kindness, and how trusting we were of each other.

Lacing up my shoe

When I was growing up, I learned on my mother's knee a song she had learned from her mother. It was sung to the same tune as Hatikvah, but with these words:

When I was single I had nothing to do.

I'd sit by the window, lacing up my shoe.

Now that I am married I have too much to do.

I can't sit by the window, lacing up my shoe.

One cries "Mama! Put me into bed!"

Another cries "Mama! Give me a piece of bread!"

I washed them, I fed them, I put them into bed.

Then I said to my husband, "I wish I were dead."

My mother's sister Mimi told me that her family learned the song in the late 1920s or early 1930s when it was played on WEVD, a Yiddish radio station in New York City that Grandma listened to every Saturday night.

My aunt, mother, and I thought the song was very funny. I'm always surprised that people are shocked and appalled when I tell them these lyrics. Perhaps one needs to have a New York sense of humor (from the last century). I give the lyrics here so they don't die when I do (though perhaps some would prefer that they did).

Does anyone else know these lyrics?

What's wrong with choosing a woman?

A small group of faculty, staff, and visiting faculty was having lunch in the dining hall of a Harvard dorm one day in 1990, while I was visiting Harvard. 

To convince us that Harvard treated its Afro-American Studies department very poorly, someone exclaimed "Harvard even chose a white woman as interim chair." She emphasized both "white" and "woman", with greater stress on "woman", to make the point that both were problematic.

Without thinking, I blurted out, "What's wrong with choosing a woman?" 

The senior staff person who had spoken was herself a white woman. She was surprised by the question, and she stumbled as she tried to explain how choosing a white woman undermined the department and showed Harvard's disdain for it, since clearly they should have chosen a black man. She seemed reluctant to back down, but I think she eventually wondered whether she was on shaky ground.

Whenever someone shows that they (subconsciously or otherwise) believe that putting a woman in a job devalues that job, I'm disappointed. (I'll leave to those who've thought more deeply about it than I have the question of whether choosing someone white to head Harvard's Afro-Am department undermined that department.)

More than a decade later I was asked if I'd be interested in a professorship at a place I'll call Cheshire Cat University. During my interview, female CCU grad students told me about a history of problems with the treatment of women, and how the math department had tried to address it.

At my interview with the Dean I mentioned this, and asked about the situation for women. He had heard nothing about the problems in the math department. But he told me he had set up a committee to deal with women, and made Professor Lion the committee's chair. The Dean said he thought it was smart to appoint many men to the committee and a distinguished man as committee chair, since that gave the committee more credibility.

I knew that Lion knew much less than I did about gender discrimination in academia and what to do about it. The Dean gave me the impression that I wouldn't be chosen to lead such committees, and would be passed over in favor of less knowledgeable men, whose maleness would give a "committee about women" more credibility. When the Dean spoke about Lion as if he were higher than me in the academic hierarchy, I realized that the Dean didn't have a clue that I was being hired as senior faculty and Lion's rank was no higher than mine.

The Dean wasn't the only one at Cheshire Cat who seemed clueless. A bulletin board in a hallway had names and photos of all the mathematics graduate students. I counted that more than 3/4 of the grad students were male. But when I met with the department head, he very confidently told me that the grad student gender ratio was 50-50.

The grad students took me on a lovely hike, where I heard more stories from the unhappy female students. 

When I returned to the bulletin board to confirm my computation of the gender ratio, I overheard Professor Lion in his office telling someone what a great time I had on the hike, and how impressed I was with how happy the female students were. I don't know where he got that from. Certainly not me.

Staff without Passwords

(This story hearkens back to Staff with Forks.)

D was a nice, highly competent member of the Math Department staff. She was so conscientious and kind that before she left for a job in a different department, she spent her last two weeks making the computer files and emails easy for her successor to use. D told me that the staff should just call her if they had any trouble finding anything after she left.

Soon after D's last day, I stopped by to welcome her successor E to the department. 

It transpired that E was struggling because she didn't have the computer password that would allow her to access the old files.

I told E that D had gone to great trouble to get the files ready for her successor, and that D had said she was willing and eager to help out after she left. Let's just phone D, who still worked on campus, and ask her how to access the files.

Both E and her boss, the department manager, were horrified that I would consider contacting D after she left the department. One simply doesn't do that at UCI.

No wonder it seems as if the university has no institutional memory.

"Your daughter will burn in Hell"

At a parent-teacher conference when I was in first grade, my teacher told my mother that I would burn in Hell since I didn't believe in Jesus Christ. 

At least, that's what my mother told me years later, when I was in high school or junior high.

That explained a lot. Such as why it had seemed as if my first grade teacher hated most of the class.

When I was in first grade, I hadn't even heard of Jesus Christ. I'm sure I never discussed him with the teacher. She must have been making assumptions about me based on my last name.

What did my mother do about it at the time? 

Nothing. She felt powerless. She was afraid I'd be retaliated against if she complained. She didn't see any path that would make things better.

My mother waited to tell me so as not to traumatize me. I was already traumatized enough by that teacher. When I complained to my mother back then, my mother told me that the teacher was mean because she was a frustrated spinster. I thought that was an odd and uncharacteristically bitter comment, but it makes more sense now in light of what the teacher said at the parent-teacher conference.

By the time I was in high school, my mother began to push back when she saw injustices against me. It's possible she felt more comfortable with the high school's powers-that-be than with my grade school's principal, whom she didn't trust.

After I graduated from Ivy League schools and became a professor, I noticed that my colleagues refused to put up with bad behavior from their kids' teachers. They raised a fuss and got things changed. My parents' striving for upward mobility paid off, moving me into a socioeconomic class with higher expectations. 

Nowadays, anyone can complain about anything on social media and get teachers in trouble, whether or not they deserve it.

To this day, thinking of my first grade teacher still conjures up visions of Satan and me amidst crackling flames.

The Statue of Jakob Herz

It looked a bit like a large tombstone. Each time I passed it as I biked down a side street during my stay in Erlangen, Germany, I wondered why it was there. One day, I stopped to find out.

I propped my bike against a nearby fence and walked around the obelisk, looking for clues. One side had German text that translates to "We remember Jakob Herz, to whom citizens of this city erected and destroyed a monument." Another side seemed undecided as to whether it was the curriculum vitae of a person or of a monument.

According to German Wikipedia, the stele was erected in 1983 "to represent `a monument to a monument' and to commemorate the original statue."

The original statue of Jakob Herz (1816-1871) was erected in his honor in Erlangen's main town square on May 5, 1875, and was a larger-than-life statue depicting the man himself. It was torn down on September 15, 1933, the day after a decision to do so was unanimously passed by the Erlangen city council.

Herz was a much-loved surgeon and teacher who was named an Ehrenbürger of the city of Erlangen in 1867 and became the first Jewish professor in Bavaria in 1869, two years before he died of sequela from health problems incurred from his service as a physician in the Franco-Prussian War. The 1875 statue was funded by public subscription, and seems to have been the first monument in Germany to honor someone Jewish.

The 1875 statue of course had a face and a body (presumably an accurate depiction of Herz). The much smaller 1983 obelisk contained no images.

From what I saw during my stays in Erlangen between 1988 and 2000, I thought that Germany generally did an impressive job of trying to come to terms with the Nazi period. Much better than what I would expect from the U.S., which seems more susceptible to historical amnesia. But the contrast between the statue of Jakob Herz and the "monument to a monument" stuck in my head.

Thanks to Jakob Herz, I'm now much more likely to notice the many reminders of the anonymity of the "other", faceless and often nameless, perhaps relegated to a number (as in "six million Jews"), while members of one's own "tribe" are humanized and treated as individuals with faces and bodies. Once one learns to see such disparities, one sees them everywhere.

Don't Label Me!

I went to a short-lived writing group on Zoom early in the pandemic. I think it only lasted the one session. Our facilitator asked us to write down four words that describe ourselves. 

My immediate reaction was that I hate being labeled by others, and it's only slightly less distasteful to apply labels to myself. Then I wrote down "label-averse". On further reflection, I added "mathematician", "beach-loving", and "fairness-obsessed".

When we went around the Zoom room giving our labels, someone asked me, "Why do you consider yourself a mathematician?" 

It hadn't occurred to her that I might actually be one.

I laughed and explained why (PhD in mathematics, math professor for more than 35 years, many research papers published in mathematics journals).

Why am I averse to labels?

Labels can sometimes be helpful. But labels are what we use to stereotype people, to put them in boxes so we can treat them a certain way. Nearly every time someone has told me, "I knew what you'd think about that," based on some stereotype they had about me, they were wrong.

I already regret the term "fairness-obsessed". That's what people call it when they want to sneer at concerns for fairness.

If you insist on labeling me, I guess I won't cringe at "beach-loving" and "mathematician". As far as I know, no one has questioned my "beach-loving" label, or sneered at me because of it, but there's always a first time.

My Bluff

As I told a colleague afterwards: 

"The committee meeting was a total waste of time, though perhaps somewhat amusing. It consisted of B and C yelling at each other, and interrupting me whenever I tried to speak. I raised my hand for awhile and eventually gave up. When I was finally given an opportunity to speak, I said:

(1) Robert's Rules of Order are there for a reason,

(2) I think it would be helpful if one person (C, who was the committee chair) ran the meeting and were in charge, and called on people fairly and equitably, and everyone were given fair opportunities to speak and not be interrupted. 

C said that she's not very good at running a meeting. I said I'd be happy to do it.

W once told me that what helped her most as Chair of her department was being the mother of middle school boys---she dealt with her colleagues the way she dealt with her sons. I felt as if today's meeting was like a playground argument."

Before the next meeting, I asked C why she didn't simply bring the contentious issue to a vote, rather than engage in endless argument meeting after meeting. "You have the votes on your side. Let's just vote on it and move on." Both B and C had grown up in communist countries, and they might have been struggling to figure out how to function in a democracy.

C asked me to run the next meeting. I constructed an agenda that we sent out to the committee in advance. That was not a standard practice in my department.

When I was on the Council of the American Mathematical Society (AMS), someone told me that the people who have power are the people who know Robert's Rules of Order. I walked across campus to the library in search of Robert's Rules of Order. I checked out several large old dusty volumes, along with one thin pamphlet that was basically a cheat sheet. Back at my office, I read the cheat sheet. I realized I was never going to get through the large tomes before the meeting.

I took them to the meeting anyway. It was at least a good

weight-bearing exercise. I dropped the high stack of books down on the desk. They made a satisfying thump. I welcomed everyone, said we'll follow Robert's Rules of Order, and pointed to the impressive-looking stack of thick black books. I didn't point out that I hadn't read them. My colleagues looked cowed.

I had been on enough AMS committees to know how to run a meeting. As a stickler for fairness, I tried hard to make sure everyone who wanted to had a chance to speak and feel heard. I probably came close to obeying Robert's Rules of Order, in spirit if not in the details.

Someone made a motion and we discussed it. When it looked as if the discussion had run its course and B was getting ready for a fight, I asked: 

"Is there any more discussion on the motion ...," 

B opened his mouth to speak, and I continued: 

"... that hasn't already been said?" 

B froze for a moment, then his mouth closed. We voted, B's side lost, and we moved on to the next agenda item.

I wrote up minutes after the meeting, and C forwarded them to the committee. Again, something not normally practiced in my department.

I'll amend the advice that the way to have power is to know Robert's Rules of Order by adding "or make it look as if you do."

Likely Weekend

When I applied to some Ivy League colleges, applicants received postcards in the mail, sometime before the final decisions, stating whether their admission was likely, possible, or unlikely.

Brown University invited those who got "likely" postcards (at least the reasonably local ones, such as the New Yorkers) to visit for a couple of days, so Brown could try to convince us to go there. They brought the New Yorkers there on buses.

When we 16- and 17-year-old high school kids got off the buses, we were met by students who had promised to put us up in their dorm rooms. The host for a friend of mine didn't show up. My host wanted to take me and leave, but my friend (whom I'll call Jane) didn't want to be left alone, and convinced me to stay while she waited for her host.

After everyone else was gone, and Jane's host still hadn't appeared, at Jane's insistence my host grudgingly took the two of us back to her dorm room.

My host had a bad cold. It was long ago that she had agreed to take in a prospective student, thinking it might be fun and she'd be doing a good deed. Now that she was ill it no longer sounded like fun, but it was too late to back out of it. After some small talk with my host, Jane and I figured out we weren't wanted and went off to wander the campus.

That evening my host sent us to a party in the dorm. The music was much too loud, and there was way too much beer. The party-goers got drunker and wilder, and someone threw a beer bottle through a window. Broken glass swam in the pond of beer that covered the floor.

A Brown undergrad took Jane aside to chat with her. Eventually Jane returned to inform me that the undergrad had invited her to his dorm room with the excuse that the party's music was too loud to talk over, and I had to go with them. Assuming she wanted to go but was wary enough to want a chaparone, I followed along behind Jane and the undergrad. I was happy to escape the rapidly rising beer pond.

The Brown student had a friend from Bowdoin visiting for the weekend, so there were four of us.

The dorm room had exactly two chairs. Jane ran over to one of the chairs and sat down. The Brown guy plopped into the other chair. That left just the bed. The bed was in a corner of the room, so its head and right side were up against walls. I sat near the corner between the two free sides. The Bowdoin boy sat next to me.

Eventually, he put his arm over my shoulder. I moved away, to disengage. A few minutes later he moved closer. Shortly after that, he again tried to put his arm around me, and I moved further away. This continued, as we gradually moved from the free corner of the bed towards a wall. Jane watched our slow motion pantomime in amusement, and had trouble stifling her laughter.

I worried about what I'd do when we got to the wall and he had me trapped. 

The one good thing about the guys being amazingly drunk was how frequently they had to run down the hall to pee. 

Each time the Bowdoin boy left to pee, I stood up, walked back to the corner of the bed (to maximize how long it would take for him to push me to a wall), and sat down. When the Bowdoin boy returned, the cycle started all over again.

I stayed because I assumed Jane (inexplicably) wanted to be there. Finally, both guys left to pee at the same time, leaving Jane and me alone. I quickly asked her, "Do you want to be here?" She replied, "No!" 

I grabbed her hand, pulled her out the door, and ran down the hall. Just before we disappeared down the stairs, I heard the guys call out to us as they exited the men's room.

Perhaps our Thank You cards to Brown University for its kind hospitality should have consisted of the one word "unlikely".

I was glad I hadn't drunk anything at the party and was clear-headed. After a few parties at still-largely-male Ivy League schools, I quickly learned not to drink alcohol at college parties. 

I also abandoned the ideas, ingrained in American girls of my generation, that women mustn't hurt men's feelings and have to help men save face. I think male classmates appreciated when my rejections of their advances were clear and direct, so they didn't needlessly waste their time with someone who wasn't interested in them.

Conflicts of Interest --- Say what you mean, mean what you say, and don't change the rules of the game

My main advice on Conflict of Interest policies is: 

Say what you mean, and mean what you say.

My main advice on enforcing Conflict of Interest policies is: 

Don't change the rules in the middle of the game.

Someone I'll call Y was on a panel to evaluate proposals. He had followed the Conflict of Interest policy to the letter, reporting in advance, in writing, all the conflicts of interest he was supposed to report.

However, in the presence of the entire panel, the Program Officer who ran the panel claimed that Y needed to recuse himself from the discussion about a proposal written by someone I'll call Q. According to the Program Officer, Y had a conflict of interest with Q, because Q was a co-author of X, and X was Y's wife.

Due to her many experiences with discrimination based on marital status, X kept her personal and professional lives separate, and did not discuss her personal life in professional settings. Neither X nor Y had ever told the Program Officer about any personal relationship between them. Anything the Program Officer thought he knew came from gossip. The Program Officer's discussion, in front of the panel, of his assumptions about X's and Y's personal lives violated their privacy. 

The official Conflict of Interest policy did not state that being a relative of someone's co-author constituted a conflict of interest. Y pointed this out to the Program Officer, who still insisted on recusal.

Curiously, for a later panel, that same Program Officer decided not to recuse himself when he expressed support for a proposal submitted by the husband of his own collaborator.

The last people to realize they have a conflict of interest are the people who have a conflict of interest. That's why it's important to have a clear, unambiguous algorithm for recusal, rather than letting people decide for themselves.

Similarly, the last people to realize that it's not OK to deviate from the official policy or make ad hoc decisions on a case-by-case basis are the enforcers of the policy. Many cases I saw personally where someone was held to a more stringent Conflict of Interest policy than the official one involved a woman, and the attitude of the male enforcers was, "This doesn't smell right to me. It feels like she's trying to get away with something."

Don't change the policy in midstream, and especially, don't change it in midstream based on a particular case; it's easy for the enforcers' prejudices to override fairness. When something doesn't technically violate the policy but "just doesn't smell right" to you, that doesn't justify making new rules on the fly. If it's not right, your Conflict of Interest policy should have covered it. If an objective party determines that the policy needs changing, change it after the current round; don't enforce a different policy than the one that's in place at the time.

Conflict of Interest policies often include personal, financial, professional, and other types of conflicts. Some policies require giving out much more information than is necessary, and sometimes that information gets circulated to co-PIs or others who don't need to know it. It should suffice to recuse oneself and say that one has a conflict of interest that falls under the policy, without being forced to divulge details about the conflict (e.g., one's marital status, or who one is married to).

To summarize, conflict of Interest policies should:

    (1) be clear, unambiguous, and sensible;

    (2) not require people to divulge irrelevant or unnecessary information;

    (3) be sent to everyone who needs to abide by it, early enough to give them a chance to refuse to take part in the activity to which it applies.

A one-to-one correspondence

"The proportion of female mathematicians who are married to male mathematicians is much higher than the proportion of male mathematicians who are married to female mathematicians. So women must be going into mathematics to find a husband, while men do math because they're interested in it," male mathematicians have told me over the years, in all seriousness. 

Nowadays, some might call this "boy math". Whenever I hear this logic I reply, "Do you agree that there is a one-to-one correspondence between the set of female mathematicians married to male mathematicians and the set of male mathematicians married to female mathematicians?" 

They agree. 

I continue, "So the number of female mathematicians married to male mathematicians is exactly the same as the number of male mathematicians married to female mathematicians. The large difference in percentages is simply because mathematics is a male-dominated field."

They're astonished to realize that the numbers are exactly the same. There's something counterintuitive about it and it takes awhile to sink in, even for mathematicians.

Flirting with students

Lolita (probably not her real name) waltzed into the last class of the semester, just as the class was ending. Her blouse was so low-cut that it would now be called a wardrobe malfunction, her skirt was short and tight, and she twirled her hair and smiled seductively as she spoke to the professor in a soft, husky voice.

Professor Q smiled broadly. He was totally smitten. It wasn't just her hair that she was wrapping around her little finger.

As she continued to twirl her hair, smile, and bat her eyelashes at him, Lolita asked Professor Q for course notes so she could study for the final exam. Professor Q flirted back at Lolita, and then turned to me and asked me to lend Lolita my notes. He knew I was a good student, and had (strangely) complimented me on my handwriting---he knew that I would have good notes.

I had never seen Lolita before. She hadn't come to a single class. I didn't know her name. 

I had worked hard in the course and taken good notes. I wrote them in a three-subject notebook, so when I gave Lolita my notes, I gave her all my notes for three math courses I was taking that semester. Notes that I needed myself to study for the final exams. While I didn't think that Professor Q's request was reasonable, I didn't think I could say no to him.

Another student told me later that Lolita was a senior who had already submitted her applications to med school. Lolita majored in math since it was a major with very few requirements. For this course, she just needed to get by. She didn't bother going to class since she could use her sex appeal to get what she wanted.

I did somehow manage to get her to give back my notes before my final exams---late enough to make me anxious, but early enough that Lolita was miffed.

Why do I remember this story? Because it was one of several episodes that taught me how women were viewed at some of the top universities. These stories had an impact on how I view Harvard, the mathematics community, and academia. The faculty gave the female students incentive to flirt with them. But it was the job of the faculty to treat students fairly and equitably, and not be influenced by flirting or by how the students dressed. If the faculty were showing favoritism to students who flirted with them, they weren't doing their jobs.

Years later I tried to talk to Professor Q about discrimination at Harvard and some of his unfair or problematic treatment of women, including his more recent behavior towards young female mathematicians. I felt that I was in a better position to talk to him about it than were more junior colleagues or students, and I hoped that by talking with him I could help them. Professor Q treated it like a joke and exclaimed, "but Alice, I LOVE women!" as he pretended to leer at me. 

Whenever I try to talk to him about it, he evades, dodges, or acts uncomfortable. The information is not welcome.

Sometimes, it's more than cluelessness.

Advice on Advice

She generally gave herself very good advice (though she very seldom followed it)

                                        —Alice’s Adventures in Wonderland, by Lewis Carroll

I've given advice elsewhere. Here, I'll give some advice about advice.

My most important advice on advice is to value advice from those who have experience and expertise more than advice from those who don't.

When I arrived at the University of California at Irvine as a professor, I was told that the math department had a program where math majors could request a mentor to advise them on applying to grad school, and faculty could volunteer to mentor students. 

Over the years, students and colleagues had sought my advice and seemed to value it. So I volunteered to be a mentor, and was assigned a senior.

The senior wanted to get a PhD in mathematics, but insisted on only applying to Masters degree programs. She thought that a Masters degree was a prerequisite for applying to a PhD program.

I advised her to apply to PhD programs, for several reasons. Such programs would provide funding, while Masters programs were more likely to make students pay. At my previous university, Ohio State, the bar was higher for students who already had Masters degrees than for those who didn't, so a Masters degree could be a disadvantage when applying for a PhD program. If she got a Masters degree and then decided to go elsewhere for the PhD, she could still do so. Plus, graduate admissions committees that felt she wasn't ready for the PhD program could decide to admit her to the Masters program.

The senior told me I was wrong. Why? Because some first year grad students told her that one doesn't get into a PhD program without having a Masters degree. She believed that they knew more than I did about getting into grad school, even though I had served on graduate admissions committees and the students hadn't.

Other professors gave the senior the same advice that I had. I hoped that by getting the same advice from other faculty, she'd learn to trust me and find my mentoring more useful. But the senior only applied to Masters programs, and didn't come to see me again.

Sometimes the right people to ask for advice are the people who know you well. (Knowing you well also counts as experience or expertise.) I occasionally get emails from students I don't know, in various parts of the world, asking me for advice specific to their situations. While I can sometimes give them very general advice, I emphasize that for specific advice, much more valuable is the advice they should get from professors who know them well and the people from whom they've taken courses. 

My advice to advisors is to make clear the limits of your relevant expertise and experience, and state your best guess as to how much confidence the advisee should or shouldn't have in your advice. If appropriate, suggest who else might be able to give more reliable advice.

I'll end by emphasizing the limits of my experience and expertise to advise on advice. Don't just listen to me. Be open to advice from anyone, paying special attention to those with expertise and experience, and to those who know you or your situation well.

An All-Star Cast

The first mathematics talk I ever gave was a job talk at Brown University on February 1, 1984, and my second talk was in the Harvard Number Theory seminar exactly a week later. It had an all-star cast, including Harvard Professors Barry Mazur and John Tate and Yale Professor Serge Lang.

Right before the talk, I noticed that some of my friends, who were sitting in the front row, were giggling. It was a bit disconcerting when they refused to tell me what they were giggling about; they said they'd tell me afterwards.

I began my talk, and started to write on the blackboard. 

Serge Lang screamed, "Stop! Stop! I can't stand it any more!" 

I stopped. I had barely said anything. Could I have already said something wrong? What could I have said that would upset Serge Lang so terribly?

"The chalk is screeching on the blackboard!" he explained. 

Tate told me to break the chalk in half so it wouldn't screech. I pointed out that all the chalk was tiny---too small to break in two.

We all waited while Barry Mazur ran out of the room, and ran up and down the fifth floor hallway, looking for an open office with chalk. 

Eventually, Barry came back with the report "No chalk". What was I to do? 

Tate handed me a chalk holder into which I could insert the tiny chalk and use it in a way that wouldn't screech. 

Serge calmed down. (He probably went to sleep; I didn't hear from him again.) My talk proceeded uneventfully. But I learned how many Harvard professors it takes to calm down Serge Lang.

What were my friends in the front row giggling about? They were trying to decide whether to tell me that the newly-famous mathematician Gerd Faltings was in my audience. I hadn't yet met or seen him, so I didn't know he was there. That's just as well. There were enough stars to worry about.