Death is never welcome but it is especially disturbing when it hits unexpectedly and someone who is comparatively young – all the more so someone as vibrant and larger than life as Tom Wolff. 

The Talmud in tractate Sanhedrin has a back and forth discussion among Rabbis arguing over whether the primary purpose of a eulogy is to comfort the survivors or to honor the dead. In the end it concludes that the primary purpose is to honor the dead. This makes eulogizing Tom’s mathematical side especially difficult because it is his work that truly honors him, not my mere words. In some ways, I feel like pulling down a blackboard and talking about Tom’s theorems, but that’s not appropriate here so I’ll have to settle for talking about some of his virtues. 

Here, the Talmud also has advice but this time easy to deal with. In tractate Berachos it says that one is allowed to exaggerate the virtues of the dead – slightly – but not to the point of attributing virtues that were not present. The difficulty here is not finding virtues but in deciding on a limited number that fit into a brief eulogy, and as for exaggeration, that’s unnecessary, since in those aspects that I want to talk about, Tom represents a maximal point.

So I’ll focus on five words that try to capture Tom as a mathematician:

The first is brilliance. Of course, non-mathematicians tend to regard all serious mathematicians as brilliant, since we are a sort of priesthood that speaks an incomprehensible language. But I don’t mean brilliant in that sense but from the view of a professional mathematician. Believe me, professional mathematicians don’t often describe their colleagues as brilliant, but Tom’s insights were often so stunning that the word applies.  For example, I was told the story of a major analyst literally falling off his chair in surprise at reading one of Tom’s recent papers. Allow me to quote here from a letter we got from Peter Jones, the mathematics department chair at Yale: “The hallmark of his approach to research was to select a problem where the present tools of harmonic analysis were wholly inadequate for the task. After a period of extreme concentration he would come up with a new technique, usually of astonishing originality. With this new technique and his well-known ability to handle great technical complications, the problem would be solved. After a few more problems in the area were resolved, the field would be changed forever. Tom would move on to an entirely new domain of research, and the rest of the analysis community would spend years trying to catch up. In the mathematical community, the common and rapid response to these breakthroughs was that they were seen not just as watershed events, but as lightning strikes that permanently altered the landscape.”

The second is skill. Outsiders may think that to have brilliant insights you must have technical ability but that’s only partly true. Tom went way beyond mere technical facility. He was a master craftsman of the tools of analysis. I saw this in my own joint work with him. We wrote a paper that neither of us would describe as brilliant although it has been widely used since because it provided a method that others could use as a starting point. The work began when I put together some ideas of others and tried to understand their implications and came to some useful conclusions so long as a certain technical fact was true. I spent about a week working on it to no avail so I spoke to Tom. We talked about it for about an hour but it didn’t crack. The next morning though Tom walked into my office with a solution. 

The third is passion – the central word – as one would expect of the third word out of five. Carol learned, as the wives of most great mathematicians have, that she had to share her husband with a mistress called mathematics because the commitment, focus and concentration that Tom gave to the subject can only be described as passion. One example of this is the most common memory I’ve heard in the past week from as varied sources as a group of undergrads that came to see me to what Caltech’s Provost told me. That’s of Tom pacing up and down on the walk outside Sloan with a cigarette in one hand and a huge cup of coffee in the other,   totally oblivious and clearly in very deep thought.

The fourth word is honesty – an uncompromising intellectual honesty. Some mathematicians when they become as established as Tom was, develop a kind of arrogance where when told something they never ask for details but act as if they’ve known that since they were in grade school. And in the other direction, they’ll often wave their hands on issues where they assume eventually they’ll have the details although they don’t yet. Not so Tom. He always probed with questions without a thought that someone might think him dumb for having to ask and he was always careful about the status of anything he asserted.

When I was picking the five words, I had trouble figuring out the right one to capture the last aspect I wanted to and then within a few minutes I got two emails that used the same word – generosity. Tom not only loved mathematics – he loved mathematicians. He clearly felt part of his responsibility was to find young analysts in obscure places with real talent and make sure they got recognition. He was a demanding but respected teacher and a superb mentor of both graduate students and postdocs. The irony in this was that Tom was so very shy – often painfully so – but he overcame his shyness to be able to interact with other mathematicians.

Allow me to quote from two of the many emails I’ve gotten about Tom in the past week. First: “I was a student of Tom Wolff at Caltech 9 years ago. He taught me real analysis. It was the most difficult, and best, math class I have ever taken. He had a profound impact on my life, all in a short ten weeks.” And from one of his coauthors: “As one of the many who has benefited tremendously from Tom's mathematical ability and extreme generosity, I would like to ask you to give Tom's family my sincere condolences. Tom was a fine man and it is a great pity that he left so early. He's helped me a lot, more than any other mathematician, and I'll always be grateful for his help”.

Carol told me she was Tom’s number one mathematical groupie.  I’ve no doubt that’s true – but Carol, we were all his groupies.