# Thomas Brylawski

Thomas Brylawski was born in 1944, and grew up in Washington D.C. He attended the Massachusetts Institute of Technology for his undergraduate degree, finishing with a Bachelor of Science in 1966. He then went on to Dartmouth College for his graduate work, and completed his Ph.D. under the direction of Gian-Carlo Rota and Robert Norman in 1970. After his Ph.D., he moved to the University of North Carolina, Chapel Hill, where he spent the rest of his career.

Thomas H. Brylawski was one of the most engaging mathematicians of his generation, full of life and wit. He made an enormous impact on all who were lucky enough to know him. He had tremendous energy for anything that caught his attention, once staying awake for thirtysix hours to construct an algorithm to solve Rubik’s cube, and that same energy went into his talks, his conversations, his children, and his mathematics. Many of his papers in matroid theory from the 1970s and 80s are still widely cited. Moreover, Tom had an uncanny ability to draw in an audience with his humor and unique speaking style, as anyone who witnessed one of his talks can attest.

Tom grew up in Washington, D.C., and his friends remember his precocious talent in mathematics, his very quick wit, and his complete lack of organization. This last part of his personality was obvious to his friends early on; in 6th grade, Tom’s teacher had to ask one of Tom’s friends to straighten Tom’s desk. This was a lifelong affliction — many years later, those visiting his office in Chapel Hill would be unable to locate his desk.

His friends recall how Tom managed to find the humor in just about any situation. He loved games and puzzles of all sorts. One summer, while in high school, he worked for an operations research company, where he was supposed to be modeling elevator waiting time in multi-story buildings as a Markov process. A friend who worked with him notes that the real achievements that summer were, however, in the card game, hearts.

Tom was an undergraduate at MIT, majoring in math. Early in his undergraduate career, Tom took a circuits class with C.L. Liu. He loved the material, which included lots of combinatorial problems, for instance, finding the resistance in an n×n grid. On the other hand, he also signed up for a calculus class with Gian-Carlo Rota, who would later become his Ph.D. advisor. Rota walked in and declared that there were simply too many students in the class, so he began lecturing on algebraic topology. This had the desired effect — Tom, and several others, dropped the class.

While at MIT, he enjoyed a wide variety of non-mathematical activities, including, according to one of his fraternity brothers, his fondness for creating mathematically precise large oil paintings. His interest in art was serious, and it would take a mathematical direction later in his career. Tom had many hobbies, and he spent hours playing cards, usually bridge. He was also a good athlete, playing tennis and an intimidating brand of ping pong. He also loved rock and roll, especially Elvis. Tom played guitar and sang enthusiastically his entire life.

Tom went to Dartmouth for his Ph.D. While still in graduate school, he married and started a family. Working with Rota at MIT involved commuting from Hanover to Cambridge, which he did frequently. During this time he met several combinatorialists who would become good friends, including Henry Crapo, Curtis Greene, Richard Stanley, Neil White, and Tom Zaslavsky. Since he was a student at Dartmouth, he still needed an advisor on the faculty of Dartmouth; Bob Norman was Tom’s official advisor.

Brylawski's early work used ideas and tools from category theory to understand the Tutte polynomial of a matroid. Indeed, this idea already appeared in his thesis, which made constructions in matroid theory similar to the Grothendieck group. He developed similar ideas in two papers in the Transactions of the American Mathematical Society. Another influential early paper of Brylawski's, published in the same journal, described the influence of a modular element in the lattice of flats on the characteristic polynomial of a matroid.

Brylawski also contributed expository chapters to several matroid theory books that appeared in the Encyclopedia of Mathematics and its Applications series published by Cambridge University Press. The Tutte polynomial chapter, written jointly with James Oxley, has over 400 citations.

In addition to his work in matroid theory, Brylawski also had an interest in mathematics in art, particularly in the role of symmetry in art. He gave lectures on mathematics in art on two occasions at the National Gallery of Art in Washington, D.C.

A Special issue of the European Journal of Combinatorics in 2011 was dedicated as a tribute to the work of Brylawski.