What are Mathematicians Really Like?

Pamela Aschbacher wrote the article What are Mathematicians Really Like? Observations of a Spouse, that appeared in the book I, Mathematician edited by Peter Casazza, Steven G Krantz and Randi D Ruden. We give a version of this article below. Pamela Aschbacher doesn't identify the mathematicians from whom she quotes, but most are quite obvious - a nice exercise for the reader. We strongly recommend the reader to look at other articles in I, Mathematician. We think it is an excellent book.

What are Mathematicians Really Like? Observations of a Spouse, by Pamela Aschbacher.

"What's it like living with a mathematician?" I hear this question a lot - probably more than if I were married to almost any other kind of professional. What is implied is: What are "they" really like? - as if they were exotic beings from another planet. And indeed, someone who does math all day long, eagerly thinks about it in his spare time and on vacation, and sees it as "beautiful" is, frankly, NOT like most of us.

I've spent many years living around university research mathematicians as I've tagged along to countless dinners and conferences, spent vacations with mathematician friends, and shared stories with math-spouses over many a walk or cup of tea. Out of curiosity I've informally asked my husband and his colleagues about what they do, how they came to this career. and why they work so hard despite lower pay than in many other positions they could probably hold. I've also discussed with a lot of other math spouses how this career choice impacts their lives. Eventually, it occurred to me that it might be interesting to try to explain to non-mathematicians like my friends what this life is like. In the past year I've also explicitly contacted over a dozen friends who are (or were) also math-spouses to check that my observations and experiences are not anomalous. My attempt here is not meant to be social science research or tabloid fodder. Rather, it merely reflects my own curiosity and desire to open a window on the mathematician's world from my decidedly non-mathematical but nearby vantage point. Unfortunately, my sample is largely limited to the male of the species, as there have been few women research mathematicians of my generation.

By the way, the quick answer to the initial question above is: living with them can be great, but yes, sometimes they do seem to live on another planet.

What Do They Do?

Many of us non-mathematicians have no clue what research mathematicians do when they are "doing math." A good reason for this, they tell me, is that it is not what our high school or most college math courses entailed. How were we to know? They were called "math" courses. This confounding of arithmetic, algebra, even calculus with "doing real math" undoubtedly is why acquaintances who learn that my spouse is a mathematician often say something like, "Oh, it must be nice to have a husband who is good at balancing the chequebook." Let me just note that this assumption is wrong for many mathematicians. In fact, my non-mathematician friends tend to be much faster at divvying up a restaurant cheque than the math groups I've eaten with. Mathematicians are good at abstract concepts, not necessarily numbers (unless maybe they are number theorists).

When I've asked mathematicians to explain to me what they do, they usually describe it as solving problems, creating theories, showing that some things are false or true, and/or generating some machinery that constitutes a theory. Some problems are big and important; some have little consequence but are of historical interest. Some modest problems, when embedded in a larger context, build up knowledge to solve the bigger problems. Just to give you an idea of the range of production, a single math proof can range from one page to 1500 pages or more. It might take a few months to several years to prove. Some assertions are around for fifty years or more before someone actually finds a way to prove them.

Part of what makes a "good" mathematician, I'm told, is the ability and willingness to find a problem whose solution would be helpful in the field, to have a productive way of looking at the problem, and to put in the effort to actually solve the problem and write it up so others can use the result. Not so different from other kinds of problem solvers. What seems to be valued in the math community is having creative, original, new ideas; being able to solve problems and create theories: knowing things that other people don't: and having a large body of work. Unfortunately, like many other creative fields, one-hit wonders are common. Some people solve one good problem but are not able to do much else over the years. As in life so in math: it helps to be lucky - to be in the right place at the right time. People considered to be really good mathematicians have usually done several good things. For example, one not only solved a conjecture that had been unsolved for fifty years, but also developed new techniques to solve such problems. And they seldom have dry spells; with their expert knowledge of what's important in their field, they know what the important problems are and nearly always have something to work on.

As I pondered what it must be like to create theories in math, I have asked several mathematicians: Is math something like an unseen star, out there to be discovered (the Platonic view), or something we create to make sense of our world (the Kantian view)? To a person they all told me: Oh, it's definitely the 'truths' of the world waiting to be discovered!

I've also asked: How do you select the problems you work on? To this I've gotten quite different responses, and when asked in a group setting, the mathematicians were quite surprised at their different approaches, as they had never shared this with each other. One friend told me:

Problems seem to select me! It's just so exciting. A problem sort of chooses you, and you can't stop thinking about it. At first, you can't figure out how to go about it. You try something, and it doesn't work. You get clobbered! You try something else and get clobbered again! Eventually you get some insights and things begin to come together. Everything is moving. Each day things can look different. It's very exciting. Eventually you've solved it all and it's a great feeling! Then you have to write it all up (groan). Sometimes I do "pro bono" work, when someone comes to me with a problem, and if I think I can solve it quickly in a matter of days, I'll take it on.

But another mathematician in the same conversation told me he is more active in selecting problems, but he ascribes the difference in approach to the nature of their respective fields of math:

For me, approaching a problem is different. I don't feel "clobbered." I can usually see lots of different ways into it - it's more a problem of which one to invest my time in working on. I have some sense of what the important fundamental problems are in my discipline and try to spend the majority of my time on them. Also I try to change the thrust of what I work on every few years, partly not to be bored, but also to extend myself in different directions. If I have the necessary math background, I almost never find a problem I can't solve. Sometimes it would take a lot of time to learn enough background to be able to solve a problem so I have to decide whether it's worth it.

I think our differences reflect the differences in our fields of expertise. In my field there are plenty of techniques for approaching a problem so there's room to create your own techniques. There's a lot there to try to understand, and it's not a problem to try to find a foothold, as in his field.

I wonder if anyone has studied this issue? Do problem-solving approaches vary more within fields or between fields? If approaches tend to be idiosyncratic, they may reflect some hard wiring in the brain we have yet to understand. Perhaps functional MRI will eventually be used to explore questions like this.

What is This Passion for Math and How Does It Develop?

The mathematicians I've known see beauty, wonder, harmony in the universe through mathematics and have a very aesthetic sense of it - something most non-mathematicians can't quite understand. We might feel satisfied when we solve a problem but pure math is the intoxicating discovery of something previously unknown, using very abstract thought. To me it seems a bit like discovering the existence of a galaxy that we can't actually see but must infer from its effects on other bodies in the universe. It is fortunate that mathematicians tend to be motivated by their passion for knowledge creation, not for fame or fortune, since academic salaries are not high, given the time and effort devoted to advanced degrees and postdocs, and the average person could probably not name a famous mathematician (beyond perhaps Pythagoras or Euclid). Within the field, however, people can gain some small fame from having their names assigned to the things they discover or prove, e.g., Lie groups, Frobenius groups, Suzuki groups. Still, according to the people I've known, it's more about the discovery itself than being famous as the one who made the discovery.

Most of the mathematicians to whom I've posed a question about how they were drawn into math have said they feel they are just born that way - and that there is a strong self-selection process in which many people are turned off and away from math but a few are drawn towards it by its beauty and elegance - words that non-mathematicians typically do not use about the subject!

However, as one math spouse explained it, while her husband's love of math seemed innate, his children may well have benefitted both from the genes he passed on and the model he provided:

When he was young, he fell in love: (1) with painting and art and (2) with math. He says that for a while the two were tied but painting was never in the lead. Eventually he realised that he was much better at math. If I, after knowing him for some 35 years, had to analyse his choice, I would say that his passion for the beauty of math was what overtook all else. I think for him it's almost an addiction to the art of beautiful mathematics: its form, its balance and its ability to clearly explain the almost unexplainable. Whenever I've asked him to try to explain his work to me, his eyes sparkle and he gets an animation in his voice and gestures that are not present at any other time. I believe that my husband's love of mathematics is so heartfelt that no one ever needed to explain that math was beautiful to our daughters. They truly felt that, like the art we love and have in our home, math was an art to be appreciated and that the pursuit of trying to understand it was a very worthwhile undertaking.

A few mathematicians told me they found their passion for math early in life. For example, one told me that like many young boys, about age 9 he was very interested in rockets, so he got a book about them from the library (this was pre-internet days of course), but he could not understand it. He showed it to his economist father, who said, "No wonder, it's full of math," and proceeded to teach his son some math. The son "got caught up in the wonder and beauty of it" and kind of lost interest in the rockets.

A woman mathematician told me that her interest in math grew out of a high school interest in science:

My exposure to astronomy at the Green Bank Observatory in high school was a turning point for me. I was fascinated by all the machinery, by the vast reaches of space, and the fact that we could see objects so far away. I started college as an astronomy major, taking math and physics, and discovered that I really loved the physics and could study astronomy through physics without going to remote observatories. And then I discovered that math could do everything, and that I really loved it.

In fact, most of the mathematicians I've discussed the topic with did not discover the beauty of math until college or graduate school, and it was sometimes by accident. One told me that he became interested in math when he couldn't get the history and philosophy courses he was interested in at a big public university and happened to take a decent math course instead. Many said they entered college more interested in other subjects such as history, literature, engineering, or physics, but they discovered that they liked math and did better in those courses. For example, one told me how a combination of college experiences ignited his math interest:

In high school I didn't think a lot about what I wanted to be, I just sort of drifted through life ... When I went to Caltech, I took all the usual courses. I didn't like the chemistry lab - hated the details - didn't do so well in physics class with Feynman. He gave problems you had to solve by guessing the right math model. I was frustrated because the TA liked my model one week, but the next week after he'd learned what the professor wanted, he said my answer was wrong. I did better on math-related parts of physics than the other parts and I had some interesting math classes in analysis and algebra where the professors were quite enthusiastic. So sort of by a process of elimination, I became a mathematician. I liked it, and it seemed to suit my interests and the way my brain works.

Sometimes a college instructor gave pivotal advice, as one spouse told me:

My husband did not think of being a mathematician in high school. He was under family pressure for a particular career, and that's the direction for which he prepared himself, not thinking of anything else. Fortunately in college, however, his professors recognised his math abilities and urged him to think about that field instead.

For some, a career as a research mathematician is fraught with practical challenges - job offers may not be where the spouse can get a job or wants to live, academic postdocs and starting salaries are lean, and at times the job market has been so tight that people left the field in frustration - but math seems to have a strong pull for many of them nonetheless. One woman mathematician I know had several good academic positions but gave them up to live in the same country as her husband and children, where the only relevant position she could get for several years was teaching in a technical college. I saw her at a math meeting after several years' absence, and she explained she really missed being a research mathematician and had come to assess whether it seemed feasible to re-enter the field. Fortunately she did and eventually was able to secure a research position in her adopted country. Another friend left math a few years out of graduate school when the job market was very tight and he could not get a tenured position. He became a physician and enjoys his work, but after a while he missed the intellectual challenge of math. Fortunately, he found a way to do some math on the side with scientists at the local state university.

Doing math is just so compelling for them that most mathematicians I know would rather be doing math than any other job in the world. Some of them love teaching classes too, and most agree out of duty to be a department chair, a dean, or an editor at some point, but doing math remains their deep calling:

As Chair of the math department, my time is filled with administrative tasks and I don't have enough time to work on my math. But in two years I'll be able to give up that job and give up editing a journal so I can devote myself to my own problems for two years - ahhhh, heaven!

So Do They Really Write Theorems on the Backs of Napkins?

In a word, yes. One thing I learned early on was not to throw away scraps of paper with math symbols on them, no matter how old or grungy. The best I could do was to create a special place to corral the odd bits so they would not go missing. I've asked my husband about this and he says it occasionally helps to write something down or draw pictures or graphic representations of his thoughts. What are these? Little circles and squares to help him remember different mathematical objects and their relationships (like "something is the product of two groups with a third group acting on top of them" - whatever that means), and he uses both standard and unique elements in his own personal shorthand. He jots them down on napkins, receipts, the backs of other pages, anything at hand when the thoughts come.

Concentration and Parallel Processing.

So what are mathematicians like when they are working? Well, in what other job can you work while lying in bed, waiting in line at the DMV, or singing along with a CD? Some mathematicians really can do these things while they are deep in mathematical thought. I suspect that, for many of them, math is nearly always going on somewhere in their brains. When I asked my husband what it takes to be able to do math well, he gave first priority to their amazing powers of concentration.

You have to be able to focus and concentrate for an extended period of time and follow a train of thought without writing it down. It's an absolute necessity in order to be a mathematician. But it can be dangerous. You're shutting out everything else. For example, you can't possibly allow yourself to do it while driving!

He often thinks about math when falling asleep or in the early morning as he's beginning to waken but it can also prevent him from relaxing enough to sleep. He thinks a little about math while walking his usual route to school and likes having that time to do this. Somehow he is able to parallel process enough (perhaps using a kind a of auto-pilot) not to stumble, and he says when he has to cross a busy street on the way to campus he changes focus to "reality."

To me, this ability to concentrate is one of the most extraordinary things about mathematicians! How can they manipulate abstract concepts like "groups" in their minds without writing much down and despite the sort of distractions that irritate the heck out of the rest of us? My husband claims that with practice over the years he's gotten better at concentrating. This kind of concentration is just beyond anyone else I know. Most of us math-wives are in awe of it - although at times it evokes frustration and/or laughter.

At a wonderful math meeting we attended on Crete, about thirty mathematicians and assorted spouses had a free afternoon and went for a guided hike in the mountains (populated mainly by sheep, a shepherd or two, perhaps a few wolves, and one or more caves where Zeus was purportedly born). After the hike we were to have dinner at a tiny village at the bottom of the mountain, then a bus would return us to our lodgings in another tiny village on another mountain. (Did I mention it felt like we were 1000 years back in time, out in the middle of nowhere, and could not speak the language?) About 5:00 pm, when it was time to head down the mountain to dinner, two mathematicians were nowhere to be found. We spent an hour scouring the area for them to no avail and began to get very worried about them. Eventually it got so late that the hike leader continued the search herself while the rest of the group virtually ran down the mountain to beat the quickly descending darkness (of course we hadn't brought flashlights since we hadn't expected to be out so late). With speed imperative, most of the group began to scramble down a steep and fairly straight downward animal track in a crevasse, while a few others took a steeply winding trail covered in chewed up concrete (called a "road"). About an hour after darkness fell, the groups had made it to the bottom, although one person had badly sprained an ankle navigating the crevasse. In the village we discovered the two missing persons, completely unaware of our troubles. They had been deeply discussing math since the afternoon and, oblivious to our potential concern, just ambled away from the group and headed down the road, merrily talking math all the way.

And then there was the fellow (who will remain nameless) who, deeply involved in thinking about math, left a math meeting at its conclusion without remembering that his wife had come with him on that trip!

Another mathematician was at home with his son while his wife was at work.

Of course he was doing maths, leaving our son, who was not yet two, to amuse himself. After a while he was disturbed by a knock on the door. It was the village policeman (this was in the far-off days when villages had policemen). "I just thought you'd like to know that I've spent the last half hour following your toddler around the village," he said. "I didn't want to talk to him in case it frightened him, but he's been wandering the streets happily and has just come home again."

To be fair, the husband had no idea that his son knew how to open the back door - but, according to his wife, he had been totally oblivious to his son's absence. A friend told me that her mathematician husband had been so focused and deep in mathematical thought that he never even noticed a moderate size earthquake. For him, being able to concentrate to this degree is just part of his nature - like breathing or sleeping. Indeed, at times, when working on a most difficult problem, he even works in his sleep. Now and then, he will wake up having solved a large equation that was an integral part of the "big picture." My friend does most of the driving as she worries that her husband could easily fall into thinking about math and miss his turn or get into an accident. My own husband has adopted a way of strategically driving slightly ahead of the flow of freeway traffic specifically to avoid slipping into "mathland." If he is concentrating hard enough on driving, his mind doesn't wander to math. Long before computers could do parallel processing, married mathematicians had perfected this ability. Many of them have adapted to the needs of their partners by appearing to listen while actually deep in thought. A wonderful example of this skill occurred three days after two of our friends brought their second son home from the hospital. It was a Monday morning and the wife had to drop the older son off at pre-school. Before she left, she walked over to where her husband was preparing his classes, reminded him that the baby was sleeping upstairs and told him that he should wait until she returned in a few minutes before leaving for classes. He looked at her, nodded and said, "See you soon." She returned fifteen minutes later to find the baby still asleep upstairs and her husband gone. She called him at school and asked, "Did you forget something?" "What do you mean," he replied ? "The baby," she said! I learned early on in our marriage to spot "that look in his eye" that reveals he is thinking about math while carrying on a conversation with me. His responses are usually quite appropriate in the conversation, but there is a slight delay like a phone call between the US and Europe. It feels as if he is working about twelve feet under water and then comes up to a depth of about two feet when I ask a question - but he's still under the water. I eventually learned to politely ask, "Are you thinking about math?" The reply is usually, "... mmm, a little."

A friend told me her mathematician husband has always had the most amazing ability to concentrate totally on a problem, but at the same time his mind is filing away what she is saying to him.

I will tell him something that I need him to remember, see that he is abstracted, and say, "You didn't hear a word I just said!" He will slowly (really just a few seconds) redirect his attention to me and repeat back what I just said. We developed one coping mechanism for this in our early years, when we were driving across France after a conference. He was driving and I said something that I felt required at least an acknowledgement. I stopped chattering and waited. Nothing. I said, "T.R.A.A." He looked startled and asked what I had just said, so I repeated, "T.R.A.A. - That Requires An Answer." And he answered the question within seconds. For a couple of years I used "T.R.A.A." whenever I needed his attention.

Many of us mothers have learned to multi-task, for example, to talk on the phone while cooking dinner and answering children's questions at the same time, but it's not the same. None of those tasks requires the same abstract depth as math. One of my friends noted: "At work, I could talk on the phone with a student while answering email and thinking about a report I was writing - but none of those requires the same focus as mathematics!" I have been interested in this issue of concentration since first encountering it many years ago and have discussed it from time to time. For example, my husband likes to listen to music while doing math, but a friend who's a mathematician says he just can't do that; the music gets in the way. But not only does my husband listen to the music while thinking math thoughts, he sings along with it. It got to be a joke when my mother would call, hear him in the background from the other room, and casually ask, "Is that [him] singing?" and I would say, "Yes, he's doing his math." I also finally discovered why he watches B-movies on the weekend. For years I just figured he had lousy taste in movies, but I noticed he didn't seem that involved in them and finally asked why he watched them. It turns out that they provide just the right amount of white noise for him to be more productive in math.

Sometimes I can think better when part of my brain is sort of distracted by music or something on TV that I'm half-watching. There's sort of less tension. If it happens, it happens; if it doesn't, it doesn't. Sometimes it's better not to try too hard, not to think in too linear a fashion.

He also says he usually sits at the back of the room for talks at math meetings so that if the talk is boring or out of his field, he can think about his own math. He says his colleagues seem to adopt the same strategy so no one is offended by this practice.

I suppose mathematicians aren't necessarily different from others who work largely with their minds. Theoretical physicists are probably quite similar; professional chess players are famous for their memories. But face it, most of us non-mathematicians just can't do this with our minds.

Math Identity - How Do They See Themselves?

I imagine the other authors will say far more about this than I could. However, I'll make one observation that they might miss because I believe they take it for granted. I've noticed that, when asked in a mixed group what they do for a living, they do not call themselves a "college professor" or "math professor," which would be more broadly understood. Rather, they refer to themselves as "mathematicians," even though the listener might not know what that really means or might be put off by it (usually saying something like, "I always hated math in school," or "I never was any good at math.") I notice the same happens when my husband has to fill out tax forms or other paperwork asking for his profession. Even at the risk of being misunderstood or put down, they see themselves as mathematicians first - i.e., people who discover/prove mathematical truths. This is the essence of who they want to be, the part of their job with which they most identify, the portion that carries the most importance for them, even those who also enjoy and may excel at being a teacher, department chair, or dean (titles to which some listeners might accord more status than to "mathematician").

I believe their strong sense of identity is nurtured and enhanced by working within the same small community of research mathematicians all their work lives. Over time, they accrue shared experiences (like the Crete hike), compare common concerns (like how to recruit the best graduate students and young faculty), and develop fluency in their common math language. Since much of their interaction is at conferences and meetings where the point is to publicly share and critique their work, they get to know each other well, assessing each others' professional strengths and weaknesses. They quickly learn whose talks are worth going to, whom to ask if they want information about a topic. They also get to know one another's personal characteristics revealed over the many hours spent together at professional meetings, having meals or drinks together, discussing university and world events, and participating in recreational events like walks or tours planned for meeting participants and their families. There is a wonderful comfort in working with people - a kind of math family- whom you know well and can trust to share your work ethic and professional values, to appreciate your enthusiasms. No wonder they enjoy their professional meetings so much. They provide warm reward for the long hours and hard work that doing math inevitably entails.

At the same time, mathematicians' sense of identity is probably also reinforced by the fact that many non-mathematicians do not know what they do and tend to hold them at arm's length, ascribing to them various negative stereotypes. I perceive that many mathematicians are saddened when others proudly proclaim about themselves that they are "not good at math," implying that this is a positive attribute and that they have no desire to appreciate mathematics. This seems to be an advanced version of the anti-intellectualism rampant in high school and American society in general. Mathematicians are smart, so they are doubly rejected, but from that rejection is born a stronger group identity. In addition, the math group is, overall, a really nice, interesting group of people and one I'm glad to be part of!

What Do They Value?

Mathematicians are committed to ideas, to learning, to developing knowledge for its own sake. The usual fame and fortune seem not particularly seductive for them. Many math spouses told me that this quality is one of the things they love about them. We respect their dedication to their work and the high standards they have for it. Most mathematicians are excited by the challenge of their discoveries, and they tend to feel lucky that someone will pay them to do what they love. There are a few math prizes for extraordinary achievement, some with a little money attached, but it's not usually a lot and is basically for travel to work with others. They can be competitive, but the stakes are lower than in other fields, so they can afford to share their unfinished work, unlike scientists in many fields. Few of their math colleagues are interested in or capable of beating them to a solution. Since their work is public and its value so readily apparent, they cannot fool their colleagues. Their primary reward then is the hard-earned recognition and respect from their peers.

Social Skills

The stereotype is that mathematicians aren't very social, but in reality there is great variability in their verbal and social skills. Some of them can't be bothered with small talk, but others are great schmoozers who can tell delightfully entertaining stories. Many may seem slightly introverted or shy at first, but once you get to know them they are quite personable. As one math spouse noted, many mathematicians like her husband are interested in a lot of different subjects (e.g., food, wine, art, travel, science, languages, music, and theatre) so it is easy to find a common interest when meeting someone new. Some of them thoroughly enjoy their roles as teacher, advisor, department chair or dean, which all require a lot of social interaction. Some are like a parental figure for their students, maintaining fond contact with them even after graduation.

How Has Being Married to a Mathematician Affected Our Family life?

In thinking about this question, I have concluded that the social and geographic aspects of mathematicians' work can strongly influence their families' lives in positive ways. Working in a U.S. university has an international flavour for mathematicians, as many of their European, Asian, Indian, and former Soviet Union colleagues spend years of their careers here. In addition, research mathematicians often attend several math conferences or meetings each year with others in their field, at which they discuss their latest work and, in the process, get to know one another. These meetings are quite international. When held in the U.S., there are still many foreign mathematicians who attend as visitors or are grad students, post docs, or instructors temporarily studying or working in the U.S. For meetings held in Europe, probably half the attendees are from the U.S.

Math meetings are relatively easy for mathematicians (and often their families) to attend. Since mathematicians don't have to run a lab like many other scientists, it is relatively easy for them to get away for such meetings, and their travel expenses tend to be paid by grants from the U.S. government or a foreign one. If the meetings are not during the summer, mathematicians just have to find someone to teach their classes and avoid leaving during times of important committee work (e.g., during admissions season). Some can even arrange to do all their teaching in two terms, leaving the third free for travel. English is nearly always the language of the meetings regardless of where they are held.

The majority of meetings my husband attends are focused on his particular math specialty, and his colleagues around the world number perhaps only 200-300 people, about 50-75 of whom might attend a typical meeting. When feasible, spouses and children may accompany them. Through repeated shared experiences with this relatively small but international community, mathematicians and their families knit together friendships all over the globe. When I accompany my husband to a meeting, I often have the chance to see other math spouses who have become friends over the years. Even if much time has elapsed since we last met, our common experiences and interests allow us to pick up nearly where we left off years ago.

Sometimes families can live in one place for a month to a year, living more like locals than tourists. Their children can go to the neighbourhood school and acquire a foreign language. For the month we lived in a Paris suburb when our daughter was

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, she began to babble nonsense syllables with a French accent when playing with other children in the communal sandbox. Three years later when we were in Oxford for three months, she developed a temporary English accent. This early language experience may well have influenced her later interest in and ear for languages.

I realised how much I cherish these opportunities when I chatted with some tourists while we waited in line in the Piazza San Marco to see the duomo in Venice last year. They had taken a behemoth cruise ship to visit five big European cities in as many days, and they loved being able to sleep and eat on the ship. I, on the other hand, had just spent two weeks in Venice while my husband taught a math course to E.U. grad students. I must have walked nearly every street in Venice, talking to local artists and students, eating cichetti for lunch and fabulously fresh seafood for dinner at little places recommended by our local friends. I found tiny museums and fascinating local shops off the tourist track, watched a traditional boat race from the venerable Grand Canal home of a local mathematician, and attended a math soiree on the small island where Venice originated. Each day was a new gift of delicious experiences. How could I not feel far more fortunate than those tourists!

All this exposure to the people, language, culture, and food of so many other countries helps us look outward, become interested in others, and consider different ways of being and thinking than we otherwise might. This is not unique to mathematicians, of course, but they may be able to do more of this sort of travel than many other professionals, whose meetings may be larger and less frequent, usually located within the U.S., or tend to resemble typical tourist-style travel. I feel incredibly grateful to have visited so many fascinating places. The many opportunities our family has had to develop friendships with people all over the globe have greatly enriched our lives - largely due to my spouse being a research mathematician.

Language and Communication in a Math Family.

I've found that the language of our family conversations can be slightly different from non-mathematician families, particularly an emphasis on precision of language and thought, which is crucial in math. In addition, the vocabulary of math, logic, and probability infiltrates the everyday speech of our family and others I've known. When we use these terms outside the family or math community, however, it can result in odd sideways glances. Here's a sample with some translation:

Math terminology	Normal language
John is the random variable.	As soon as we know what he wants to do for dinner, we can plan the rest of the day.

It's a non-trivial task.	It's hard.

It's hopelessly difficult.	It's really hard.

It's intuitively obvious.	Any dolt should know this.

They have to worry about the 2-body problem.	It's hard for a married couple to both get academic jobs in the same location.

Boy, the chance of that happening is epsilon!	A VERY tiny chance, close to zero.

We thought it was impossible to be both sexy and a mathematician, but John is the existence proof.	John's being both proves it's not impossible .

Jane takes her interest in photography to the $n$ th degree.	Her interest is a bit extreme (she just bought a $2000 camera).

We are asymptotically approaching an agreement on which movie to see.	We won't be seeing a movie tonight.

Their friendship is asymmetrical.	John gets to do what he wants a lot more often than Jane does.

Math also influences the way my husband remembers things. For example, once he revealed that he remembers my birthday by recalling that it's a prime number.

Math Spouses.

I have not noticed obvious patterns in the types of women who become math spouses beyond being smart, well-educated, self-sufficient, and accomplished. They tend to have careers outside the home, but these span a very broad range of fields such as psychology, social work, science research, history, educational research, higher education administration, law, business management, visual arts, music , nursing, teaching, and writing. A precious few are mathematicians themselves. For the most part, we non-math spouses do not substantively understand the math that our husbands do, but fortunately we don't need to. We quickly learn the structure and regularities of the job, so we can be sympathetic about whether their department will hire the person they want to recruit or whether they will have to put much of their own research on the back burner for three years if they agree to become the next department chair. In the more successful marriages, the mathematician will do the same for his spouse! In the early years of our marriage I was a bit awed by the depth of his focus on math, compared to my multiple but shallower interests both within and outside my career field. Eventually I realised that we each have a different kind of intelligence and a unique mix of talents, and that both are valuable. Over the years, if we are lucky or willing to work on it, we develop mutual respect for each other's strengths as well as tolerance and support for each other's weaknesses. One of my friends captured this spirit well when she described their relationship.

At first, I admit, there was an adjustment. I had thought of myself as a fairly bright person. It was eye-opening to first understand how fast his mind works, how incredible his memory is and how extensive his abilities are. From having memorised all of Hamlet at one point, to memorising the first book and some of the second book of the Iliad just for fun, to being able to sing Brahms's 'Four Serious Songs', Gilbert and Sullivan, and Tom Lehrer. But I came to realise that his world still needed my world, and my world needed his world. After all these years, I'm still awed, frustrated, uplifted, inspired, and fascinated by him.

On the day after I sent a draft of this chapter to a math-spouse friend, she sent me this return email, which seems to confirm these observations:

Hi, Pam,

Coincidence of the century. This afternoon we were at a talk by a very prestigious university prize winner. The title of his talk was, "I Want to be an Algebraic Geometer" and he talked briefly about why he became a mathematician and why algebraic geometry. His reasons were "the beauty of math" and the ''joy of algebraic geometry." At the end of the talk he thanked his wife of 28 years, who had given him the peace to do his research.

Last Updated March 2024