156 John Mighton at university, I decided I would have to give up on my dream of becoming a mathematician. I did not develop the confidence I needed to return to math at the University of Toronto until I was thirty-three. In 1995, when I was in the fifth year of my program, the Fields Institute opened on the campus of the university, and I started attending lectures there regularly. It is hard to describe how lucky I felt to have the opportunity to hear some of the greatest minds in mathematics share their thoughts on the very mysteries that I had dreamt of learning about as a child. When I heard Alain Connes present a new application of non-commutative geometry in physics (that had only occurred to him few months before his talk), or when I saw Vaughan Jones cover a black board with a new calculus of knot diagrams, or when I heard Steven Cook speculate on some novel applications of complexity theory, I felt that I was watching history in the making. I knew that all of these new ideasâ€”that were being discussed with very little fanfare in the lecture hall of the Fieldsâ€”would not only shape the course of mathematics but would also eventually find applications in nearly every sphere of science and technology. And I knew that most of these applications would be almost unimaginably different from the applications for which the ideas were first conceived. In 2000, I was thrilled to learn that I had been accepted as a post-doctoral student in the Fields thematic program on graph theory under the supervision of Derek Corneil and Mike Molloy. In my first year at the Institute, after I had attended many lectures and taken part in many discussions with my fellow students and my supervisors, it slowly dawned on me that the method I had developed in my doctoral thesis to compute knot polynomials might have broader applications in graph theory. That year, in the hallway of the third floor,I also met one of my mathematical heroes, William Tutte,