My chances at this point of writing a paper with Erdős are probably very small. My chances of writing a paper with one of Erdős’ collaborators is also quite small. I had assumed that I had not even met — let alone talked math — with anyone with Erdős number one, but consulting with this link shows this is definitely false; I had a number of delightful chats with Andrew Granville at Oberwolfach in 2015. Still, given my interests, I imagine I am destined to always have an Erdős Number at least three. And now I have achieved that lower bound, having just written a paper with Don Zagier (and Stavros Garoufalidis).
I first met Zagier in 1993, during my last year of high school. He was the Mahler lecturer, a position which carries the responsibility of giving as many lectures as one can on mathematics (and number theory in particular) all around Australia. My brother encouraged me to play truant from school and sneak into a colloquium talk by Zagier, who talked (with characteristic enthusiasm) about Ramanujan’s Delta function and the Birch–Swinnerton-Dyer conjecture. My brother also introduced me (this very same day) to Matthew Emerton, who talked to me about math for three hours; in particular he talked about elliptic curves and Mazur’s theorem on the possible torsion subgroups over So it was a very auspicious day for me indeed! At the time, I was enthralled by Edwards’ book on the Riemann Zeta function and was expecting to become an analytic number theorist. But on that day, I completely abandoned those plans and decided to do algebraic number theory instead.
Zagier gave another lecture the next day (which I also skipped school to see). This time it was on volumes of hyperbolic manifolds and their relationship with the dilogarithm and the Bloch group. It is remarkably pleasing then to now — almost 24 years later — write a paper with Don and Stavros which is related to the theme of both those talks, namely the Bloch group and modularity.