Written: Oct. 24, 1995.
In Regis's book on the Institute for Advanced study, somebody is quoted saying: ``Mathematics is so hard that a mathematician can only work a few hours a day, the rest of the time he is bugging everybody else''.
Indeed, mathematicians are one of the most arrogant creeds, although for the most part, they keep their arrogancy within, when they try to linearly rank the subfields of math, and the practitioners of math, where their own subfield, and self, are at the top (or close to it, there is always a Margulis or a Gelfand who is slightly better.)
Sometimes, however, they try to point out how stupid non-mathematicians are, especially when they try to use mathematics. Some, like that enfant-terrible from Yale, are fond of combating `charlatans' in Political Science (they usually put a quote around the `Science' in PoliSci, to indicate its bogusness), who allegedly abuse mathematics. In doing so, it is they who are being the charlatans. Huntington did not use sheaves or etale-cohomlogy to make his point, but fifth grade math. Lang is no more qualified to comment on the math than any MITS, and is completely incompetent to judge the work as a whole, since he knows nothing of political science.
Another breed of charlatans, who however, have very good intentions, and are genuinely concerned about the issue, are celebrated mathematicians who crusade against `Calculus Reform' or other reforms. They are world-class mathematicians, but that does not make them authorities in teaching Freshman Calculus. They are usually excellent teachers, but only to the top 5%. They have no expertise or feel for teaching the average or below-average student. While they are entitled to be heard, it should be remembered that they are speaking as laymen and rank amateurs in the field of Mathematics Education.
Fortunately, the intersection of the set of Great Mathematicians and Great Mathematical-Educators is non-empty, witness Bressoud, Strang, and many others.
So let mathematicians stick to math, and whenever they apply it elsewhere, they should do it in collaboration with experts in the other field.
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