This award provides particpant support for the Mathematical Olympiad Summer Program, which brings together 60 highly talented students for an intensive three-week program of training and instruction. This award also supports two new initiatives in the summer program: a research component in the instruction, and a program for women students that will allow eight young women to represent the United States in a prestigious international mathematics competition.
The United States has sent a team to the International Mathematics Olympiad each year since 1974. A founding objective for this global competition is to establish a foundation for future scientific collaboration between promosing students who will form the new generation of researchers in mathematics. The International Mathematics Olympiad is widely regarded as a pinnacle achievement for young mathematicians.
For over 50 years, the International Mathematical Olympiad (IMO) has stimulated pre-college students to pursue their talents in Science, Technology, Engineering, and Mathematics. In the United States, it furnishes the context for the Mathematical Olympiad Summer Program (MOSP), which brings together the top 60 students identified by the national selection competition. This training camp has historically provided high-level enrichment and guidance to these potential future leaders, and it is structured as an intensive 3-week training camp in which students engage in mathematical activities from day to night. This award supported two new initiatives which leverage the existing Olympiad infrastructure. The first used the new female-targeted editions of the IMO (the China Girls' Math Olympiad, a multinational competition organized by China, and the European Girls' Math Olympiad) as context to substantially increase the participation of women at the highest levels of the United States Olympiad program. Over the grant period, 10 girls were invited to the Math Olympiad Summer Program each year, where they developed their mathematical breadth and depth, and built a strong network. The international events further expanded their network to global-scale. The second initiative added a research dimension to MOSP by taking advantage of its pool of faculty and alumni, many of whom have moved into professional research careers. The MOSP staff roster includes representatives from every career stage, from first-year undergraduate to tenured professor. This award effectively broadened the scope of the program, as instructors made efforts to link instruction with research, and to incubate interdisciplinary collaborations within the MOSP faculty itself. An evening seminar was introduced into the MOSP routine, running from 7-8pm on alternate nights. The speakers were MOSP instructional staff who had gone on to graduate school and beyond. The mission was to convey the spirit of each speaker's current area of investigation, in terms which were comprehensible to the high-school students. The highlight was a new system, which was piloted for a segment of the instructional staff, loosely based on the successful model of the modern research university. In this new approach, the PI and other senior instructional staff had the explicit objective of mentoring the junior staff on research projects, in addition to teaching courses to the high-school students. Many of the research collaborations were intentionally conducted in public (over a wide variety of hours), in a large common lounge where students typically congregated to relax. This inspired numerous inquiries from the students, who then learned not only about the problems at hand, but also about the research process. Each summer had an average of 4 research collaborations involving undergraduates, spanning topics as diverse as representation theory, combinatorics, economics, and theoretical computer science. Many of them produced substantial progress. In two cases, the results reached the level of mainstream peer-reviewed scientific journals or conferences, and those two papers have been accepted for publication. In both projects, the undergraduate research assistants made core contributions. As a result, several talks were given on these two projects at conferences and seminars across the country, by the PI and by the student co-authors. A number of the other investigations are still on-going. In conclusion, this pilot has demonstrated the proof of concept for a new platform, which brings together talented high-school students in a vertically-integrated research and learning environment. The Math Olympiad Summer Program will now permanently switch over to this model, which melds a high-school enrichment camp, an REU, and an inter-disciplinary research workshop into a coherent, symbiotic entity.