To devise a foolproof strategy for bidding chess, a variant of the game in which players bid for the right to move instead of taking turns, you might need longer than a lifetime. It’s the sort of task Yale math professor Sam Payne calls “easy to understand, but impossibly difficult” — and the sort of task undergraduates with an interest in creative computation will get to tackle this summer at the inaugural session of Summer Undergraduate Math Research at Yale (SUMRY).
The ten-week SUMRY program, whose application launched on Wednesday, will provide up to 20 undergraduates who have taken higher-level math classes with about $4,300 each to conduct research with co-directors Payne and Yale math professor Amanda Folsom, and graduate and postdoctoral mentors. Participants can work either in teams of three to four on projects the SUMRY coordinators have proposed or on topics they propose themselves, and will have the chance to learn from guest speakers and present their findings to their peers.
While nearly all Yale’s undergraduate science majors conduct research, Yale math professor Roger Howe said that the gap between the undergraduate math curriculum and the research frontier can make doing math research difficult for students not yet in graduate school. Folsom said the projects at SUMRY were designed to be approached by students who are curious about studying math outside the classroom, but might lack the preparation to participate in graduate-level work.
“There’s a concern that in order to do math research, you have to have taken 10 years of classes and know every intricacy of the problem before you get started,” said Susie Kimport GRD ’15, one of five graduate student mentors Payne and Folsom handpicked for SUMRY. “What’s really great for these students to see is, just one or two classes out of calculus, there’s already a lot of interesting problems you can do.”
Though the projects at SUMRY might be more accessible for undergraduates, they will still pose a significant challenge. Payne said that while the average class problem set takes students about 20 hours to complete, students at SUMRY will be working on projects for weeks and there is no guarantee they will find solutions by the end of the summer.
Still, he added, there will be ample help along the way. Payne, who personally advised undergraduate math researchers last summer in a pilot version of SUMRY, said this year he introduced a faculty and guest lecture series, in addition to weekly meetings where participants will share their progress with their peers. Graduate mentors, who will work closely with participants throughout SUMRY, will spend the beginning of the program familiarizing them with the skills their projects will require and assist each team with writing their final research papers. Later, students will have the opportunity to present their findings at national math conferences to undergraduates from other schools. During the upcoming school year, those interested will prepare their research for publication in professional journals.
“As undergrads, we take in a lot of knowledge,” said Brian Lei ’16, who worked with Payne, Alec Arana ’14, Michael Garn ’15 and Seung Hyun Lee ’16 last summer on the bidding chess problem. “But when you graduate, your job will be to produce knowledge. When you’re an undergrad, it’s great to be able to experience both sides.”
Lei said although their work was not the most mathematically complex, researchers at the conferences they attended had nevertheless shown interest in their contributions to a still-fledgling field of study. Lei said that students with an interest in math research, whether math majors or not, will benefit from the opportunity at SUMRY to pursue new avenues of investigation.
For Payne and Folsom, part of the pleasure of research lies in its pursuit. Both said they expect and hope participants will encounter dead ends and wrong turns as they work, which they agreed are just clues to the answers they seek.
“That moment that you finally solve a problem is so far beyond what anybody can feel finishing a problem set, and we want people to have that experience,” Payne said.
“On one hand, you’re bound by a set of formal rules that math obeys,” Folsom added, “and yet it’s still up to us and our creativity to discover what mathematics is. I think that’s one of the most beautiful things in the world.”
Although sources for SUMRY funding are not yet set in stone, Payne said potential sources include the provost’s office, in addition to his personal grants.
Applications for SUMRY are due on Feb. 1.
Correction: Dec. 6
A previous version of this article omitted Amanda Folsom’s role as co-creator of the program with Sam Payne. It also attributed a quotation to Payne, that was in fact spoken by Amanda Folsom.