When 14-year-old Thomas Hameister first began noodling the problem sets sent to him from the University of Wisconsin-Madison's Department of Mathematics, he thought they were "unsolvable."
He didn't win the Math Talent Search that year.
But that didn't stop the Neenah, Wis., native from signing up every subsequent year to compete in the department's contest, open to middle- and high-school students statewide. Senior year, his tenacity paid off. On May 2, Hameister became the 50th winner of the annual Math Talent Search competition, netting a $24,000 scholarship to UW-Madison.
"It was very, very good news," says Hameister, now a first-year student in the College of Letters & Science. "I believe that the more exposure you get to stuff that's over your head, the better you become."
That's the idea behind the Math Talent Search, according to Assistant Professor of Mathematics Melanie Matchett Wood, who helps coordinate the contest. She says the professors who write the problems know that middle- and high-school students won't necessarily know how to do them right away.
"We ask them to use the skills they have, but think in a new way," she says. "The Talent Search is not just about finding the right answer, but about the reasoning process the students go through to find the solution."
The Math Talent Search, which began in 1963, emphasizes proofs, rather than numbers. Participants receive five sets of problems via email over the course of the school year (each set has five problems). Top scorers (there were 26 this year) are invited to the Honors Day ceremony held at UW-Madison's Van Vleck Hall. Before the festivities, however, students must complete the final challenge: a proctored exam. The top scorer wins the scholarship to attend UW-Madison.
"Math Talent Search is a great way to engage and encourage students in math, and has identified Wisconsin kids who would go on to become mathematicians — or find careers in finance, computer science, and statistics," says Matchett Wood.
Po Shen Loh spoke at this year's 50th anniversary Awards Luncheon, just before Hameister was announced as winner. Loh, an assistant professor at Carnegie-Mellon University, won a silver medal in the International Math Olympiad in 1999 and now coaches the USA International Math Olympiad team.
"This was the very first math contest I entered, and it helped me get to the International Math Olympiad," Loh told a roomful of parents, participants, and faculty. He encouraged students to "try harder, and think bigger" and said that while proofs and logic are difficult, they are what higher mathematics is all about.
Hameister is getting a taste of that now. At SOAR (Student Orientation Advising and Registration), he applied to work as an Undergraduate Research Scholar with Professor Gloria Mari Beffa, chair of the mathematics department. Beffa is working with three undergraduates on a research question related to both Lorentzian and Galilean geometry and how the geometry of twisted polygons relates as the speed of light goes to infinity.
"It's almost overwhelming how much you must know before you can do any semblance of thinking about what the research question is," says Hameister. "I got very lucky to be able to work with Professor Beffa. She's awesome."
Sample problems Thomas had to solve:
1. A palindrome is a number which reads the same forward and backwards such as 1441 or 35253. Find the largest five-digit palindrome that is divisible by 101.
2. 2013 students each roll 9 standard six-sided dice and record how many times each of the numbers 1, 2, 3, 4, 5, 6 appear. Show that there are at least two students who recorded the same result.
3. We wrote integer numbers on the vertices of a tetrahedron (one for each vertex). Show that if the sum of the numbers on each face is divisible by five, then all the numbers are divisible by five.
Achieving the necessary focus can pose a challenge. Hameister turns off distractions ("even music") and seeks a solitary spot overlooking the lake, or a bench in Allen Centennial Gardens.
"It's the kind of thing you have to figure out for yourself – what's your own best study environment?" he says. "When I get to a really difficult problem, it helps to look up from the page and see something beautiful in nature."
But he is a bit mystified by some of his own mental process.
"It's weird how I figure some things out," he says. "When I was working on Math Talent Search problems, it might come to me while I was shooting basketball with my brother. I'd say — wait! That’s how you do it! My family got used to that."
Hameister intends to major in math, with maybe a double major in chemistry or physics.
"I definitely want to go as far in the field as I can, academically," he says. At this point, he is thinking less about what he'll do for a career, than about the "amazing opportunity to study what I love."
John Karl Scholz, dean of the College of Letters & Science, calls this the primary phase of determining one's life direction.
"That first year is an opportunity for L&S students to discover more about what they love to do and are good at, while also giving serendipity a chance to create a spark," he says. "Then we challenge students to ask: 'How can I take this further?'"
For Hameister, math will always light the way.
"I guess I am drawn to the innate beauty of it," he says. "I appreciate that math is more than a set of skills you apply to things. It's something that explains and gives you a better understanding of the way things are. Math makes you think."