Organizers: Abbe Herzig, Amy Cohen-Corwin, and David Manderscheid

December 4, 2006 - December 8, 2006

A healthy mathematical community is good for the United States. The current level of technological development and concomitant prosperity is heavily dependent on the influence of mathematical culture and ideas. Thus it is a matter of great interest, and utmost concern, to guarantee that a broad cross-section of able and ambitious students with an interest in mathematics can succeed in their studies and contribute to American mathematics Corporations with federal contracts may need to staff certain positions with citizens or permanent residents in the mathematical sciences. They look to American graduate programs to meet their hiring needs. Resources will flow from American sources (e.g., federal agencies, corporations, and private foundations) in response to the success of mathematics and the availability of a productive mathematical workforce.

Current data from the Joint Data Committee of the American Mathematical Society and other professional societies in mathematics and statistics show that, of Ph.D.s in the mathematical sciences awarded to U.S. citizens or permanent residents, fewer than 30% go to women and fewer than 7% to African-Americans, Latino-Americans, and Native Americans combined. These figures indicate that the under-represented populations constitute a huge untapped resource for growth.

Some snapshots of problems or disincentives faced by women and people of color and even by graduates of many U.S. colleges and universities are these:

The female student takes undergraduate courses in both chemistry and mathematics. In thinking about entering academe in one of these two disciplines, she notices that there are many female chemistry faculty and very few female mathematics faculty.

* Equity issues: Women and people of color learn that they do not receive the same pay, perks, and treatment as white men of comparable ability, experience, and training.
* Students with ability and interest in mathematics may not receive useful and supportive information from faculty about career opportunities in mathematics-intensive fields. Such information is not reliably available from families, especially those families whose members are not already college or university graduates.
* A high tech company has a big contract with a U.S. funding agency. It seeks to expand its workforce, particularly in the mathematical sciences. But it does not see the American mathematical community as producing employees that it can use.
* A woman, in considering whether to go into academe, notices that private companies offer paid maternity leave while universities tend to offer negative time on the tenure clock.
* Women are comfortable going to work in an environment where there are other women. Many mathematics departments have few if any women. The Harvard mathematics department has never had a woman faculty member. MIT has had only one or two. People are not comfortable studhying or working in environments where they feel isolated or marginalized.

Typically, national educational systems outside the United States devote post-secondary education solely to the major subject. Thus a foreign applicant to a U.S. doctoral program has had to 3 to 5 years of full-time study of mathematics beyond the level of calculus. By contrast a typical applicant from a college or university in the U.S. has had only 2 or 2.5 years of half-time study of mathematics at a comparable level.

Graduate education is very expensive. Many highly developed countries have only gotten into the business of developing graduate programs rather recently (in Italy, for instance, the Ph.D. is less than twenty years old). The United States has been, and continues to be, one of the great bastions of graduate education in the world. However, it is a fact that slightly under half of all the Ph.D.s in mathematics that we produce each year go to Americans. And that percentage is declining each year. Our skills at attracting able and dedicated students to graduate study in mathematics, and then retaining them in our Ph.D. programs, are underdeveloped. The mathematics profession, at least in academia, has tradionally had a "sink-or-swim" mentality. This workshop is dedicated to changing that mindset.

The U.S. is rightfully proud of the scope and quality of its graduate education. It attracts students and faculty from around the world. This system of graduate education is, as noted, very expensive. Departments are under pressure to ensure that their doctoral students finish successfully in a reasonable length of time. In some cases, this provides a disincentive to admitting U.S. applicants.

In fact the participants in the present workshop consist of groups of three from eight different universities. Each group has a commitment from its university administration to implement whatever policies or ideas may grow out of this workshop. The workshop intends to address three key issues connected with graduate education for American students:

* How to attract American students to advanced mathematics education.
* How to retain students in a graduate program once they are matriculated.
* How to prepare graduate students for entry into the mathematics profession.

Part of the picture these days---as opposed to fifty years ago---is that a student with mathematical training has so many career choices. The student with a Masters or Doctorate degree in mathematics can go to work in the genome project, in the financial sector, in the computing industry, in biomedical engineering, and in a number of other facets of modern life as well. Today, teaching is just one of many choices. Of course this is all mathematical science, and we would encourage our students to consider any of these career paths. But the Ph.D. has traditionally been a limiting rather than a diversifying degree. The typical Ph.D. student is unaware of the many choices that are available. Put in other words, most Ph.D. students think of themselves as clones of their thesis advisors. We need to change the way that we educate our graduate students about the world around them.

Inequities and bigotry that continue even until today have also caused people of color to be cautious of the mathematics profession. In particular, faculty at predominantly black colleges are hesitant to recommend their best students to good math programs (which tend to be at predominantly white colleges). The mathematics profession is perceived to be a "white" profession. It is not very visible to young people raised in an economically disadvantaged environment. Put in other words: To a a bright and ambitious young person raised in such circumstances, careers in medicine, engineering, and law are obvious choices with immediate social impact. Mathematics is much less prominent on the radar screen. And it is also not perceived, in many cases, as being very welcoming.

Much is known about how to address the concerns and issues mentioned above. However, this knowledge has not been widely disseminated and has not been widely deployed. This AIM workshop intends to spread currently available information, to discuss issues and concerns, and to assist participating teams to develop concrete plans for furthering their ongoing efforts to address these issues---in both the short term and the long term.

Some innovative faculty have initiated successful programs to attract and retain graduate students. They concentrated particularly on students from underrepresented social groups. Many of the prime movers in these programs are now approaching retirement age. We need to recruit and train a new generation of mathematical scientists who will play the role of "organizers" in getting things moving to develop graduate programs in the direction that we want them to go. Part of the function of this workshop is to find means of achieving this particular goal.

While there have been many prominent and successful individuals who have been active to redress the recognized difficulties both in their home departments and in the broader mathematical community, the organizers of this workshop believe that American mathematics should not have to rely solely on pioneers and heros and the successors that they may attract. Rather, there should be a broad, deep, and sustainable change in a substantial number of institutions of higher education. This workshop is one step in that direction. Mathematicians, influenced by this program, will not only prove great theorems, and teach future generations of students. They will also develop the infrastructure of the subject for a more broadly representative mathematical community.