Philsang Yoo heard a patter of footsteps behind him, turned away from a blackboard cluttered with mathematical formulae, and saw that three more students had entered the lecture room. His eyes widened. “I didn’t expect so many,” he said, chuckling uneasily. By now about thirty people had crowded inside, and several of them seemed to be compulsively counting and recounting themselves, unable to believe that so many Yale students would want to attend a public lecture on “Quantum Field Theory for Math Majors.” Yoo is a professor of mathematics; in front of him there were mathematics majors, physics majors, students who had taken Directed Studies, two amateur poets, a journalist, a gray-bearded professor who intermittently pulled out an inhaler, and, sitting quietly in the back row, a junior with blue eyes and hair the color of sunburnt hay who would, in a few days, be flying back to Oxford to study mathematics far away from Yale.
Connor Halleck-Dube ’19 is the sort of student that Yale has been eager to attract for decades. He’s someone who knew something about general relativity before stepping foot on campus, who was comfortable with proof-based mathematics before the first lecture of Math 230. There are many reasons he decided to study abroad in his junior year, one of which was the sparsity of Yale’s offerings in abstract algebra.
“Why don’t we have a class in homological algebra?” he later asked me over dinner in an incredulous tone. “That’s really important for anyone who studies anything in algebra.” Oxford does have an undergraduate course in homological algebra, along with a mathematics faculty who, in Connor’s opinion, commit far more attention to teaching undergraduates than the faculty of Yale.
After Yoo’s lecture, with several other students gathered around, Connor put his feet up on the chair in front of him, leaned back, and began describing one of the most memorable dinnertime conversations he had overheard at Oxford. He had been sitting at a table in St. Catherine’s dining hall. Nearby, a group of senior tutors had been discussing how they could shape the incoming class of math majors. There was a particularly gifted student in the new class. “How do we structure this course to challenge this student while not leaving all the others behind?” one of the tutors had asked. Connor had listened to the conversation, entranced and dumbfounded.
“I mean, can you imagine Casson and the other senior math faculty at Yale sitting down and saying, ‘How do we want to shape the math majors in the Class of 2019?’” Connor asked us. There was a chorus of muffled laughter. It wasn’t the sort of thing any of us had overheard or could imagine overhearing at Yale. As a senior majoring in mathematics and physics, I have never taken a course in mathematics taught by a full professor. In fact, I had never spoken with Andrew Casson, the director of undergraduate studies (DUS) in mathematics from 2012 to 2018, before interviewing him for this article.
***
Five years ago, as a junior in high school, I didn’t plan on applying to Yale. I was interested in mathematics, physics, and engineering. I daydreamed about proving the Riemann Hypothesis or spearheading the nanotechnological revolution in Silicon Valley. Yale, I was sure, wouldn’t be right for me. Then I began receiving personalized emails and letters and brochures: assurances that modern-day Yale was right—right for any STEM major, far more right than Stanford or Harvard or MIT.
In 2007, former Yale University President Richard Levin set a goal for the university: an incoming class that was 40 percent STEM. In an interview with the Yale Daily News, Ayaska Fernando, the former director of STEM recruitment at Yale, said that in 2009 the admissions department began sending a Yale brochure to every student who scored a five on an AP Physics exam. In the same year, members of Yale’s admissions department began traveling to parts of the country known for producing strong STEM students to host specialized “STEM forums.” In 2011, Yale inaugurated Yale Engineering and Science (YES) Weekend—an admitted students event designed to convince students with strong technical skills to matriculate. In the spring of 2012, the university reached Levin’s forty-percent benchmark, and today the proportion of STEM majors is close to fifty percent.
Fifty percent, that is, among the matriculating pre-frosh. Among the seniors, it’s closer to thirty.
Why is the attrition rate so high in STEM? Andrew Casson told me that the mathematics department currently has a record number of majors. “We undoubtedly have more students, but we don’t have more faculty,” he said. “On the whole, I would say we’re more understaffed than we were [a decade ago].” Roger E. Howe, a former mathematics chair, told me that the department now relies on Gibbs Professors—post-docs with a three-year teaching contract—as a direct result of the longstanding shortage of tenured professors. “We had a couple of losses and retirements, and then we were seriously undermanned,” Howe said. “And I felt that the administration didn’t take the situation as seriously as it should have.”
Ronald Coifman, the Phillips Professor of Math and Computer Science, was more blunt. “There used to be twenty-five [mathematics professors]. It dropped down to twelve. Now it’s moving back towards twenty-five. We’re not moving up; we’re moving back to ground level.” Coifman’s assessment of the situation in applied math was even harsher. “Applied math is not just understaffed—it’s underwater. It doesn’t really exist. The university likes to say it does.”
Corey O’Hern, the DUS for mechanical engineering, told me that the number of junior and senior majors in his department has quadrupled since 2004. The number of ladder faculty (tenured or tenure-track instructors) is less than it was in 1996. As DUS, O’Hern is responsible for providing academic advice to the roughly 100 junior and senior mechanical engineering majors at Yale. He is one of only 13 ladder faculty in the Department of Mechanical Engineering and Materials Science. “We’re on the low end of small,” he told me. “If you increased the faculty, we’d still be small. You start losing intimacy at maybe thirty faculty.”
James Slattery, the associate provost for research at Yale, declined to comment on understaffing. Slattery remarked, though, that Yale has invested in upgrading campus facilities, including a renovation of Sterling Chemistry Lab and the construction of the Center for Engineering Innovation and Design—an interdisciplinary hub for student design projects. “STEM continues to be a focus for Yale and will continue to be for the foreseeable future,” Slattery emphasized.
Several senior faculty told me that understaffing almost certainly contributes to the high attrition rate among undergraduate STEM majors. I spoke about the twin issues of attracting and retaining STEM majors with Stephanie Spear ’19—a senior astrophysics major who last year served as head science tour guide for Yale Admissions. Both Spear and Colin Hill ’19, last year’s head engineering tour guide, told me that on tours they always emphasize the personal attention STEM students receive at Yale: the small classes, the ample opportunities for independent research, the close relationships with faculty members facilitated by the remarkable student-to-faculty ratio. “Even on our STEM tours themselves, we really try to emphasize the small-group environment,” Spear told me. Engineering and science tours are designed to be significantly smaller than regular campus tours.
Spear admits, though, that she may be painting an overly rosy picture of life at Yale as a STEM major. The high proportion of the incoming class planning to major in STEM, Spear told me, is a tangible result of Levin’s changes. “As far as retention goes,” Spear said, “I think the bigger question is, ‘Why are we not retaining these students over the course of four years?’”
***
When Alex Gartner ’19 visited Yale over YES Weekend in the spring before her first year, she quickly (?) heard about the small classes and close relationships with professors she would enjoy as an engineering student. She spoke with chairs of departments, received a likely letter, and was told repeatedly about the celebrated one-to-one student-to-faculty ratio in engineering.
It’s unclear how the admissions department concocted this statistic. When I told O’Hern about it, he was incredulous. And when Alex arrived at Yale the following fall and took Multivariable Calculus for Engineers (ENAS 151)—a 50-student introductory course required for most engineering majors—it was hard not to notice a discrepancy between the picture painted in YES Weekend and her actual experience as an electrical engineering student at Yale.
“At the beginning, you could definitely see that the professors didn’t care,” Alex said. “Teaching was a side job that distracted from research.” The professor for her calculus course initially did not offer office hours; later, under duress, he agreed to hold them for half an hour after each class. The course was an ordeal. Online evaluations from Yale Course Search include the following: “The class was basically self-taught,” “I would not take this class again even if I was paid to,” “Take it with a different professor. You might want to still be an engineer if you take it with someone else,” and, “Please God don’t take this course.”
By Alex’s senior year, only one professor had spoken with her about graduate school or career opportunities. She has consistently had to find summer internships on her own. “I’m now questioning whether or not to pursue engineering after school as a career,” Alex told me. “I feel severely unprepared for engineering in the real world, particularly when I hear about some of the engineering work friends at other schools have done.”
There are many prospective Yale STEM majors who, after an intensely unpleasant experience in an introductory class, decide they don’t like STEM as much as they thought they did. Take Charlie Romano ’19, who started out as a double major in music and biomedical engineering. The biomedical engineering major has an extraordinarily extensive list of prerequisites; over his first two years, Charlie took introductory courses in chemistry, biology, and mathematics, most of which had over 100 students. Finally, after a full two years of preparatory coursework, he took his first class in biomedical engineering. “Probably the worst class I’ve ever taken,” Charlie reflected, grimacing slightly at the memory. “[The professor] was a really brilliant guy, but he didn’t care about teaching at all. The definition of dispassionate.” The semester afterward, Charlie dropped the biomedical engineering major and decided to focus exclusively on music. In music, needless to say, he is not taking 100-person classes.
In moments when the university has faced fiscal troubles, STEM departments have often been the first to face budget cuts. The origins of the understaffing issue in math, engineering, and several other STEM departments can be traced back to just such a moment twenty-seven years ago. There are many departments with stories to tell about the 1990s. Perhaps none of them, though, has a story as distinctive as that of engineering.
***
In 1991, twelve members of Yale’s Faculty of Arts and Sciences were asked to perform an unpleasant task. The university was struggling: revenue sources had dwindled, departmental expenses had burgeoned, and numerous facilities (including the residential colleges) were in desperate need of costly repairs. If Yale was to survive, then costs had to be cut. The twelve faculty members appointed to the Committee on Restructuring the Faculty of Arts and Sciences began developing a plan to reduce ladder faculty positions by 15 percent.
The committee members were probably not warmly received by any of the departments they inspected, but they were especially mistrusted by the engineering department, which had always had an up-and-down relationship with the administration. Forty years ago, Yale Engineering enrolled close to a thousand majors—nearly 25 percent of all Yale undergraduates—and it was estimated that the university had produced 15 percent of all engineers in the United States. But there was something suspiciously vocational about engineering that did not sit well with the more classically minded members of the administration. According to professor emeritus of geology and geophysics Robert Gordon, who began teaching metallurgy at Yale in 1957, “Misconceptions about Engineering appear to have been deeply imbedded in the Yale administration. Rumor had it that the president and provost saw what we did in the Metallurgy Department as a form of advanced blacksmithing.”
During the presidencies of Alfred Griswold and Kingman Brewster, the Yale undergraduate admissions office favored students with strong liberal arts backgrounds over those with technical skills. This preference, along with a reorganization of Yale Engineering that combined all of the previous three departments into one, had catastrophic effects. In 1966, the Engineers Council for Professional Development—a national organization that evaluates engineering programs—denied accreditation to Yale’s newly reorganized engineering department. By that time, there were only 48 engineering majors and 116 science majors at Yale.
By 1991, Yale Engineering had split back into three departments, regained accreditation, and had a respectable number of majors. But the department was still a far cry from what it had once been, and it would never regain its former prominence without significant expansion. In its formal report, the Committee on Restructuring the Faculty of Arts and Sciences wrote, “The chairs also believe that engineering as a whole cannot and should not be expected to reach national prominence unless it is allowed to grow substantially.”
The committee members were not willing to guillotine engineering wholesale. But they were willing to cripple it. In its final report, the committee recommended recombining all of the engineering departments and eliminating nearly 23 percent of junior faculty-equivalent positions. By comparison, English and History—both of which were independently larger than all of the engineering departments put together—would each suffer a reduction of about seven percent.
The backlash to the committee’s recommendations was immediate and fervent. The Faculty of Arts and Sciences set up an independent review committee a month after the initial report came out in January; by March, the independent committee had rejected many of the restructuring committee’s resolutions. The provost resigned in March. By April 1992, the president of Yale and the dean of Yale College had followed suit.
When Richard Levin was elected to the Yale presidency in 1993, he must have been keenly aware of the circumstances that led to his predecessor’s resignation. Levin had been one of the 12 faculty on the restructuring committee. In a recent interview, he reflected that the 23 percent reduction recommended by the committee was far smaller than what the administration had initially proposed.
“The administration was suggesting, for example, closing engineering. Closing sociology. It was pretty drastic,” Levin told me. “There was a lot of skepticism about whether we could have a competitive engineering department at Yale.”
Levin did not share that skepticism. After the university’s finances improved, he began to invest heavily in STEM. He appointed D. Allan Bromley—a former U.S. presidential science advisor—as dean of the engineering school. In 2000, he announced a 500-million-dollar plan to upgrade the university’s science and engineering facilities (only two new science buildings had been constructed at Yale in the past 30 years). In 2007, he announced that undergraduate admissions would seek to attract an incoming class consisting of at least 40 percent STEM majors.
But as the number of STEM majors at Yale increased, many faculty became increasingly uneasy. Who would teach all the new students? Would the administration begin hiring a significant number of new faculty in STEM departments? The answer appeared to be no. While a few departments expanded, many others did not.
“We never made a big announcement or a specific initiative around increasing the number of faculty in STEM as a whole,” Levin told me. “When we started, the faculty were underutilized.”
***
John Wettlaufer, the DUS of applied mathematics, does not feel underutilized. “I don’t have enough time to meet with students. I don’t have enough time to supervise undergraduate research projects. I only have a certain bandwidth to be an advisor to students,” he told me. “Our applied math students are a great source of help and energy for the program. It seems that every time we hire a faculty member, another institution is hiring three.”
At Harvard, the equivalent to the DUS of applied mathematics has undergraduate assistants who help provide academic advice to students. When I asked Wettlaufer how close Yale was in STEM to more technical universities such as Harvard or MIT, he responded with repressed amusement. “We’re not very close. At Harvard they’re hiring left, right, and center. They have hired two full-time lecturers as associate directors of undergraduate studies in applied mathematics, who teach and advise students. At MIT, of course, there’s no comparison. They have some 40 instructors or lecturers across pure and applied mathematics. In my opinion, the commitment of those institutions to STEM fields is much higher, and you can see that just from the number of faculty and lecturers that are being hired.”
The small number of faculty hires has certainly contributed to poor advising. But it has also prevented Yale from increasing diversity in many STEM departments that continue to be overwhelmingly white and male. In upper-level math courses, there are rarely more than three or four female students. Hee Oh is the only female professor in the mathematics department. She is the first tenured professor in the department’s history.
A few years ago, six undergraduates surveyed undergraduate mathematics majors about exclusion and diversity. They published the results in the Iota Report, which recommended, among other things, implementing an improved advising system and increasing diversity among faculty and graduate students. “Students look up to their professors and graduate TAs as mentors and examples,” the authors noted. “It matters when they do not see anyone successful in the field who looks like them.”
The surveys and testimonies in the Iota Report make another point plain. The students who turn away from mathematics, either as a result of poor classroom experiences or poor advising, are often women, members of racial minorities, or students without access to advanced mathematics courses in high school. In departments with poor advising and overworked professors, the students who change majors are frequently those who already feel out of place. Students who come in without adequate preparation, in particular, are often forced to leave STEM.
“Coming from a low-income, academically deficient background meant Yale would be hard for me, and I knew that before I showed up,” one student wrote in her testimony for the Iota Report. “But there was no way for me to know the extent to which my background would limit me over the next four years. A place that is defined by the opportunities it provides became the site for me to learn the areas in which I was limited. I quickly learned all STEM majors were inaccessible to me.”
Faculty advisors play a crucial role in all departments at Yale, but they are especially important in STEM fields. A student who has never taken an English class can pick up the Iliad, flip to the twelfth book, and become entranced by Sarpedon’s speech to Glaucus. But no student who hasn’t studied advanced mathematics can pick up Dummit and Foote’s Abstract Algebra, open it to chapter four, and marvel at the elegance and versatility of the Sylow Theorems for finite groups. Faculty in STEM fields who care enough (and who have enough time to care) about undergraduate education can provide a human face to subjects that, on their own, often appear sterile and inaccessible. At Yale, that human face sometimes never appears. When it does, it’s almost always white and male.
***
“I haven’t met a single other black or Hispanic math major in my time at Yale,” Elisa Martinez ’18 mentioned offhandedly. Martinez, her friend Nathan Nuñez ’20, and I were sitting in the Pauli Murray dining hall on a dark evening last spring. Nuñez had been telling me about Being Human in STEM—an intercollegiate program founded at Amherst that aims to bring attention to exclusivity and lack of diversity in STEM fields through student-led projects. He was part of a team that focused on surveying Yale’s mathematics department.
“The math department doesn’t really care about the human element of its students,” Elisa continued. After years of taking math classes, this had become apparent to both of us. It cares about whether its students are able to figure out the problem sets and do well on exams.
There are some math professors who care very much about the human element. Patrick Devlin—a Gibbs Professor and the current instructor of Math 230-231, an intensive introductory sequence for students interested in pure mathematics—is one of the best-known. Devlin helps his students form study groups; he sends them encouraging emails when they feel disheartened; and, in both Math 230 and another of his courses, the first-year seminar Math as a Creative Art, he tries to convey the beauty of mathematics to his students. “I think Pat is trying to heal the perception of math as a dry and sterile subject,” Lauren Chan ’21, a student who took Math as a Creative Art, told me. “I think he’s trying to convey that math is touchable, it’s reachable—it’s human.”
Research in mathematics—like research in most STEM fields—is highly collaborative. Yet all too often, math majors work on problem sets, study for tests, and learn material on their own, particularly if they are somehow set apart from the other students. Almost all of the women I interviewed for this article emphasized the simultaneous importance and difficulty of finding study groups. Ami Radunskaya, the president of the national Association for Women in Mathematics and a professor at Pomona College, also emphasized that an inclusive culture must be a collaborative one. “In my classes,” Radunskaya told me, “I insist on collaborative work. The goal should be to make collaboration the norm. One of the most important things is ensuring that people don’t get isolated.”
When I asked Radunskaya about the lack of diversity in Yale’s mathematics department, she told me that this is a problem almost everywhere. Yale is hardly unique. But there are things that Yale and all other universities could do to improve. Several universities have experimented with a double-blind reviewing process when hiring faculty to prevent discrimination. Others have invested in cultural awareness training and in creating a collaborative culture among undergraduates. “It’s really important to have open discussion about these issues,” Radunskaya said. “It’s a very slow boat to turn—this institution we call academia is very old-fashioned. There are so many things we cling to.”
Since the Iota Report was published, the mathematics department has implemented a peer tutoring system—one of the report’s recommendations. In 2017, an undergraduate organization named Dimensions was founded to support women in mathematics at Yale. And this year, the mathematics advising system expanded: there are now two DUS’s, and mathematics majors are also paired with an additional faculty advisor. But the department is still one of the least diverse at Yale. Hee Oh is still the only female professor in the department’s history.
Elisa knows some mathematics professors, such as Devlin, who are making an active effort to increase the department’s diversity. But she knows many others who seem to think that diversity isn’t a significant issue. Last fall, shortly after a Yale Daily News article on the gender disparity in the mathematics department came out, Elisa was asked to stay after class in a mathematics seminar taught by a senior faculty member. She was the only woman in the seminar, and the professor wanted to ask her why the News was making diversity such a big issue. He didn’t treat his students differently if they were women, the professor told Elisa. Why did it matter so much that there weren’t more female professors in pure mathematics? Elisa, confused and dispirited, had not known what to say.
***
There are some STEM departments at Yale that have improved markedly in the past decade. In 2015, Yale announced that it would use gifts from two donors to create seven new faculty positions in computer science—the largest expansion of the department in more than 30 years. The Department of Computer Science has invested significant resources in providing peer tutors and teaching assistants for most of its courses, which are often large but are well-regarded. All of the students I interviewed who had taken courses in computer science praised it. “I don’t think that the math department is as invested in its students as the CS department is,” Yuxuan Ke ’19, a double major in mathematics and computer science, told me. Carter Page ’19, an economics major who abandoned pure mathematics after a disheartening introductory course, told me that he has never had a bad experience in computer science. “I have yet to take a CS class that has not been incredible,” he said.
When I asked O’Hern, the DUS for mechanical engineering, about the inconsistent quality of introductory mathematics courses, he mentioned the calculus course Alex took in her first year. Previous instructors for the class once tried to split it into two sections, but the administration blocked the division, in part because it would have lessened the teaching load of the two instructors. When I asked Roger Howe a similar question, he mentioned that the mathematics department does not spend significant time teaching incoming Gibbs Professors how to be engaging instructors. “They don’t get any training here,” he told me. “They’re just sort of supposed to be able to go into the classroom. We don’t do anything to get them up to speed.” And when I asked Levin why his administration set a goal for 40 percent of the incoming class to be prospective STEM majors, he spoke about the attrition rate offhandedly. “We knew the erosion was nearly 50 percent,” Levin said. “If 40 percent said they wanted to do science, then about 20 percent actually ended up doing science.”
Yale has reached and surpassed Levin’s 40-percent benchmark, but it has done so without expanding many of its departments. When I talked with O’Hern and Coifman about the severe understaffing in departments that have not been expanded in decades, I was reminded of the question that head science tour guide Stephanie Spear had put to me in my interview with her: “Why are we not retaining these students over the course of four years?”
And when I heard Levin discuss the attrition rate as if it were an unfortunate inevitability rather than a fixable problem, I was reminded of my earlier conversation with Elisa, when she described her fruitless conversations with faculty who didn’t seem to care that women and racial minorities are being driven away from mathematics.
“You get the feeling that no one higher up really cares about this issue or really wants this fixed,” Elisa said, frustration evident in her tone and expression. “And I think that’s true. No conversation I have ever had with anyone higher up in the math department has convinced me otherwise.”
***
Correction: Yale announced that it would use gifts from two donors to create seven new faculty positions in computer science in 2015, not in 2007.