Variation on a Theme

Reading articles that make reference to mathematics and talking to people, I have the impression that mathematics almost entirely is concerned with computation with numbers. I usually find myself in a delicate situation when being asked what kind of topics I study in my math classes, which increasingly are becoming obscure to the uninitiated; the bafflement mixed with some frustration is not hard to see in the face in my interlocutor when I try to explain as simply as I can what these topics are. After a long pause nearing to some awkwardness, with me confronted with passive eyes and a sardonic smile betraying any apparent expression of interest, one response usually is, “Isn’t math about numbers?”. During such time, I figured it might not make too much of a difference to attempt to explain that this is not always the case. Indeed, results from Google Images for “math” tend to suggest to me that this conception of mathematics as being only about numbers is more prevalent than I have thought.

This has led me (as I did for my last post) to take a look at the Greek word for mathematics that tends to be associated with the Greeks (at least, as far as my reading goes). Mathematics is derived from μαθηματα (mathemata) from which one gets μαθημα (mathema), meaning learning, knowledge, act of study. These meanings do not seem to suggest any reference to numbers although one may argue they encompass numerical computation if considered as a form of inquiry. For example, by this interpretation, if one asks about the size of the Earth, the “math” is more about the inquiry about the size than it is about the process of computing such size. Similarly, the math is in the asking about the length of a hypotenuse of a right triangle rather than in the formula one obtains to compute such length for a given right triangle. This might then explain why many areas of mathematics categorized as “pure” tend to deal less with numbers and focus more on reasoning. Another consequence of this interpretation might be to see a mathematician not as a specialist of numbers, which rather is restrictive, but as a thinker whose scope of inquiry goes beyond areas that might involve computation. This could explain the conspicuous relationship of mathematics to philosophy in the past, where a clear distinction between the mathematician and the philosopher seemed difficult to establish; for example, would one consider Plato and Aristotle as philosophers but not as mathematicians and consider Frege and Bertrand Russell as mathematicians but not as philosophers? Such distinction does not seem obvious to me. After all, if mathematics means learning, philosophy (φιλοσοφια) means the love of learning, where learning is taken as synonymous to wisdom.

What then explains this actual perceived trend in which mathematics seems to be relegated entirely to numerical computation and philosophy seems to be totally detached from it to the extent that I have heard some people averring, “I am a mathematician not a philosopher” or “a philosopher, I am. Leave the details to the mathematicians!” ?

So, let me know what you think?

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