Most scholars spend the bulk of their time focused on issues which, though important for their fields, are of little immediate interest to the general public. How should these scholars contribute their expertise to public discourse? In some fields this is easily done. It is always interesting to hear what Middle East scholar Bernard Lewis has to say about current affairs in the Middle East. I always enjoy hearing any four economists give their six different prescriptions for optimal economic policy. For a mathematician studying, say, nonlinear partial differential equations or algebraic K theory, however, it is not clear how his expertise contributes to public discourse.
Among my nonacademic mathematical contributions is the fielding of mathematical queries from the general public. Often these questions require little mathematics beyond 8th grade algebra. The (usually college educated) questioners are chagrined if I point this out to them; so, I have learned to keep this observation to myself. I wonder if high school teachers receive similar queries.
Many questions are just bizarre. Once a man phoned to ask me what were the names of the large numbers after million and trillion. Perhaps he was doing research for Nancy Pelosi's budget advisor. I pointed out that this was not a mathematics question and the answer was surely available on Wikipedia, but he didn't take the hint; so, I pulled the answer off the internet while he was explaining why he needed this information. My answer (or more accurately Wikipedia's answer) satisfied him, but then he wanted me to connect him to someone in the physics department who could answer his questions about stellar evolution. When I told him that I couldn't connect him, he replied, "Hah. You know all those big numbers but don't know how to use a telephone." Some of these folk just seem to want to talk. I always give them a moment to convince me that they don't intend to donate money to the Department before sending them on their way. A month or two ago I received a call from a man who told me that he had received an advertisement for a mathematics book sale, and he wanted me to be aware of the low prices. I asked him if he wanted to donate books (not a good way to use his funds). He said, "No." Was he a salesman? "No." Then why was he calling me? He just wanted me to be aware of the low prices. I didn't bother to tell him how many flyers and emails I get from publishers every week, but I did get him off the phone quickly.
Enthusiastic amateurs are a more difficult group to satisfy. The Department receives a constant trickle of manuscripts from amateur mathematicians who claim to have solved some famous conjecture or, more often, claim to have solved some problem that mathematicians proved a hundred years ago has no solution. Folks, if we have proved that there is no solution, then as far as we are concerned, the problem is finished. We are not going to spend lunch reading through manuscripts so that we can tell the authors what their mistakes are. Sometimes I try to farm out amateurs' manuscripts to postdocs to read, but I rarely get any takers. Most requests to review these are left unanswered. Since manuscripts can be posted on the arxiv, I don't feel too guilty about this.
The last category of query consists of students at other schools trying to get me to do their homework for them. I had a long spate of requests from students with Turkish email addresses, wanting help with engineering calculus homework . I don't know how I got on their list. I decline all such requests.
I bet no one writes Bernard Lewis to ask him for help on their homework.