In my experience during eleven years as a student and teacher of mathematics, professors and students talked about what was going on in various fields of mathematics, about who was doing what kind of research, and about the actions and personalities of particular mathematicians, but I never heard professors or students say anything about whatever benefits their work might bring to the human race—except on one single occasion:
During my second year at Berkeley, I notified the mathematics department that I planned to resign at the end of the academic year. Some time thereafter I received a phone call from Professor X, a big wheel in the department, who said that he and another big wheel, Professor Y, wanted to talk with me and ask me to reconsider my decision to resign. Eventually I met with X and Y in the latter's office. I had been looking forward to the meeting because I expected it would give me an opportunity to air my feelings about the pointlessness of mathematical research. In response to my effort to explain those feelings, Professor Y tried to justify mathematical research by asserting that it helped “the starving children in Asia.” This was a catch-phrase commonly heard at the time (circa 1969): Americans were supposed to feel sorry for “the starving children in Asia,” and our country was supposed to do something to help them.
I told Professor Y that I didn't believe my research was doing anything for the starving children in Asia. He seemed taken aback. “You mean,” he replied, “you don't think your work helps the starving children in Asia!?”
My work was in an area of pure mathematics that had no foreseeable or probable connection with practical applications of any kind. Y's field was symbolic logic. If a man were genuinely interested in helping “the starving children in Asia” he would go into agricultural research, or economics, or the sociology of “underdeveloped” countries, or another field that had some known relationship to the plight of starving children. He wouldn't choose symbolic logic or pure mathematics on the wildly speculative assumption that his work might one day find an application that in some way would help starving children. Y's parroting of the hackneyed formula “help the starving children in Asia” was clear proof that he had never given any serious thought to the question of how, if at all, mathematics-related research would benefit the human race. He had chosen symbolic logic simply because it served his personal needs. Then, when he was challenged (probably for the first time in his life) to explain why mathematics-related work was of value, he could think of nothing better than the platitude about “starving children in Asia.”
Professor X was a vastly better mathematician than Professor Y and a far more intelligent man generally. Ignoring Y's remarks about the starving children in Asia, X told me that a couple of years earlier he might have felt the same way I did about the pointlessness of mathematical research, but, he added, “I don't feel that way now.” He explained that his interest was held by the continuing discovery of new applications of his field, which was functional analysis. I think he meant applications to other parts of pure mathematics, but even if he was referring to technological applications he made no claim that his work was in any way beneficial to humanity.
My conversation with X and Y ended in an impasse. But it is interesting to note that on the only two later occasions on which I had contact with X, his behavior toward me was cold to the point of rudeness.
I wrote the foregoing account in 2009, forty years after the conversation here related, but in doing so I was not relying primarily on forty year-old memories. I had written down the most important points in some autobiographical notes that I composed in 1979, ten years after the events.