MIT’s “Dream Team” Wins SIAM Award for MCM 07June 12, 2007
Martin Bazant, MIT’s MCM coach, with graduating seniors Daniel Kane, Dan Gulotta, and Andrew Spann, a prize-winning team throughout their four years at MIT.
If you've followed the Mathematical Contest in Modeling for the past four years, three names probably sound pretty familiar: Dan Gulotta, Daniel Kane, and Andrew Spann.
The three MIT seniors have participated in the MCM since their freshman year, when they earned the second-highest ranking ("Meritorious"), along with the Ben Fusaro Award for the most creative solution. Since then, it's been "Outstanding" all the way, topped off with the INFORMS Award for the best paper on the discrete problem in 2006 and with a SIAM Award in this, their final year together.
"The string of success by this team is truly inspiring, and to my knowledge, unprecedented," says Martin Bazant, an associate professor of applied mathematics at MIT and the institute's MCM coach since 2001.
But this team's MCM involvement dates back even further than freshman year. Both Spann and Gulotta competed in the high school version of the MCM (HiMCM), and when they arrived at MIT, Spann did some recruiting.
"Spann handpicked his teammates from among his fellow freshmen, [and] came to me with what would become MIT's Dream Team," Bazant explains. "He was proactive and determined to compete in the MCM from Day 1 at MIT."
And compete they did, despite their busy schedules. All three team members, on their way to graduate school, are leaving MIT with double majors: Gulotta and Kane in mathematics and physics, Spann in mathematics and chemical engineering. Yet somehow they managed to find time to not only compete in MCM, but to be wildly successful in each contest for the past four years.
What made that possible, Spann says, is that the contest doesn't especially require training during what he calls the "off-season." But, he says, "you do need to spend an immense amount of time during that 96-hour period being focused on your work for the contest, so I'm glad it only occurs once a year."
This year, those 96 hours ran from February 8 to February 12 (see "Mathematical Contest in Modeling 2007: A Judge's Perspective"). As always, the contest offered participating teams the choice of two problems: one continuous and the other discrete. In their first three years, Bazant's "Dream Team" consistently chose the discrete problem, and in studying this year's choices, the students' initial instinct was to go for the hat trick in "Outstanding" discrete problem solving. The discrete problem involved airline boarding, and Spann was already familiar with some of the research literature on the topic.
Kane, however, had other ideas. The continuous problem was about gerrymandering: Teams were asked to "develop a model for ‘fairly' and ‘simply' determining congressional districts for a state." Kane felt that the gerrymandering problem offered the team more options than the airline boarding problem, and spent the first night of the contest experimenting with ideas for it.
"One of the first things I tried was to minimize the mean square distance of people in the same district," he says. "After looking at the problem for a while, I reformulated it in terms of moment of inertia, and figured out how to determine the regions given their centers of mass.
"[That] allowed me to show that the regions would be convex---which I think is what finally convinced everyone to go with this problem," Kane explains.
Kane's best idea turned out not to be novel. "It was similar to some of the very first ideas that researchers had proposed when studying the problem in the 1960s," Spann explains---but then, this isn't the 1960s.
"We had access to faster computing resources than those researchers did, so we were able to present the results in a new way," Spann says. Gulotta, who handled programming for the team, found a way to use data from the Census Bureau's database, and the students were able to compute results for any state they wanted to investigate. With Spann doing most of the writing and organization, Gulotta doing the programming, and Kane focusing on the development of the mathematical model and analysis, the three closed their MCM run with a bang.
"Individually, [these] students are clearly very gifted," Bazant says of the team members. "However, what impressed me most about the team and their solution papers was their ability to work closely together with highly complementary and well-orchestrated contributions. I think the whole was really more than the sum of its parts."
That the students were able to combine their insights and work together in a mathematical competition is not surprising in light of their individual histories: All three claim longtime interest in mathematics and its practical applications, and all three have significant experience participating in--and winning--academic competitions.
Gulotta traces his interest in physics to a book on atoms that he read as a fourth grader; from that point on, he read as much as possible about nuclear energy and subatomic particles. He went on to take a physics class as a freshman in high school and, he says, "really enjoyed being able to use mathematics to predict things about the real world." He took a National Outstanding award in the HiMCM, and was a gold medalist in the International Physics Olympiad.
While in high school, Spann too became a regular participant in academic competitions: MATHCOUNTS, the USA Mathematical Talent Search, the US Mathematical Olympiad, and the Physics and National Chemistry Olympiads (as well as the HiMCM). He entered MIT with a strong mathematics background, but decided to enroll in chemical engineering because of his previous research in chemistry.
"I discovered that chemical engineering had very little to do with chemistry, at least as I had perceived [it] in high school," he says. "I actually liked this aspect, so I stayed in chemical engineering and later added mathematics as a double major when it became apparent that I could get a math major by taking enough math classes for fun."
As for Kane, his goal has been to become a mathematician "ever since I decided that I didn't really want to be a fireman at about five." Kane, whom Bazant refers to as a "perennial Putnam fellow," is also a two-time gold medalist in the International Mathematical Olympiad, and he recently received the 2007 Morgan Prize.
With his "Dream Team" preparing for graduation, Bazant reflects on their myriad achievements over the past four years, culminating in this year's SIAM Award. With no SIAM Annual Meeting scheduled this year, Gulotta, Kane, and Spann will be recognized for their achievement at the 2008 Annual Meeting. Each team member will receive $300 and student memberships in SIAM.
In the meantime, Bazant is hopeful that MIT's MCM success will continue. "This will be a tough loss for MIT, but we had another Meritorious team this year, and growing interest in the MCM," he says. "Hopefully we will keep the streak going."
Michelle Sipics is a contributing editor at SIAM News.