Reflections on Ronald Graham by Steve Butler

Ronald Graham passed away on July 6 at the age of 84. We present reflections on Ronald Graham by Steve Butler.

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Getting to work with Ron Graham

Ron Graham has helped transform the mathematics community and in particular been a leader in discrete mathematics for more than 50 years. It is impossible to fully appreciate the breadth of his work in one sitting, and I will not try to do so here. Ron has put his papers online and made them freely available, a valuable treasure; and there are still many a hidden gem inside of these papers that are waiting to be picked up, polished, and pushed further.

I want to share about how I got to know and work with Ron. To be fair I knew about Ron long before I ever knew Ron. He was that rare pop-star mathematician who had managed to reach out and become visible outside of the mathematical community. And so as a teenager I read about Ron in a book about Erdos. I thought to myself that this guy sounds really cool and someday I might even get to see him give a talk (if I was lucky).

I went to UC San Diego for graduate school and after a series of near-misses ended up studying under Fan Chung. I passed Ron in the stairwell once, and then also helped them move some furniture between their two adjoining homes (graduate students are great for manual labor). But I became determined to try and find a way to start a conversation with Ron and maybe work up to working on a problem. So I took the usual route: I erased the chalkboards for him.

Before his class on discrete mathematics would start, I would come in and clean the chalkboards making them pristine. It also gave me time to occasionally engage in some idle chat, and he mentioned that his papers list was far from complete. I jumped on it and got to work right away and put his papers online and have been maintaining that list for the last fifteen years. This turned out to be no small feat and required about six months of work.  Many papers had no previous online version, and there were even a few papers that Ron had written that he had forgotten about! But this gave me a reason to come to Ron and talk with him about his various papers and then he would mention some problems he was working on with others and where they were stuck and thought I might give them a try.

So I started to work on these problems and started to make progress. And Ron saw what I was able to do and would send me more problems that fit my abilities and interests, and I would come back and show him partial solutions, or computations, and then he would often times fill in the gaps. He was fun to work with, because we almost always made progress; even when we didn't make progress we still understood things more fully. Little by little our publications (and friendship) grew and we now have 25+ joint publications, and one more book that will be coming out in the next few years about the enumerating juggling patterns.

After all of that though, I discovered something. I could have just gone to Ron's door and knocked and he would have talked to me, and given me problems (though our friendship would not become so deep if I had chosen the forthright method). But almost no graduate students in math were brave enough to do it; they were scared off by his reputation. As a consequence, Ron had far fewer math graduate students than you would expect. (To any math graduate student out there, don't let fear stop you from talking with professors; many of them are much nicer than you think, and the ones that are not nice are probably not that great to work with.)

So one of the most important lessons I learned from Ron was the importance of kindness. Ron was generous and kind to everyone (and I really stress the word everyone) that he met. It didn't matter what walk of life you were in, what age you were, or what level of math (if any) that you knew, he was kind and willing to share his time and talents. He always had something in reach in his bag or pocket that he could pull out and show someone and give them an unexpected sense of wonder.

Richard Hamming once said "you can be a nice guy or you can be a great scientist", the implication being that you cannot do both. Ron showed that you can be a nice guy and a great scientist. And I believe that a significant portion of his success is owed to his being kind; all of us should learn from his examples and show more kindness towards others.

This is only one of many lessons I learned from Ron. Another thing I learned from Ron is the importance of data. I have seen multiple times when we would work on a problem and generate data resulting in what I thought were hopeless numbers to understand. But Ron looked at that same data and with a short bit of trial and error was able to make a guess of what the general form was. And almost inevitably he would be right! One way that Ron could do this was to start by factoring the values, and if all the prime factors were small he could guess that the expression was some combination of factorials and powers and then start to play with expressions until things worked out. Even when I knew what he did, I still am amazed that he was able to do it.

I will miss Ron, I will never have a collaboration as deep, as meaningful, and as personal. I am better for having worked with him, and learning from him about how to be a better mathematician and a better person.

Thank you, Ron.