Postcards from the Rogue Valley

In the small world of academic mathematicians, my family has the reputation of having the longest lineage of all: four generations of math PhD’s and professors. I am the exception. However, I grew up in this intimate world. For twenty years, my father was the chairman of the mathematics department at Princeton University (where Albert Einstein had an office down the hall) and this was the air I breathed. I’m indebted to my brother, Thomas Tucker, for helping me fill in blanks in this story.

The conversations at my dinner table growing up were not exactly normal.

My father presided—the head of our dining table at night, and of the Princeton mathematics department by day. His method: tossing out riddles and problems looking for a solution. My middle-school–aged brothers, two and four years older than me, participated eagerly, chewing over possible answers along with their vegetables.

 “A 300-foot train is traveling 300-foot per minute must travel through a 300-foot-long tunnel. How long will it take the train to travel through the tunnel?”

“Is it drier to walk or run through the rain?” 

Sometimes my father offered a mini-lecture, typically an introduction into the mathematical world of theorems. The “four-color theorem” received far more air time, in my opinion, than it deserved. (The theorem states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color.)

I was a lagging participant—too young, way over my head, and not a fan of pop quizzes. 

One night after I’d attempted a few uneducated guesses, my oldest brother pronounced me incapable of abstract thinking. Coming to my defense, my mother countered that I would be good with people.

I spilled my milk, ran to my room, packed a bag, and headed into the night. But fifteen minutes later I was sneaking back in.

My tribe

Solving math problems over the dinner table wasn’t the only marker that set my world apart.

Along with playing capture the flag, my playmates in Princeton’s faculty housing and I sometimes argued (gulp) about whose father was smartest. We based our reasons on their fields, from physics to romance languages. Nobody won, but one justification held true: the Princeton mathematics department, then as now, stood atop the math world, training some of the world’s most renowned mathematicians.

When I was ten, my friends and I created the “Saturday Explorer Club,” hopping on our bikes to tour the outskirts of Princeton. One of our favorite destinations were the woods behind the Institute for Advanced Study. Founded in 1930, the Institute quickly became a haven for brilliant scientists escaping fascism in Europe. Albert Einstein was certainly the best known, but his early companions included other intellectual titans: John von Neumann (known for his early work in computers), J. Robert Oppenheimer (often credited as the “father of the atomic bomb”), and Kurt Gödel, the most famous logician of all time.

Though independent from Princeton University, the Institute and the mathematics department were closely linked. Einstein’s first office was in the math department’s Fine Hall, where my father (A.W. Tucker) had taken up residence the year before as an assistant professor. My own connection to Einstein was secondhand: his next-door neighbor, also a mathematician, adopted one of our kittens. (He promptly named it Epsilon, a mathematical term indicating that a given quantity is small, close to zero.) 

The math department had its own luminaries, largely unknown outside the world of mathematics, but well known inside. They populated the stories my father told about the Princeton math department and beyond; his impeccable memory won him a reputation as the department’s historian and raconteur. For me, they became characters in a novel whose names I still remember.

My father

Like most kids, I didn’t really know what my father “did” for a living, except that he was a mathematician, a word I learned to pronounce early on. As I moved from addition and subtraction to long division, my father transitioned from topology (“the study of geometric properties and spatial relations unaffected by shape or size”) to game theory, and later to what’s called non-linear programming. His achievements in these fields were substantial, along with his pioneering role in the publishing of mathematics and the reform of mathematics teaching.

The only contribution of his that I vaguely understood, though, was “The Prisoner’s Dilemma,” a well- known problem where two parties (e.g. prisoners), separated and unable to communicate, must each choose between cooperating with the other or not. The highest reward for each party occurs when both parties choose to cooperate. Otherwise, it becomes a zero-sum game: one party’s gain equals another’s loss.

When I was seven, my father became chairman of the Princeton math department in 1954, giving me a better title for what he “did.” He served as chairman for 20 years, a record, retiring in 1974. 

While not a risk-taker—in our family, my mother occupied that role in spades—my father was a determined enabler, standing up for colleagues and graduate students who wanted to chart their own course. (I remember my parents discussing department politics at the dinner table as I wondered about the rumors they alluded to, regarding a visiting Scottish mathematician who strolled the campus in a kilt and no underwear.)

My father’s enabling included taking on a Ph.D. student named Marvin Minsky whom others dismissed, and who became a pioneer in artificial intelligence. He also mentored the department’s first female graduate student. In the oral examination that she needed to finalize her Ph.D., one of the three examiners (my father and two other professors in her field) asked her a question that my father feared she couldn’t answer. But before she started to speak, the two other professors got into a heated debate about the relevance of the question. When they came back to earth ten minutes later, my father assured them that she had answered the question satisfactorily (she hadn’t spoken), and she passed. (Of all my father’s many stories, I liked this one best.)

Arguably his best known student was John Forbes Nash, Jr., who won the Nobel Prize in 1994 for his thesis on game theory, written 50 years earlier under the supervision of my father, the only faculty member willing to take him on. Nash’s story—he descended into schizophrenia shortly after completing his thesis and battled his way back for years—caught the eye of a journalist, Sylvia Nassar, who then spent months interviewing my father the year before he died. That led to her award-winning book, A Beautiful Mind (1998). In the movie version, starring Russell Crowe, Judd Hirsch played my father.

My father supported Nash throughout his life, including when schizophrenia took him down and during his re-emergence years later.

Fine Hall

The building that housed the Princeton mathematics department was as grand as its occupants. The architect who designed it had pledged to create an environment “any mathematician would be loath to leave,” the Princeton University Alumni Weekly noted in 1931.

To me it was a castle, and I loved to visit.

Fine Hall, which became synonymous with the Princeton math department, was an architectural masterpiece. The entrance was grand, the spaces were enormous, the walls were paneled with American oak (with concealed chalkboards), and the leaded windows bore mathematical symbols. A large common room invited conversation, chess, and five o’clock tea.

Instead of an office, each professor had a study. As a little girl, it took forty steps for me to cross my father’s study—it encompassed a fireplace, an ornate rug, a vase, a davenport and overstuffed chairs, a wooden desk bigger than my bed, and books and papers everywhere. I remember asking my father, “Why does everything smell old?” 

Making casual conversation was not a strong suit among Fine Hall’s occupants. I knew this firsthand. If you combine the cocktail era of the 1950s, my father’s duty as social conductor, and my mother’s inclination to be the Gertrude Stein of mathematicians (she grew up around mathematicians too), you end up with what seemed a constant in our faculty home: cocktail parties. 

While other girls my age were learning to make their bed with hospital corners, my mother coached me on how to draw out shy mathematicians as I circulated hors d’oeuvres. I developed a set of questions. Where are you from? (Many of the mathematicians linked to the Princeton mathematics department were foreign-born). Do you play an instrument? (Allegedly, mathematics and music were inextricably linked.) What’s the best thing that ever happened to you? (This was my favorite question.)

As the party wore on, I also joined in the free-form square-dancing, resembling bumper cars, that overtook the large entrance hall in our house. But I sat out the contest to see who could longest balance a broomstick on their palm. I couldn’t believe my eyes: grown men with famous brains swerving in one direction and another, led by a broom. The diminutive topologist Ralph Fox was a standout, perhaps because he was closer to the ground.

(Did you think mathematicians were straitlaced?)

I was a good sport when it came to celebrating my birthday in the company of mathematicians four times my age. I shared my birthday with a mathematician and family friend known for his drinking as well as numerical analysis; the date also coincided with the August meeting of the American Mathematical Society, a pilgrimage in our family. The party, typically staged in a fancy restaurant, always had the same ending: the birthday boy and I, feigning surprise, would gather at the end of the table and blow out the candles on the cake, applauded by a dozen mathematicians and their spouses, many well inebriated by then. (I hoped in vain that when we returned home, I might get one of those pony-riding or face-painting birthday parties with my agemates.)

When I was sixteen, John Nash came to visit my mother and stepfather in Santa Monica, on the rebound from his debilitating schizophrenia. My parents left me alone with Nash for a weekend (I can’t remember what pulled them away) and he paced the floor in our small home. Desperate, I suggested that we drive to the beach—I had just got my driver’s license—and watch the waves, despite the cold and gray. We walked the beach for two hours. I did my best to engage him in small talk, to keep my anxiety at bay. Forty years later, when I chatted with John Nash at my father’s memorial service, he said he remembered that day.

The Queen of Science

I have an enduring image of my father, sitting in our “TV room” in Princeton, watching the Yankees or college football with a long yellow pad on his lap and pencil in hand. Years later I would watch my older brothers, both mathematicians, strike the same pose. When my younger son, Dan, announced at age eight that when he grew up, he wanted work he could carry around in his head, I suspected he had inherited the family gene. (His Ph.D. in statistics landed him a stint as a sports analyst for the Dodgers.) 

I was good at arithmetic, but I barely absorbed the world of mathematics and mathematical thinking. It seemed ethereal, a world of proofs and theorems pulled from the sky, then finding their way into down-to-earth applications, a transformation I didn’t understand. My mother was right: I would work with people. I majored in the social sciences in college and graduate school, then carved a career as an advocate for progressive public education. (That pursuit defied my father’s deep belief in elegance as the holy grail of problem solving. “An elegant solution, simply put, overwhelms you with a sense of its rightness,” he would say. “It is one you can re-create, that inspires you.”)

More than half a century later, I’ve dipped into the questions I never asked myself when I was younger, the mini-lecture that never graced our dinner conversation: How does math connect to the physical world? 

I had never wondered why a rainbow is curved or why left-handers aren’t extinct or a lightning bolt is like a blood vessel.I never got my head around Pi: infinite and, by definition, unknowable. I had been incurious about the patterns that fill our universe and mathematics’ role in deciphering these patterns, earning it the title of the “Queen of Science.” 

Even if I’d had the capacity for abstract thinking, I lacked the patience for the long haul figuring that undergirds so much of the “solving” in mathematics. The “four-color conjecture”—which sent me running from the dinner table and into the dark when I was nine—first posed in 1852, was finally proved in 1976 with the aid of a computer.

Two years ago, I learned about the underground threadlike fungi that link nearly every tree in a forest, sustaining for 1.3 billion years the life of trees and all that depends on them. Today, I’ve learned that mathematics not only lives invisibly in abstract objects, but also visibly everywhere in nature, even where we are not expecting it. It helps explain the way galaxies spiral, a seashell curves, patterns replicate, and rivers bend. Even subjective emotions, such as what we find beautiful, can have mathematical explanations. 

It’s been worth the wait.

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