Bibliographical notes:

Horace Mochizuki was bom in California in 1937. He grew up on a farm in the Great Central Valley. He was educated at the University of Redlands and received his Ph.D. from the University of Washington, Seattle. He has been on the faculty of the University of California at Santa Barbara since 1965.

In 1985 I stood here and delivered a series of lectures on the work of Horace and myself. It is a sad occasion on which I address you again today, sharing some thoughts of Horace.

I mention also my sadness at the passing of Roger Lyndon the previous year. Two of the most important mathematical influences in my life are gone, but more important, the personal loss is overwhelming.

St Andrews is a fitting place to share memories of Horace, as he was closely involved with Groups-St Andrews. St Andrews had many pleasant associations for both of us. We attended the first conference in 1981, and it was immediately after that meeting that Horace made a crucial mathematical discovery which I will later discuss. He did not attend Groups-St Andrews 1985, but as already mentioned, I spoke extensively about our then recent work. We had both looked forward to this meeting until Horace became ill.