by Jean Joseph
After reading Katz’s article “Gender, Race, and Sexuality in Mathematics,” Wolcott’s article “An argument for ‘meta-mathematics’,” Moore’s biography, and Gödel’s biography (which I am still reading), it seems there is a recurrent theme, a theme which I’ve been thinking about for quite a long time: mathematics education need not be only about doing mathematics but needs to encompass other areas of knowledge or, at least, make students aware of other facets of mathematics other than solving problems.
At first, this attitude toward mathematics education may seem a waste of time. One may argue that future mathematicians, or mathematicians, should only learn how to tackle mathematical problems. It is no doubt an indispensable skill that all mathematics students need to have (and I hope to become a better problem solver during my stay in graduate school), and it’s a skill, I think, students should be taught very soon since it seems to enhance one’s analytical capability. Nonetheless, however abstract mathematicians want to build a world for themselves, they live in a society with other people that are not mathematicians, where they must interact with them at some level. As a result, some understanding of human psychology and of the fact that other people may have different perspectives on the same issue would be quite necessary (Even among mathematicians I’ve read of countless disagreements because of divergence of views).
In this article, I try to widen the notion of “meta-mathematics” mentioned by Wolcott in that these other areas that are not necessarily about mathematical research may not be related to mathematics; I think some other areas, not necessarily having mathematics as their main focus, such as moral philosophy, psychology, politics, sexuality, literature, need not be total strangers to mathematics students, or mathematicians, since they live in a society that have complex norms and mores that have some influence on them whether or not they want it and since there are other aspects of their own lives they will need to deal with, which they might not find much help from a proof of a theorem but maybe from a story they’ve read from a novel.
But one may argue that students may do all these extra-activities on their own. Could they even if they wanted? It seems many graduate students do not have such a luxury when they have to focus on their math classes and on the ones they teach. Although it may not be practical to make students take as much literature or philosophy as mathematics, maybe one-fourth of the classes could have been in non-mathematics classes or classes, which I call mathematical humanities, such as the ones mentioned by Wolcott. For example, though I don’t think Gödel’s mathematics graduate curriculum did have these non-math classes (so far in my reading there has not been such reference), he had a regular interaction with philosophers, social scientists, physicists during his involvement in the Vienna Circle, which seems to have a significant influence on his work in mathematical logic. Also, Moore has been known to discuss politics in his classrooms when students were not able to come up with a proof to some assigned theorems (but I don’t think he thought it necessary for his students to do anything other than math). And to go even further, it seems many ancient Greeks could not even be classified in a single category: Plato usually is mentioned as a philosopher, but couldn’t he be seen as a political scientist with his The Republic or a mathematician with his view on the ontology of mathematical objects, which, by the way, greatly influenced Gödel and Einstein who were seriously alienated in the postmodernist time in which they were living (As a matter of fact, many mathematicians consider themselves Platonists). When it comes to Aristotle, was he a mathematician, physicist, politician, literary critic, philosopher? It’s hard to know since he was involved in all these areas. What about Bertrand Russell? If one had only known him as a mathematician and later heard that he was awarded a Nobel Prize, wouldn’t it make sense that this person might ask if there was a Nobel Prize for mathematics? And if he or she was told it was in literature, would it be impossible that this person might think that it probably was another Russell? Well, I can imagine such a scenario if this person is of the opinion that a mathematician’s job is to only do mathematics; however, it seems, historically, a mathematician was seen more as an intellectual capable of taking part in discourses other than mathematics, and, in their education, they were expected to be acquainted with non-math subjects and other facets of mathematics, like its history and philosophy (as far as I know, it seems many scientists in the past also were known to be well versed in non-scientific areas such as the arts; maybe it is a modern view that an expert must exclusively focus on the small island of his or her area of expertise).
What do you then think? Does your curriculum have only math classes? If you were a graduate student a long time ago, how different was your curriculum from modern ones in term of the types of classes you were supposed to take? If you’re a student outside the U.S., how liberal do you think your program is?