Profile of the Week: J. P. Grossman – Do What You Enjoy!

excerpt from A Mathematical Mosaic: Patterns & Problem Solving

J. P. Grossman
Born March 23, 1973

J. P. Grossman’s playful approach to life was evident from an early age. In kindergarten, he developed an enduring interest in taking things apart: clocks, calculators, watches, radios – even computers and a mechanical record player. His ingenuity didn’t always meet with popular approval, however; he was once sent to the principal’s office for working too far ahead of his class.

“Taking things apart” to understand them typifies J.P.’s method of learning. In Grade 9, he and a friend read an article in Discover magazine about fractals, at the start of the fractal craze. They were curious to find out how fractals worked. The first hurdle was to understand this mysterious “i” that appeared in the equations as the alleged square root of –1. Rather than ask for advice and risk being told that their questions were “too hard”, they played around with the concept of “i” and figured out how it worked. (This is the philosophy of the explanation on “i” on page 223.) They then wrote computer programs to generate fractals on whatever machines they could find, starting with a Vic 20 and working their way up, beginning with BASIC and learning other languages as they needed them. (Two fractals appear later in this book, Sierpinski’s triangle on p. 111, and the Mandelbrot set on p. 195.)

In Grade 10, J.P.’s competition career took off, thanks to his intuitive approach to mathematical challenges combined with his ability to pick problems apart. In Grade 11, he won the Canadian Mathematical Olympiad for the first of three consecutive years, easily qualifying for the Canadian Team to the International Mathematical Olympiad. During his three years competing at the IMO, he won two Silver Medals and a Gold Medal. In his second-last year of high school he won the USA Mathematical Olympiad; the next year Canadians were no longer allowed to take part. While studying mathematics, physics, computer science, and electrical engineering at the University of Toronto, J.P. achieved the highest honor of Putnam Fellow in the North American Putnam Mathematical Competition three times in a row. (You will meet many more Putnam Fellows later in this book.)

J.P. then went to MIT for a Masters degree in computer graphics. He went on to earn a Ph.D. at MIT in computer engineering, focusing on massively parallel computing. As his wife, Shana Nichols, was completing her Ph.D. in clinical psychology at Dalhousie University in Halifax, Nova Scotia in Canada, he took a post-doctoral position in Dalhousie’s math department and worked in combinatorial game theory and networked information spaces.

He’s continued working in game theory, and is the co-inventor of the game Clobber, that has attracted attention for being an “all-small” game (a technical term) that is both mathematically interesting and fun and challenging to play. The first competitive clobber tournament was held in Germany in 2002.

Clobber is played by two players, White and Black, on a rectangular m x n checkerboard. In the initial position, all squares are occupied by a stone, with white stones on the white squares and black stones on the black squares. A player moves by picking up one of their stones and clobbering an opponent’s stone on an adjacent square (horizontally or vertically). The clobbered stone is removed from the board and replaced by the stone that was moved. The game ends when one player, on their turn, is unable to move, and then that player loses.

After his postdoctoral work, J.P. headed for the mountains, spending two years working for a software development company in Colorado Springs before being recruited by D. E. Shaw & Co. in 2005 to work on a large special-purpose full-custom parallel machine to accelerate molecular dynamics simulations. “I’ve been involved in architectural simulation, hardware design, and hardware verification, and I’ve gotten my math fix from working on techniques for analyzing the differential equations describing the time-evolution of a chemical system, as well as converting these equations of motion into a discrete-time simulation.”

Along with his talents in mathematics, J.P. pursues many other interests, including chess, soccer, skiing, and mountain biking. A jazz enthusiast, he is also an accomplished tenor saxophone player.

What J.P. loves most about mathematics are the ingenious leaps required, “putting together two facts that seem unrelated.” He finds that he has become experienced in “making connections between different things just by recognizing certain patterns,” both within and outside the field of mathematics. One of his favorite examples of this principle is The Magic Birthday Predictor Cards (p. 21). When he saw this trick at a young age and realized how it worked, he had a sudden insight into binary numbers.

Another favorite problem of his that connects seemingly unrelated ideas is the following.

A large rectangle is partitioned into smaller rectangles (with sides parallel to the large rectangle) such that for each smaller rectangle, at least one of the side lengths is an integer. Show that the larger rectangle also has this property.

J.P.’s curiosity is typical of the young mathematicians profiled in this book. Also typical is the vigor with which he pursues his interests. Rather than seeing his undiscriminating intellectual acquisitiveness as a distraction that holds him back and wastes his time, he finds it constantly driving him forward. His philosophy of life: “Do what you enjoy!”