From Pre-School Bad Boy to City College Math Whiz
Adapted and expanded here is a story from “Study With the Best,” the 30-minute TV magazine, now in its third season, that highlights CUNY’s wide array of outstanding faculty, remarkable students and alumni, and major University academic initiatives. The lively, fast-paced series (CUNY-TV Channel 75, Sundays at 8) is aimed particularly at prospective CUNY students.
One of the most prestigious annual mathematics competitions in North America is the Putnam Competition. Individual undergraduates and college teams convene at numerous sites for an all-day tussle with 12 diabolically tough math problems. Of the approximately 4,000 contestants, only five emerge victorious (they are not ranked), and last year, for the first time in several decades, a City College student, Jan Siwanowicz, was among that tiny top echelon.
“It is a very difficult exam,” says Siwanowicz, a native of Poland. “In fact, every year the median score is zero. Half the people who take the Putnam get nothing right! The questions are simply very, very difficult. They can be just a paragraph, but answering it can take anywhere from one sentence to three pages, depending on its complexity.”
In March, Siwanowicz got an email from a friend who is a professor at the University of Minnesota, congratulating him on his achievement. Since he hadn’t heard officially, he couldn’t believe it. “I called him back and said, ‘Am I really a Putnam?’ And he confirmed it. They couldn’t pry me from the ceiling for a week!
“We got a good laugh just listing the schools of the five winners: MIT, Duke, U.C. Berkeley, Harvard…and CUNY. It was unexpected, but it’s a great honor to be a Putnam.” CCNY emeritus professor Harry Applegate says winning the Putnam requires “a gift–where it comes from I have no idea–for extremely rapid problem-solving, and Jan clearly has it.” Getting the top award is a real rarity, Applegate emphasizes. “I began at City College in 1965, and this is the first one on my watch!”
Being a genius in math is a young person’s game, and Siwanowicz’s upward mobility in the discipline actually began in pre-school. “I got in trouble a lot because I have a thing about authority.” So he spent his share of time in the corner. It must have been a pretty advanced pre-school because Siwanowicz was reading a book on counting in binary. “So I would sit in the corner, with my back to the teacher, madly counting on my fingers in binary, which is the way computers represent numbers.
“For example,” Siwanowicz explains, “a number such as ‘110' normally denotes one hundred and ten, but in binary, the ‘100' portion denotes two squared (four) rather than ten squared (hundred). Likewise, the '10' portion denotes two rather than ten. The units digit 0 is still zero. So the original '110' when interpreted in binary denotes four plus two plus zero, or six.” Holding up five fingers for the camera, Siwanowicz adds, “A full slate is one, plus two, plus two squared, plus two cubed, and so on until two to the ninth, and sums up to 1,023.” Is that clear?
Siwanowicz admits that this pastime as a pre-school bad boy was “kind of weird, but it was fun for me.” It was certainly prophetic for his future math studies, which included competition on Polish math teams, which took him once to Hong Kong.
“I like the way, in math, you can take an object or a concept or an idea and look at it from different points of view. Let’s say you’re looking at a black and white quilt which has a pattern on it. You can look at only the black parts, and that will give you one representation of what the pattern really is, or you can look at the white parts and get a totally different perspective, a different concept and understanding of the object.”
That mathematician’s habit of multiple approaches, Siwanowicz says, “really helps me out in real life.” The habit is also helping him as a teaching assistant for Chancellor Goldstein, who is teaching a calculus course at Hunter College on Saturday mornings this fall. “Jan is a joy to work with,” the Chancellor says. “I have no doubt a successful graduate career awaits him.”