Once upon a time a mathematician, let's call him M, applied for a position as a mathematics professor at a postgraduate institution. During the interview, M pro

Once upon a time a mathematician, let's call him M, applied for a position as a mathematics professor at a postgraduate institution. During the interview, M proposed an unusual salary arrangement to the department chair--let's call him D. "I'm not asking for anything exorbitant. I ask only for $1 per year more than the salary of anyone else here, as a token of recognition that I am a better mathematician than anyone else in the department." D said that he would think it over. During their next meeting, M asked D what he thought of his proposal. D replied that after the deepest consideration, he had decided against it. "Why?" M wanted to know. "Because the reason for paying you that additional dollar isn't true," D replied.