Review: "Limitless Minds" by Anthony Donato
In 2016 and 2017, Anthony Bonato, a professor of mathematics at Ryerson University in Toronto, conducted a series of interviews with a dozen prominent mathematicians in Canada and the United States. A successful blogger with a large following, he first published the interviews on his blog, The Intrepid Mathematician, before recasting them in amore traditional book format. The twelve chapters, one for each interviewee, all include a biographical profile and a selection of photographs and graphics. While each interview largely poses the same set of questions, such as “How and when did you discover mathematics?” and “What research topics are you currently working on?” and concluding with “What do you see as the future of mathematics?”, each interviewee has a compelling and unique story.
Although Bonato’s book is primarily aimed at readers already invested in mathematics as a career, there is much social, political, and institutional history to be mined from these first-person accounts of life in the mathematical trenches. Emory University’s Ken Ono, whose research program includes number theory, algebra, and combinatorics, grew up loathing mathematics, despite the impressive ability in the subject he displayed in grade school. He recalls his father getting “a job as a member of the Institute for Advanced Study” in the 1950s, thanks to an invitation from André Weil. He adds, “My parents were not embraced when they came to the US. In fact, there were terrible things that happened to them because they were Japanese—they were considered the enemy. . . . [They] thought that the only way for us to succeed was for us to be great mathematicians or scientists or musicians. . . . I grew to hate math. I knew I was good at it, but by the time I was in high school, I hated math as it represented everything I did not want to be. It represented not having freedom.” He credits number theorist Basil Gordon, his UCLA advisor, with teaching him “to see beauty in mathematics and I haven’t turned back since”.
Not surprisingly, the notion of beauty in mathematics is a recurring theme of this collection. Asked what inspired her mathematical ideas, Princeton graph theorist Maria Chudnovsky says, “Things that appeal to me aesthetically. It could be a problem that seems beautiful or a concept that seems beautiful.” She elaborates, “There is math that is motivated by physics, chemistry, or engineering. That is somehow separate.
In much of math, you are just looking for the most beautiful thing you can think of. And only that determines if something is interesting or not.” Duke University professor Ingrid Daubechies offers this perspective: “Think about what it means to find something beautiful. For me, I recognize in myself a feeling of joy, awe, and reverence. It gladdens the heart and lights up the eye. Mathematics is beautiful as it elicits the same emotions in us.” Izabella Laba, a Polish-Canadian mathematician at the University of British Columbia, hedges her answer a bit: “There is a role for [aesthetics], but it’s not completely clear what is should be. . . . It might be a little bit similar to architecture. . . . The building has to stand upright . . . and at the same time, it should also be pleasing to the eye.”
One of Bonato’s goals is to inspire students to consider mathematics as a profession. Asked what advice he would give young people studying mathematics, Harvard number theorist Barry Mazur confidently answers, “The first thing I hope people learn (this applies to both undergraduates and graduates) is to respect their native curiosity. When you are curious about something, then you can ask questions that matter to you, and that’s extremely important. . . . Practice the art of understanding and respecting your own questions.” Asked specifically about advice for women, the six female mathematicians in this volume offer more nuanced responses. “For whatever reason,” says researcher Jennifer Chayes, “women tend to be less confident than men are. . . .
Women tend to take themselves out of the running before they should.” Like Chayes, Ingrid Daubechies tells it like it is: “If you are a young woman, you should not believe anyone who tells you that mathematics is not a job for women. To become a professional mathematician, you have to love mathematics. As an academic mathematician, the thing you will get the most recognition for is your research, which can be a challenging thing. . . . Research has fantastic highs that are not very frequent, and they don’t last a long time. If you love mathematics, then that is good enough for you. You can be a good mathematician as a man or woman.”
Oral histories have come into their own in recent times. Bonato’s contribution to the genre is a worthy addition to the mathematician’s bookshelf.
Published in MathSciNet, May 16, 2019
Remembering Professor John Hope Franklin
May 24, 2009
When John Hope Franklin entered the classroom, the air seemed to crackle with excitement. He was ready to lecture and we were eager to listen. At least I was, for he was the professor I wanted to be someday: polished, articulate, elegantly groomed, and full of passion and indignation when those qualities were called for. He looked like a man who had important things to say, and he said them without flinching, starting with his evocation of Abraham Lincoln and the many contradictions about him. Franklin’s course on the Civil War at Brooklyn College, which I took as a sophomore in spring 1958, met three times a week, and I faced the same dilemma each time: Should I take notes, or could I simply put the pen down and just listen. Professor Franklin’s lecture on Robert E. Lee was one of the high points of the course. Franklin didn’t just dislike General Lee, he hated everything Lee stood for as a Southerner, and by the end of the hour Lee’s character had been whittled away until nothing remained of it.
I of course contemplated applying for the year-long seminar in American Studies that Franklin co-taught with Professor Howard Hintz of the Philosophy Department. It was limited to 12 students, and I figured I just might make the alternate list. Much to my surprise, when Professor Franklin sent the postcard at the end of the term with my grade, he added a postscript, “Looking forward to seeing you again in the fall.”
The field of American Studies was brand new in 1959; we students had access to a private conference room in the library (although I rarely used it because the room was overheated and put me to sleep). The course was wrapped around a lengthy reading list of primary sources, ranging from Cotton Mather to John Dewey, and lots of Q & A; Franklin asked most of the questions, and Alan Dershowitz, another student in the seminar, aced most of the answers. I seldom dared to raise my hand, but did not entirely escape Franklin’s attention. He would glance around the room and then with a nod in my direction ask, “What do you think, Judy?”
I graduated from Brooklyn College in 1960, armed with a Bachelor of Arts diploma and an insatiable desire to see more of the world. Not long afterward, John Hope Franklin left Brooklyn College for the University of Chicago.
Our paths crossed again in 1968. By then, I had married a physicist, David Goodstein, and had nearly completed a Ph.D in the history of science at the University of Washington. David was on the faculty of the California Institute of Technology, and we were living in Pasadena. In February, David was having lunch at the University of Chicago faculty club before going on to Rome for a year at the University of Rome as an NSF post-doc. He asked his host, the distinguished literary critic Wayne Booth, if John Hope Franklin was in the room. He was. David asked to be introduced, and Booth, not knowing why David should want to meet the august Franklin, reluctantly escorted him to Franklin’s table and made the introduction. David proceeded to send my regards, and Franklin broke into a wide smile, threw his hands in the air, and exclaimed, “Judy Koral! How is she?” Booth visibly relaxed.
Several months later, Franklin came to Rome as a member of the Fulbright Committee and got in touch with us, and we arranged to have dinner at the trattoria in the basement of our apartment house on Piazza Crati. He came by cab, but we drove him back to his hotel, the ultra-fashionable Hotel Eden, not far from the Via Veneto, the preferred street of starlets and movie producer Federico Fellini. Did he like staying at the Eden, I asked. The accommodations were fine, he answered, and then added, “But I detest the fawning and the servile demeanor of the staff, from the doorman to the receptionists.” For a moment, I was back in his Civil War course and glorying in his dissection of Lee.
I never saw Franklin again. Several years ago, David and I stayed at the Eden. It was just as John Hope Franklin had described it.
Remembering Michael Intriligator
July 3, 2014, read by Marcia Goodstein, in Los Angeles, CA.
Who will tell me now which recording of a Tchaikovsky violin concerto to listen to first: the one by Jascha Heiftiz or Isaac Stern? And the little black book, with the list of your favorite restaurants in Moscow, Tokyo, and Washington, DC…where did you put it, my dear friend?
I knew him as Mike, that’s how he introduced himself to my husband David and me some forty-odd years ago at a Caltech cocktail party hosted by Alan Sweezy, one of Mike’s colleagues in the school’s humanities and social science division. There were a great many cocktail parties in honor of Mike and his chic physicist wife in Pasadena that year. We were always invited too, because the matchmakers at Caltech were convinced we would hit it off. It was, in fact, a friendship made in heaven.
Like us, they were a double Ph.D couple. The two-body problem had yet to be identified in the early 1970s, and couples with prestigious PhD’s in different disciplines were few and far between. Mike was always Devrie’s fiercest champion. Also like us, they were the parents of a growing family. We only had two kids, but Mark, our son, had no difficulty matching wits and wisecracks with their four. Marcia was the token female, the butt of many pranks and jokes.
The friendship really took hold in 1974, when David began work on his seminal book, States of Matter. We lived in a small house, and David commandeered the dining room as his writing station and insisted on silence. And so every Saturday or Sunday we would take a day trip with Mike and Devrie, with Kenneth, James, William, Robert, and my two children in their station wagon. And oh the places we went and the things we saw that year—ghost towns, dessert spas, quaint villages, the San Bernardino mountains, anyplace you could get to and back in a day, and always followed by dinner, for one and all, after we returned from our outing. Devrie usually came up with the itinerary. One time, it was a fishery, near Ojai; Mike was the driver but out of the corner of his eye he spied what looked like little red spots on one of his sons. Upon closer inspection, there were similar spots on the other Intriligator boys too. Turned out, we had a carload of kids coming down with chicken pox. We never did get to see the fishery.
David finished his book that year, but our car trips continued, now with our complete families. We went for a week or so to Santa Barbara, San Diego, Lake Arrowhead, Catalina Island, the Mohave dessert and Tijuana, and in particular the fishing villages in the vicinity that specialized in deep-fried lobster. In Mexico, Mike was tasked with finding sweet rolls for breakfast each morning, an assignment that brought a smile and a twinkle to his eye. If our trips occurred during the Christmas break, the station wagon was laden with a week’s worth of Hanukkah gifts, for their kids and ours, not to mention munchies of all kinds.
I remember in particular our family trip to Death Valley—mainly because Kenneth had a festering sore in the palm of his hand that he conveniently forgot to tell his parents about before we set out. We all took turns practicing medicine without a license on that occasion.
Mike enjoyed a good meal, a glass of merlot, and conversation. We had lots of those over the years, from shared Thanksgiving dinners to Saturday night dinners at home to meals at Musso and Frank in Hollywood and in recent years, at the Hilton boutique hotel in downtown LA.
Mike never came to our house or met us for dinner or a concert or the opera without giving us a couple of cassette tapes. He loved classical music, collected records, played them, and recorded, from time to time, some of his favorite pieces, which he then shared with us. He drove a yellow Cadillac, and Devrie would go to great lengths to find him just the right model and year for his birthday. One year, her hunt led her to an estate sale in Beverly Hills: the Cadillac wasn’t the right kind, but there was a closet full of mink coats and that is how I acquired my first fur coat.
He was generous with his compliments, with his money, and with his time.
Academics wander the face of the earth, but no one I have ever met, comes close to matching Mike’s record for long-distance travel. He thought nothing of flying half way around the world, returning a week later, and setting off again within 48 hours for another invited talk somewhere over the horizon. For many years, he had close connections with fellow academicians in the Soviet Union, and while he was treated royally while in Moscow, he had a problem of how to spend his rubles, which had to be spent within the country. On one of his last trips there, he carefully packed a humongous vat of black sturgeon eggs in dry ice, stashed it in his carry on luggage, and headed for home. The next day, the four of us sat around in their home on Foxtail Drive swilling vodka and eating blinis topped with Russian caviar.
We have mutual Italian friends, Franco and Teresa Scaramuzzi. In March 1977, Franco came by himself to Caltech. One evening, we assembled at 140 Foxtail Drive for dinner and when Mike heard that Iacopo, Franco’s son, had turned one that very day, he immediately broke open a bottle of champagne to toast the event in Santa Monica. Some summers later, they came to Rome, and together we all feasted at Franco and Teresa’s home. Mike took an unforgettable photograph of Franco in the kitchen, nursing the spaghetti to a perfect al dente consistency Mike’s photograph has subsequently appeared in more than one respectable scientific journal.
The Italian- Intriligator connection continued to thrive with the arrival in Pasadena of Giorgio Careri, a well-known condensed matter physicist at Rome. Careri’s nephew, a shy young man, was eager to take a Ph.D in economics at UCLA, following his undergraduate degree at the University of Rome. Mike volunteered to take the young man in hand, shepherded his admission to graduate school, and watched with pride when the promising economist, not so shy anymore, took his Ph.D. That young man, Vincenzo La Via, after a successful stint at the World Bank in Washington, DC is now the director general of the Italian Treasury. Mike, in turn, always wanted to meet Paolo Sylos Labini, one of Italy’s best-known economists. On one of Mike’s many visits to Rome, Careri saw to it that the two distinguished economists were properly introduced.
When their boys and our kids went off to college, we took up cruising—Alaska, the Panama Canal, the Galapagos, Greece and Turkey, and our last cruise, two years ago, around the Caribbean.
Mike danced like a pro. When the cruise band would strike up the 1925 jazz standard, Sweet Georgia Brown, the first couple on the dance floor was invariably Mike and Devrie, a joyful pair of ragtime swingers lost in each others arms.
He liked to boast that the first four books he published were written to put his four sons through the universities of their choice. He co-authored his last book with David—on a subject close to David and Mike’s heart—the scientific, political and economic choices the world faces when we run out of fossil fuels and global warming renders the planet uninhabitable—whichever comes first.
When the question of whether they should dedicate the book to someone came up, Mike thought for a moment, shrugged his shoulders, and said, “my students.” His students, his family, and the rest of us are all a little poorer today.
Remembering Giorgio Careri
Read at Careri’s memorial service, held in the Academy of the Lincei, Rome, on November 19, 2010.
Several summers ago, along with Franco and Teresa Scaramuzzi, we drove from Grottaferrata to Ponte Milvio, north of Rome’s center, to have dinner with Giorgio and Lina Careri at one of Giorgio’s favorite neighborhood restaurants, an ancient trattoria run by a formidable woman who seemed to know every one of her diners by name. The four of us arrived late, thanks to unexpectedly heavy traffic, but Giorgio was in high spirits as he greeted us. He led the way to our outdoor table, long and narrow, strategically located near the kitchen, and immediately began ordering, for himself and for us. Prosciutto and melon, gnocchi in tomato sauce, pizza Margherita, and several liters of local white wine. (That’s one of the things I remember about Giorgio.
Whenever we went out to eat, even if the Goodsteins happened to be the hosts, he always did the ordering for the entire table. On this occasion, it was hot and the patio was crowded, the weathered and gnarled vine overhead doing little to dampen the noise level. The owner, who waited on us herself, saw to it that Giorgio was served first. Giorgio also urged us to sample the baked onions, grilled eggplant, olives, and tomatoes from the buffet table set up in one corner of the restaurant. After the meal, we hugged and said our goodbyes out front, and as he was leaving, Giorgio turned to me and said, with a fond smile and extravagant wave of the hand, “Va avanti, va avanti.” Go on. And so we must.
It was Bill McCormick who introduced us, indirectly, to Careri. Bill had joined the University of Washington’s Physics Department in the early sixties, fresh from a two-year stint as a postdoc in Italy. He urged David, a newly fledged U of W. Ph.D, to apply for a National Science Foundation fellowship in Careri’s lab at the University of Rome, “La Sapienza,” which he promptly did. The NSF fellowship and the offer of a postdoc position at Caltech arrived within days of each other. With Caltech’s blessing, David accepted both and notified Careri that he would be spending the following year, in his lab, beginning that February.
We moved to Pasadena in September, 1966. Four months later, we flew to New York on the first leg of our journey to Rome, a little concerned that Professore Careri hadn’t confirmed our travel plans. The day before boarding our TWA flight to the Eternal City, we received a telegram from him (“Va bene”), which doubled our Italian vocabulary on the spot and bespoke a man who didn’t waste words—or lira, for that matter.
Our first night at the Villa Fiorita, the pensione where Careri had reserved a room for us, was daunting. Nobody there spoke English, and we didn’t know how to ask for warm milk for our daughter Marcia, age 2. We were beginning to think we had made a big mistake. And then Giorgio came bounding into our little room, waving his hands, smiling broadly, and declaring that it was time to attend the opening of a gallery show in Trastevere featuring the needlepoint work of an artist who happened to be a sister of Lina’s. The show, he noted, was directly across the street from Rome’s Regina Coeli prison, where the Germans had incarcerated Lina’s father, a member of the Resistance, during World War II. I decided to go, leaving my weary husband, who wasn’t much interested in needlepoint, to care for Marcia. On the way, we drove up the ramp to the Campidoglio (you could do that back then) in Giorgio’s little Fiat (of which he was inordinately proud), in order to admire, by moonlight, the bronze statue of Marcus Aurelius astride his horse (the original, not the copy), and then we sped off in the direction of the Tiber. Of the art show I remember little, save the crush of elegantly dressed gallery goers, downing champagne and smoking copiously all the while. And, of course, being introduced to Lina, a physician in the city’s public schools, who was an oasis of calm and comfort in the midst of the room’s high-pitched excitement.
On the way back to the Villa Fiorita, we stopped at Piazza Navona, circled the square, and then got out of the car for a closer look at Bernini’s fountains. “So this is what Rome is all about,” I thought. Pure magic, and Giorgio Careri was the magician, pulling the strings, parting the curtain, and making us at home in his city. He would also delegate several students in his low-temperature group—Turi Cunsolo, his wife Lucia, and Bruno Maraviglia—to look for a suitable place for us to live. In no time, they found us a rental flat on the top floor of an imposing 1930s apartment building at Piazza Crati, 4, complete with a wraparound terrace overlooking an outdoor vegetable and cheese market, open Monday through Saturday mornings. The proprietors of the restaurant in the basement, Stell’Alpina, helped us deconstruct the near-illegible hand-written menu and saved us from starvation on more than one occasion.
That August, everyone in Giorgio’s lab went on vacation, and he and Lina invited us to spend a week in Stintino, then a tiny speck of a fishing village in the northwest corner of Sardinia. He arranged for us to rent the house of a fisherman’s widow and to take our dinners at Silvestrino, the only hotel in town. Dinners were good (Giorgio introduced us to spaghetti alla bottarga). We would have after-dinner drinks on the patio with their friends, who seemed to us to be the cream of Italy’s intelligentsia; conversation ranged from techniques for frying peppers to how to dress a salad (ought one to add the oil or the vinegar first?) to the Free Speech Movement in Berkeley, California—and greatly improved our Italian.
The following January, shortly before we were to return to Pasadena, Careri invited me to give a seminar in the Physics Department of La Sapienza on the history of the quest for low temperatures. However, that month saw the occupation of the university’s physics building, and I froze in my tracks when I encountered a large group of bellowing, sign-waving physics students bent on discouraging anyone from entering. But Careri spotted me from the vestibule, rushed outside, took me by the hand, and marched me past the mob. He escorted me to the lecture hall and then went door to door, telling everyone the seminar would go on as planned. If he felt any fear that afternoon, he kept it well hidden.
Many years later, Careri received one of Caltech’s coveted Sherman Fairchild Fellowships and spent a year at Caltech, along with Lina and their three children. Giorgio, I remember, marveled at the library system, which allowed him to place requests for photocopies of journal articles and have them on his desk several hours later. He had already become interested in the role of water in biological systems and found it easy to meet and interact with kindred spirits on the campus. Caltech was clearly as magical for Giorgio Careri as the University of Rome had been for us. We had come full circle.