#### By Ross Mattheis

Senior Applied Math major, 2017 SURF Fellow, and OURS Peer Advisor

With a handful of exceptions (such as the Polymaths Project) mathematics research can often be a solitary endeavor. Take, for example, Yitang Zhang’s lonely path to a major breakthrough in pure math. Why is math research historically an individual enterprise? Are mathematicians generally introverts? Do mathematicians struggle to communicate with one another? Are they smelly?

More likely, math research is often done alone or in small groups because of the nature of the problem at hand. Knowing how to solve a problem in mathematics is tantamount to solving it. Not so in other sciences. Consider the four year gap between the publication of Einstein’s Theory of General Relativity and the 1919 solar eclipse; or the century that passed between the prediction and direct detection of gravity waves. Most scientific research depends on observation and careful measurement to test and validate theory.

Epistemological curiosities aside, this difference has a significant effect on the way that students (especially at the undergraduate level) encounter and participate in research. While undergraduates can contribute to research at the frontier of chemistry, biology, economics, or psychology through work generating and analyzing data, there is no comparable institution for undergraduate math students.

What is a young, curious undergraduate in mathematics to do if she cannot join – for lack of their existence – a “math lab”? A handful of good-hearted graduate students in math created Berkeley’s Directed Reading Program to address this problem. Now in its fourth year, the Directed Reading Program is designed to emulate the experience of the first year or two of graduate programs in math, at which point students immerse themselves in a narrow area of study. The program matches undergraduate mentees with graduate mentors who work together towards understanding an advanced topic usually not covered in undergraduate material. Past topics include the impressive and/or silly sounding: ‘On Hausdorf Gaps,’ ‘Moduli Stack of Elliptic Curves,’ ‘Chip Firing,’ and ‘Filters and Ultrafilters.’

Berkeley is not the first university to develop this fix for the lack of research opportunities for math students (rather, it was the University of Chicago). Successful programs at Yale, MIT, and Stanford among others are evidence of the demand for research-adjacent experiences in math and the effectiveness of directed reading programs as low-budget solution.

Of course, pure mathematics is not the only field that struggles in connecting undergraduates with research on the frontier. Other heavily theoretical fields such as theoretical physics, economics, or computer science face similar challenges. In these fields, there is often too great an amount of requisite knowledge for students to accumulate before being able to make a contribution. Consequently, the Directed Reading Program at Berkeley has already begun to branch out to these fields, supporting projects in machine learning and game theory. In the future, the graduates students who make up Directed Reading Program want to continue expanding the range of supported projects.

Is a directed reading program only appropriate for math-y fields? Perhaps not. Directed reading programs are meant to expose undergraduate students to advanced material when research opportunities are unavailable or inaccessible. Without the labs of chemists or the archives of historians, young philosophers and critical theorists may face a similar challenge to undergraduate students in math or theoretical physics. The blueprint of the directed reading program may translate well in these fields.

Today, educators recognize the importance of offering research opportunities to undergraduates. Our very own Office of Undergraduate Research & Scholarships serves as a hub to support undergraduates. The experiences of the directed reading programs in mathematics at Berkeley and elsewhere suggest that they will be an important pillar in any effort to expand early research experiences to all students.

ps. For the first time ever, the SURF program is offering a research grant for summer 2018 to a team of students. Learn more at the SURF info sessions.