# No Classics in Mathematics?

2016/11/17 Leave a comment

As far as I can remember, there has been a collection of the Great Books of the Western World in my home (though to be fair, my memory does not go as far as many other people). Looking at the collection, what strikes me most is how few mathematical texts there are. In total, there are four authors writing about mathematics: Euclid, Archimedes, Apollonius, and Nicomachus. They are confined to a single book, and all of them are from the ancient world. To be fair, part of this is how I classify things; some people might classify the works in this collection by Newton and Fourier as mathematics, but I consider them part of physics. And of course, the distinction between subjects was not clear then. (Hence the Augustinian quote: “The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell.” Here mathematicians, astronomers, and astrologers are all grouped together.) Science and mathematics (and philosophy) were all studied together and mixed together. Though some people, such as Descartes and Pascal, made mathematical contributions, but only their philosophical works are included.

In general, I wouldn’t be surprised if most well-educated non-mathematicians could only name at most one mathematical text (namely, Euclid’s *Elements*). In fact, most mathematicians (myself included) rarely read any historical mathematical texts. I can think of a few reasons for this.

One, the language, especially in older texts, tends to be archaic in unexpected ways. This is especially problematic for non-mathematicians, since reading math is already similar to reading in a foreign language. The vocabulary hasn’t quite settled and so strange words are used to describe familiar concepts, which makes reading difficult. The notation is often quite different from what we’re used to. Using letters to denote variables didn’t happen until the end of the 16th century with Viete. And it was until Euler that we had much of the modern notation that we use today. Though often times, the notation of older texts is “translated” into the mathematical notation that we’re used to today (in addition to actually being translated from their original language).

Two, the original conception of an idea may be notoriously dense and opaque, but the efforts of later people can clarify that idea and make it much easier to understand. In that case, we give credit to the original, but then never read it again. The work of Galois is notoriously difficult to read, but we name the theory after him since he first conceived many of those ideas. This is not to dismiss or minimize these people’s works. Writing new ideas without a language to describe them is going to be a difficult task, and undergoing such a task should be praised. (Though, disgesting and presenting in a clear manner these ideas is also an important task, though it seems far less glamorous.) So the original text are often abandoned for clearer exposition written by people who worked hard to digest the original work. Then this is iterated again and again until we have our modern, super clean presentation of classic works.

All this to say, while I understand it to an extent, I find the current state as unfortunate. As a mathematician, I should read the classics to better understand the material and motivation behind several turns in thought. As a person interested in mathematical popularization, I find it problematic that rather than turning to some great works of the past, we often resort to presenting a pre-digested, cleaned-up version of a classic. Though, it’s hard for me to go tell people to read the classics, since I have not done so. Maybe I’ll try to remedy that.