Sine of the Times
Yes, Bonnie Shulman began her adult life as a poet, a college dropout, a single mother on welfare. She toiled as a skivvy for Allen Ginsberg at the Naropa Institute, established a poetry press, and returned, at age thirty, to higher education as a freshman before finally obtaining a doctorate in mathematical physics.
And yes, Shulman is now assistant professor of mathematics at Bates, where she walks barefoot to class, practices Tai Chi on the Quad, and engages in scholarly feminist critiques of the teaching of mathematics and science. She researches wave propagation, lives in a geodesic dome in nearby Poland, and writes personal memos on notepads from Pizza Hut.
Bonnie Shulman is all of this. Yet she is more because she is greater that the sum of her parts.
Shulman’s parents divorced in the early 1950s, when she was a young child. She moved from her native Champaign, Illinois, to New York City with her mother, a secretary who returned to school to become an English teacher. Her father, then an agronomist, remained in the Midwest and became a professor of computer information systems at DePaul. Shulman says this parental estrangement created “the theme of the split”: a dichotomous tugging of science, represented by her father, in one direction, and of art, represented by her mother, in the other direction. Shulman responded by attempting to satisfy each parent’s opposing interests.
“I had a lot of chutzpah as a little kid. Maybe it’s natural in kids, and I didn’t get it knocked out of me,” she remembered. Always good in math and science but also intrigued with acting (“I was always a ham, totally a ham”), she anguished over attending either the professionally oriented High School of Performing Arts (of Fame fame) or the highly selective Bronx High School of Science, both New York City magnet schools. She chose Bronx Science after her mother informed her that academically there was no comparison between the two. Scholastically, Shulman soared, but by her senior year, she simmered with rebellion. Her grade-point average dropped (from 98 to 96). Interested in physics, she faced a guidance department that believed nuclear physics was the only appropriate career path — but Shulman found such an avocation repugnant. In any event, this was the early 1960s and Shulman, as a woman, received little encouragement for a career in science. She also craved a social life. “I was the perfect example of why people drop out of math and science,” she said of her departure from the science track.
“I was a bad girl. I didn’t go on to college,” she said, although she grudgingly admits that she did attend the University of Pennsylvania for one year. “It absolutely did not count,” she insisted. “It was in the sixties. I played guitar and wrote poetry. I cut class. Classes were suspended half of the time. I didn’t get credit for any of those classes,” she said. “I was rejecting all the cultural assumptions of my times.” A worshipper of Bob Dylan, she found herself writing in one of her notebooks, “Dylan quit school when he was nineteen. What are YOU doing?!!!”
Science be damned, she decided. Instead, she was going to be a poet. Shulman left college, “bummed around,” and lived on an upstate New York commune with her boyfriend. “I was here, I was there, I was totally spaced out,” she said. “With all of my shenanigans, I found I was three months pregnant on my twenty-first birthday.”
Her daughter, Hatha — named after the style of yoga, of course — was born “the summer Nixon resigned.” Shulman found herself living in New York City as a single parent in desperate poverty. The academic superstar had plunged quite a distance. “It was a scandal. It was awful,” she said. “My mother was nagging me all the time.”
To escape the physical and emotional burdens of New York, Shulman ended up in Colorado with her “other love” — writing and poetry — to which she dedicated herself by studying with poet Allen Ginsberg at the newly established Naropa Institute. “A terrific community flowered there, and I was right in the center of it,” she said. Raising Hatha and collecting welfare, which she supplemented with income from typing and secretarial work, Shulman transcribed tapes for poets — “I was Allen Ginsberg’s personal slave” — participated in jazz and writing salons, and published magazines, as well as some of her own poetry.
But suddenly, she was thirty with a nine-year-old, wearing secondhand clothes, and typing papers for students. Friends in Colorado suggested she return to college, perhaps to study English. One night, during a visit with an old boyfriend who was doing some calculus homework, she looked over his shoulder in the kerosene lantern light — he was living in the tepee where they had once lived together — and corrected some of his figures. In shock, he asked how she knew such math and became the first of her circle to uncover her hidden past: SCIENCE. That’s it, he proclaimed. That’s what you must go back to school to study. So she did.
Alphabetically browsing a list of available majors in a University of Colorado catalog, she stopped at astrophysics and embarked upon a ten-year plan. She began with astrophysics, ended up as a math major, re-entered the field of astrophysics as a graduate student, and obtained a doctorate in mathematical physics. Ph.D. in hand — her thesis was about solar coronal loops — she arrived at Bates in 1991 with a tenure-track position in the Department of Mathematics.
Wiry, with smiling green-blue eyes and closely cropped salt-and-pepper hair, Shulman darts around campus in jeans and T-shirts. Sometimes, she wears running shoes; often she does not. On such occasions, one can admire her toenails painted a sparkling blue. “It’s not just to be the aging hippie,” she explained. “I think better when I’m barefoot.”
Because she pursues many interests, she has much to think about. At the forefront of a movement dedicated to changing the teaching of science, she is a founding member of the Calculus Consortium, a group of math educators working toward calculus reform. She is similarly involved with other innovative teaching developments at Bates, including Writing Across the Curriculum (“God created this for me”) in which writing is used extensively in the teaching of science and in uniting the teaching of mathematics with biology. She advises the student group Society for Women in Mathematics and Science (SWIMS) at Bates. “It has been a place for women to gather, for whatever reason. The talk is nonstop,” she said.
Another primary concern is criticizing the traditional presentation of scientific principles as indisputable truth. The approach — analyzing and questioning what is traditional in a scholarly fashion — is the essence of feminist criticism. In her essay “Implications of Feminist Critiques of Science for the Teaching of Mathematics,” published in the Journal of Women and Minorities in Science and Engineering (Vol. 1. 1994), she wrote: “There is a core of assumptions about science that sets it apart from other knowledge systems and confers upon it a special status. This status is based on the alleged superiority of two fundamental attributes of scientific knowledge: its rationality and its objectivity.”
Yet Shulman warns that mathematics isn’t “a fixed body of knowledge — complete, certain, and absolute.” She says “we have a responsibility to acknowledge that we are also teaching values when we teach mathematics…. When we invite our students to appreciate the elegance of a proof, we should keep in mind that such aesthetic judgments also vary across cultures and genders.”
Although Shulman continues her research in wave propagation, her commitment to feminist critiques of math and science has become her priority. Within the larger mathematics community, according to Shulman, feminist critiques of science are frowned upon. “What I’m doing is not mathematics, but it certainly informs my teaching of math. It’s crucial that I’m a mathematician and do math in order to be credible,” she said of her recent scholarly forays. “I see myself as a bridge in many ways, between men and women, between math and the humanities.”
Shulman has emerged as such a figure, eager to wed the teaching and practice of science with moral values. “Knowledge without wisdom is a very dangerous thing,” she told Mary Morse, author of Women Changing Science, Voices from a Field in Transition (Plenum Press, 1994), in which she is profiled in an interview from a chapter titled “A Brave New World: Women Speak on the Future of Science.”
“Social responsibility and scientists, for instance: There is a lot still embedded in the culture that says, ‘Hey — you’re after a pure pursuit of knowledge. Let somebody else worry what happens with it. That’s not your job. In fact, that’s why there are people trained in political science. Your job is just pure pursuit of knowledge, and science is valuefree, and that’s what’s so cool about it.’ There’s a delinking of values and science, which I think is first of all impossible and not true, and leads to very dangerous kinds of knowledge.”
Shulman maintains that “the classical tradition breeds values out of you in math and science. Compassion is weeded out. The culture breeds it out of you, and it’s no accident either,” she said.
A great deal of anguished consideration preceded the switch from traditional scholarship to feminist criticism of math and science. On pre-tenure leave in 1994, she debated switching gears. She concluded that she could not pursue hard mathematics and the history and philosophy of science and mathematics simultaneously. “My contribution won’t be to leave a poem or a theorem,” she said. “I’m looking for common ground, the common denominator in human beings,” she said. “Being a pioneer in spirit, I see an opportunity to make a mark going where no one else goes, to this empty area. Most scholars doing this kind of research are not pure scientists; instead, their fields are the history of science, philosophy, or anthropology.”
Like a number of her colleagues, Shulman received a 1994 Mellon Professional Development Grant from Bates in support of specific teaching and research projects during a professional leave. Unlike many other recipients who obtained backing for a single project, she pursued a multitude of proposals: research on wave propagation; collaboration with a colleague to develop a model for the flux of large objects through the solar system; continued research in the history and philosophy of science (feminist critiques of science, in particular); and an investigation of successful undergraduate research programs in mathematics at colleges like Bates.
Indeed, Shulman envisions herself as “an existence proof, a role model.” In her most recent Statement on Teaching, she wrote, “I see my role in the classroom as both coach and cheerleader. I am firm in standards and caring in my approach. I am present as a consultant, guide, moderator, and role model.”
In 1994, as a testament to her success with students both in and out of the classroom, Shulman received the Kroepsch Award for Excellence in Teaching, an annual distinction bestowed upon a Bates faculty member. “I cried,” she said, “because it’s student-initiated.”
For Shulman, the accolade confirmed a colleague’s oft-voiced insight: “Human beings have three basic needs: food, sex, and recognition.” As she repeated these pearls of wisdom, she added, “It’s really true. I work really hard, but there is lots of self-doubt, especially because I am trying lots of innovation. The award continues to help when I’m wracked with self-doubt. It helps me to go on taking risks. The feedback and the bonding with my students sustains me through all the hardships; that’s the lifeblood of my existence. Scholarly life is personally satisfying — I’m a math nerd, pens in pockets — and I could see becoming a hermit, piled up with books. But I can’t get any of the satisfaction I get with students out of scholarly work.”
Read the words of a student who nominated her mathematics professor for the Kroepsch Award on the basis of such inventive educational technique: “Picture this: Your first day of class, and the professor walks in with six rolls of toilet paper. The first day of Mathematical Modeling she gave us each a roll of toilet paper, and we had to figure out how many pieces of toilet paper were on the roll without unrolling it. Odd? Yes. Useful? You bet. The purpose of this assignment is to teach us that the use of mathematical models is vast and frequently very difficult.”
Kelly McDonald ’97 majors in both math and philosophy. In response to encouragement from Shulman, he presented a paper last fall at the Mathematical Association of America (MAA) regional meeting in Salem, Massachusetts, on “Rotating Cylinders as Crude Aerofoils.” Next fall, he plans an independent study with Shulman on “The Philosophy of Math,” a subject he decided to tackle after making a reference to the philosopher Martin Heidegger in Shulman’s class. “She was all over it. She loved it,” he remembered. Shulman immediately shared two papers with him that she had written on the philosophy of math, a response which, McDonald said, is quite characteristic of her. “In class, when a tangential subject comes up, she says, ‘Come to my office, and we’ll talk about it,’ and she really means it. She epitomizes the attitude that we’re in college not to get a degree but to learn,” he said.
Bates senior David Ferrone is part of a joint program with Dartmouth College, where he will receive an engineering degree in 1997. “You can do really well at Dartmouth if you find out what the professor is interested in. It’s sort of a scam,” he said. It’s preferable, he says, “if you can find something you’re interested in and learn about it. That’s the best.” And that’s just what happened in a modeling course with Shulman, where Ferrone prepared a paper on the mechanics of snowboard turning. “She helped me to see what the problem was. One of the things she reiterates is that math doesn’t have to be a hard, hard science, a reduction to an ideal. There’s value in understanding a situation,” he said. “I wouldn’t have had an opportunity to give this paper in any other course. Lots of teachers are impressed by things that imitate their own values or beliefs. She comes closer to being impartial,” he said.
During her modeling class last fall, Shulman devoted two full sessions to the subject of ethics and commented on her disapproval of divorcing ethical considerations from pure scientific research. “I disagree strongly with that,” she informed her students, “but you’re free to disagree strongly with me.”
Shulman takes a very aggressive approach in her teaching. “It’s not passive,” she said.
A veteran practitioner of the martial arts, with a black belt in Tae Kwon Do and a first kyu in Aikido, she brings a large measure of internal discipline to the classroom. “I need to be engaged with what I’m doing while I’m doing it,” she said. “I’ve got nothing against entertainment, but I’m not there to do it to you, I’m there to do it with you. If you’re drifting, I’m going to reel you in. I try to be and am fairly successful at determining moment to moment temperature. I take the pulse.”
“It’s chaos,” Shulman said affectionately of her course in Real Analysis, described in the catalog as “an introduction to the foundations of mathematical analysis….a rigorous treatment of elementary concepts such as limits, continuity, differentiation, and integration.”
Math wimps beware. Shulman acknowledges that students consider it “a bear of a course,” but the description belies what one finds upon entering the classroom. Chaos, indeed.
She teaches the straight math but stresses equally the other side of the mountain. “I want them to think about who came up with these theorems. What motivated them? Was it a headache? Or a mistake? I’m not Whiggish in my view of history,” she said.
She counsels students to be patient in their work. It took mathematicians some three hundred years to come up with some of these aphorisms. “You just made the same mistake that Cauchy made. You’re in great company!” she might counsel one of them, in reference to the esteemed mathematician’s “wrong proof.”
It’s late on a Tuesday morning and Shulman, just back from a week-long teaching methods conference, seethes with energy to cover all the material on her agenda. Poised to begin, she holds a hasty sidebar conference with a student about a math project and compliments the young woman. “You have four or five really creative ideas,” she says. As equations go up on the blackboard, Shulman tends to answer student questions with inquiries of her own. “What do you mean?” she asks one young man. “What’s implicit about what you’re saying?” To another student’s suggested equation she retorts in a friendly but challenging tone, “Why would you look at that? I don’t understand.” She waits for an answer, not just from him, but from any one of them. When she doesn’t get one, she cries out: “HELLO! Are we here or somewhere else?” Sensing an air of hesitancy in their silence, she is willing to provide a bit of direction. “What’s the anti-derivative?” she asks, a touch of urgency entering her voice. “All right,” she says as she slaps the blackboard. “I’m going to make it explicit this time.”
She projects authority in a good-natured way, but remains humble and willing to stand corrected with benevolent aplomb. “I take it back, I’m wrong. Temporary insanity,” she pleads after providing an incorrect answer.
The equations continue. “I want to give you this powerful way of reasoning,” she announces as she introduces the concept of “asymptotically equal” to assist them in their work. She reassures the class that the equations will only get easier to solve. “I had teachers who not only made me walk barefoot to school in the snow but gave me hundreds of these to do as well,” she says. “You’ll be able to eyeball these.”
Answers aside, she emphasizes process. “I’m trying to give you a broader picture, a pattern, methods of reasoning,” she calls out as she lopes from one side of the room to the other. Two women in the front row are quietly conferring in steady whispers. She addresses them once and then again. “What’s the question? If you’ve got a question, I’m sure at least ten other people have it,” she says. There are thirteen students in the room. “What’s confusing you?”
“Never mind,” answers one of them.
Undaunted, Shulman replies, “What was confusing you?”
“I wrote down the wrong thing,” the student admits sheepishly.
“I hate when that happens!” Shulman says, serving up some friendly comfort.
But the whispers between these two continue, and Shulman interrupts them once more. “Share with us what you’re saying,” she implores as she commands the rest of the class: “Somebody help. Look it up.” Together the group tackles the problem, finally arriving at an answer. To encourage the whisperers, she says, “That was a good question. It helped clarify.”
After the class breaks up into small groups, one of the two women, in a bolder fashion, raises her hand to say: “I don’t understand.” Shulman answers, “So when I said a few minutes ago, ‘Does everybody understand?’ that would have been a good time to speak up.” Math cum therapy. She manages to conduct this psychological work as an integral part of real analysis, sitting peacefully atop her desk one moment, dipping, then dancing across the floor the next. “What’s a clever way you might take a derivative of this? It’s a chain rule,” she explains before breaking into a chorus of “Chain of Fools,” exposing the rich ore of sixties culture that runs through her veins.
“Let us admire this problem,” she says. “.9999… = 1” goes up on the board. “Do you accept it?” she asks with glee. When one young man responds affirmatively, she counters with a jab. “You’veseen it before, but did you ever question it? These look like two very different numbers to me.”
“Barely,” another student answers.
“Barely, BUT!” she cries out. “You should feel a little uneasy about this. If I had a million dollars and was offered $999,999, I would not be happy with the exchange.”
Fired up, she asks, “What three things did I teach you?” Again, no answers. She pantomimes, then follows with a grandiose mouthing of “read my lips”; in conclusion, she whacks both blackboard and table. “I know I made this joke before, but the most important thing I learned to do in college was to read.”
Actually, Shulman is not joking here. From her perspective, reading and writing one’s way through the sciences is an integral part of educating future generations of professionals. “I see mathematics as much more than a bag of tricks. It is a way of thinking that enhances one’s insight, understanding, and ability to critically evaluate information and relationships,” she said.
Abigail Gallup ’96, a physics major, said, “It’s definitely not your traditional course. It doesn’t get boring. I don’t have to worry if she knows what she’s talking about because she definitely does. She’s definitely a role model.”
“How’re you doing,” a student asks her one afternoon at the start of class. “Integral over time good,” she responds.
The ability to pursue such innovation impresses a number of her colleagues. Georgia Nigro, associate professor of psychology, points out that Shulman “has the rare capacity to bridge the huge gulf between science and everything else. She’s willing to experiment.” She compares Shulman with the mathematics professors whose classes she attended as an undergraduate at Brown: “They were such jerks, such sycophants. It was just torture to listen to these dorks, and Ilike calculus,” Nigro said.
Room 213 in Hathorn Hall barely seems to contain the radiant energy that emanates from Shulman and the students who visit her tiny lair. On one wall-sized blackboard, the chalk dust of hastily scrawled math proofs glistens in the sunlight. A poster of Alfred Einstein consoles a visitor with the soothing thought that whatever math problems she has couldn’t possibly be as bad as his; a second poster, equally prominent in its display, profiles the professional history of Emmy Noether, a pioneer in Modern Algebra, whose lifetime bridged the nineteenth and twentieth centuries.
Cluttering her office are the obligatory computer, books, chairs, and personal photographs, including pictures of author Grace Paley — a friend — and a very young Shulman delightedly nuzzling her daughter, Hatha, then two years old. Today, Shulman is working with Marko Radosavljevic, a senior from the former Yugoslavia, whom she and Eric Wollman, professor of physics, are jointly advising on his honors thesis, “The Vibrational Modes of the Grain Plasma and Its Implication to the Creation of Galaxies.” Shulman especially enjoys the work for this confluent physics and math project. “It’s delightful to share research interests through the work of a student,” she said.
The power of interdisciplinary sharing is almost aphrodisiac for Shulman, who continually seeks ways to merge her identities as an artist and scientist. At age forty-four, she finally feels comfortable with the synthesis she has produced. In no small part, Shulman credits the egalitarian Bates environment for securing peace in “the two camps warring, the research versus the poetry, the left brain/right brain dichotomy, the humanities and the sciences, the qualitative and the quantitative,” she said.
Not long after her arrival in Lewiston, in response to a how-are-you-adjusting e-mail query from her thesis advisor, Ellen Zweibel, at the University of Colorado, Shulman responded electronically with great enthusiasm about all the interdepartmental friends she was making at Bates. This was the sober response from Colorado: “I was here for ten years before I knew anybody outside of my department.”
“That’s the difference,” Shulman said. “Bates is providing me with myriad opportunities to focus on who I am as a human being and scholar.” At Bates, she says, education is for the faculty as well as the students. “There’s too much going on here. That’s the way Bates supports me. An incredibly rich intellectual life is possible here. For me, it’s like I died and went to heaven.”
Shulman frequently accepts invitations to visit classes outside of the math department. In an interdisciplinary methods class in which students interviewed scientists, she spoke to Nigro’s psychology students about her own professional development. With these same students, who had spent considerable time considering the role of the scientific community in the study of AIDS, she discussed the function of mathematics in the controversial Tuskegee Experiment (where researchers sterilized black men during the project). In a class called “The Rhetoric of Nuclear Culture, 1939-1964,” taught by Professor of Rhetoric Robert Branham, she joined Bates poets Robert Chute (who’s also professor emeritus of biology) and Robert Farnsworth to read poems — their own and the work of others — about “Imagining the Nuclear Holocaust” to illustrate the belief that artists speak for the culture at large. In this same course, on another occasion, she spoke about her experiences as an antinuclear activist who sat on train tracks to protest the installation of a nuclear facility in Rocky Flats, Colorado.
During her 1994 leave, Shulman gave a talk on “Ethics Across the Curriculum: Teaching Ethics in Science and Math Classes” as part of a Science, Technology, and Ethics Series. Charles Nero, assistant professor of rhetoric, attended the presentation. “I couldn’t possibly imagine having a conversation with a scientist about gender and knowledge,” he said. “I was rather surprised and thought to myself, ‘Scientists don’t really do this.’ Then I realized that these people ask these kinds of questions, too,” Nero said of her lecture, which in part explored her decades-old fascination with the moral dilemma faced by the Manhattan Project atomic scientists. Nero’s scholarship and teaching place an emphasis on “the coherence we maintain in our lives through metaphor.” Through discussions with Shulman, he has marveled at the importance of metaphors in the production of scientific knowledge. “I am fascinated by our unpredictable, nontraditional approaches to our scholarly lives,” he said.
Shulman has also found a soul mate of sorts in Judith Isaacson ’65, who taught math at Lewiston High School and at Bates as a lecturer before serving as dean of students. In 1977, Isaacson resigned to begin writing Seed of Sarah, an acclaimed autobiographical account of her experience at Auschwitz and later as a slave laborer for the Nazi war machine. Mathematics and writing link Isaacson and Shulman; the Holocaust of European Jews joins them in still another, unspoken, fashion.
“For my whole life, for no reason I can state explicitly, the Holocaust has been a key experience, my moral compass. I’ve always come back to it,” Shulman said. She grew up as an American Jew in a time when details of the Holocaust remained unutterable; not until years after the fact did she learn that her father was an American liberator of a satellite concentration camp in Germany. Her fascination with literature about this tragedy seemed shameful to her, “like an obsession. I always felt like it was pornography, like I had to read it in secret. I read the Diary of Anne Frank a million times, and people would always say, ‘Why are you so obsessed? Don’t be so morbid.'” Shulman often wondered, into adulthood, how she might have behaved in such a situation, and how such circumstances can and do recur in the presence of a world community.
“Meeting Jutka (Isaacson’s Hungarian name) was like coming out in a weird way,” she said. In fact, when Shulman cut her hair quite short last summer, she could not bring herself to show Isaacson. After several weeks of not hearing from her friend, Isaacson called and discovered that Shulman was worried her appearance would remind the older woman of Auschwitz. Isaacson insisted that she come anyway. When Shulman arrived, “she had put on very long earrings, even though she was barefoot,” said Isaacson, who greatly admired the haircut. “It’s tremendously becoming; it brings out her very witty features. Bonnie always goes to extremes, but very pleasing extremes,” she said. The haircut reminded her nothing of Auschwitz — “we were in rags” — although the bare feet did, something she did not mention.
In fact, the two women don’t discuss the Holocaust. Instead, they base their friendship on mathematics, poetry, and gardening. “I admire her so much,” Isaacson said. “She is a true scholar who is thrilled by her work. She follows a path I did not have the opportunity to pursue. Bonnie knows exactly what she wants — things don’t just happen to her. It’s a life I might have chosen for myself if I had had the choice. When Bonnie writes a poem, it is something I would have done. I relish that. To me, mathematics has always been spiritual, philosophical, and poetic, yet I’ve never expressed it” the way Shulman has.
Isaacson also admires Shulman’s work on science and gender. She shares Shulman’s concern “that math be used in a morally correct way. Bonnie has to do what she is excited about. She has to do what she is 100 percent interested in. She’s not swayed by others’ opinions. She does what’s morally right and intellectually challenging.”
While pursuing her master’s degree at Bowdoin in the mid-1960s, Isaacson encountered a morally offensive word problem presented by the professor in a course on game theory. “I was so outraged that I almost decided not to teach mathematics,” Isaacson said. Years later, knowing of her Bowdoin encounter, Shulman shared with Isaacson a textbook problem used in a teacher’s handbook printed in Nazi Germany:
“Problem 200. According to statements of the Draeger Works in Lubeck, in the gassing of a city only 50% of the evaporated poison gas is effective. The atmosphere must be poisoned up to a height of 20 meters in a concentration of 45 milligrams per cubic meter. How much phosgene is needed to poison a city of 50,000 inhabitants who live in an area of four square kilometres?” In a subsequent scholarly essay, Shulman reflected on the morality of mathematics, that supposedly value-free discipline. “Word problems are notorious for instances of sexist, racist, and other more subtle cultural biases,” she wrote.
“As a kid I wanted to be named Sarah,” says Hatha Swanson, now a twenty-three-year-old certified massage therapist who lives in Portland, Oregon, where she is studying to be a naturopathic doctor. She admires some of the same qualities Isaacson sees in her mother. “It’s over my head what she does,” her daughter admitted, but then, “it’s not so much what my mother does but how she does it. It’s more her integrity, on how she’s getting there, what she sacrificed. I utilize her strength by her example. She’s 100 percent.”
Like mother, like daughter. Hatha, an “A” student, repeated a little bit of history by running away from home at age fifteen to follow the Grateful Dead for three and a half years. “I feel like I broke her heart, but it’s mended,” Swanson said. “We’ve reconnected on a different level through science, through the issues of women and science. It’s the question of whether women are competent in the field. My mother proved that by being at the top of her class, not just getting by.”
Like most academicians, Shulman is busy and then some. She has an image of herself as one of the performers who used to appear with some regularity on the Ed Sullivan variety show, throwing plates in the air and spinning them by holding sticks in their mouths; the tantalizing possibility lingers, naturally, that all the crockery will come crashing down.
Recently, Shulman sent some quotations concerning mathematics, poetry, and art to Isaacson. Among them was this quote from the Greek philosopher Proclus: “This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect.”
This, therefore, is Bonnie Shulman, shimmering with the possibilities of discovery.
“Where Things Happen That Don’t”
As the final assignment in her course “Calculus for the Queasy,” Shulman asked students to write a poem. Throughout the semester, the class had explored mathematics in technical terms by producing serious written work on topics such as infinity, incommensurability, and the historical development of the ideas of the calculus. “I wanted to stimulate their imaginations about these ideas as well,” she said. The professor completed this assignment, as she had all others in the course, along with her students and wrote this poem, later published in Humanistic Mathematics Network Journal, No. 8, July 1993.
in fin ity
How can any thing
made up of no thing
Amount to some thing?
(A whole is the limit of
the sum of its parts)
An infinite sum of little bits
each bit a little bit less
until it is less than the least little bit
you can imagine
and yet still less
but never zero
smaller than the smallest
you tell me how small
I’ll tell you how close
and I’ll get even closer
and then get even
How close til I’m actually there?
Do we jump
from here to there
from now to then?
Is time a sequence of moments?
A stream a collection of drops?
What is it waves
in the ocean?
in the boundless sea
where things happen