William Yslas Vélez, a mathematician, University of Arizona Distinguished Professor and former president of the Society for the Advancement of Chicanos and Native Americans in Science, spoke at MIT on Monday about how to make his field more representative of the United States as a whole.

Vélez’s talk had two main strands. One was a defense of homegrown applicants to graduate programs in mathematics, whether minority or not. The other was an examination of how to encourage minorities to study math.

In the late 1970s, Vélez explained, about 75 percent of PhDs in mathematics awarded by U.S. universities went to U.S. citizens and permanent residents. Now, he said, that figure is below 50 percent. “I happen to think that we should always have large numbers of international students in our graduate programs,” Vélez said. “But 50 percent, I think, represents a system that is out of balance.”

Part of the reason for that imbalance, Vélez argued, is that U.S. universities encourage a broad liberal-arts education at the undergraduate level, while many international universities allow students to focus almost exclusively on technical disciplines. “If you’re an undergraduate math major in Mexico, that means that you took four years of math. That’s all you took,” Vélez said. “By the time you get your bachelor’s degree, you look like you had a master’s degree.” But the University of Arizona, Vélez said, prohibits students from taking more than one-third of their courses in any one department. “This is the system of education that we’ve created for them,” Vélez said. But “graduate programs ridicule them for not being as well prepared as international students.”

Moreover, Vélez said, extensive undergraduate coursework is no guarantee of mathematical creativity. He pointed to a study by Oakland University mathematician Jerry Grossman, who got his PhD from MIT in 1974, which concluded that 43 percent of math PhDs publish only one paper during their professional careers, and 75 percent publish fewer than five. “If we had focused on domestic students, would this data be worse?” Vélez asked. “I can’t imagine.”

Finally, Vélez argued, as important as generating original research may be, educating the citizenry is the chief responsibility of a nation’s universities, and universities that grant more than half of their math PhDs to foreign students are not meeting that responsibility.

The morning after the talk, in a temporary office in the math building, Vélez expanded on this idea. “Suppose you go out to public forums and tell people, ‘We want you to pay taxes into our university system so that we can bring international students in — at your expense — and educate them really well, give them the best credentials in this country so that they can outcompete your children,’ ” Vélez said. “Sell that argument to the public.”

If it’s true that universities should work harder to interest minorities in math, how exactly should they do this? During his talk, Vélez returned several times to the idea that, as he put it, “Earning a living, in the minority community, is very important. And there’s a narrow view of where a good living is to be made.” Because university math departments tend to be so focused on research, he argued, they treat undergraduate math degrees simply as portals to graduate work. That leaves undergraduates with the idea that outside of academia, math degrees afford no way to earn a living. But “the job market for bachelor’s degrees in mathematics is actually wonderful,” Vélez said. “Everybody is looking for mathematics majors. But academics haven’t quite figured that out.”

One way to impress undergraduates with the practicality of a math degree, Vélez explained, was to help them get internships where their math skills would be valued. He gave the example of a student at the University of Arizona who had grown up in a tough border town and was majoring in engineering. When he enrolled in a third-semester calculus class, he was summoned to Vélez’s office. “You should be taking linear algebra,” Vélez said. The student groaned. “If you take linear algebra,” Velez said, “I will get you an internship this summer.” Then he showed the student a flyer for a summer internship program that prominently featured the figure “$3,250.” “And he said, ‘I can’t pay $3,000,’ ” Vélez said. “I said, ‘They’re paying you. Plus your airfare. Plus your living expenses.’ Okay, so he’ll take linear algebra.”

But supplying students with such opportunities requires cultivating relationships with prospective employers, Vélez said. “Go to the national meeting of the American Mathematical Society,” Vélez said. “Go down to the exhibit booth. Who’s there? Booksellers. Who’s there to hire you? Only the National Security Agency. What’s the impression? Mathematics is good for teaching. IBM should be there. Raytheon should be there. Google should be there. Microsoft … has a math department, right? They should be there.”

If math departments can persuade minority students that math degrees are practical, Vélez argued, increased minority enrollment in graduate math programs will be inevitable. And that, in turn, will provide future generations of minority students with role models and mentors. As Vélez put it the morning after his talk, “It should be the mathematics that you should find so exciting that it should encourage you to go on. This is a pattern that I see over and over again.”