On the name of this blog

Before I loved mathematics, I loved language. I still do love language, especially the fragmented patterns of etymology that let us guess at the meanings of some, but not all, unfamiliar words in our own and other languages. It's a fascinating web of connections, and my picture of it grows every time I learn a new word.

In college, I studied ancient Greek, and one of the first words I learned in my first Greek class was the word for student. It is μαθητης; transliterated, it would be something like mathetes. This is only one of the 13 entries in my Greek-English lexicon for words beginning math-, and every one of them has to do with learning.

These are the words that our English word mathematics comes from. In fact two of the entries in my lexicon already refer to mathematics and mathematicians. The Greeks had many words for various arts they studied, and mathematics isn't the only one which has kept its meaning in modern English; rhetoric is still the art of speaking persuasively before a crowd, and philosophy still the pursuit of wisdom through concentrated thought. But mathematics is the only discipline  whose name also means, literally, that which is learned or studied.

This isn't, of course, the only possible etymology for a word which means mathematics. It is, however, a powerful one. For many things we do, we have instincts and history going back even before we were human. We tell and listen to stories so naturally because we are social animals, and stories are part of the bonds that hold us together. Our instincts for mathematics, though, are quite limited. Most people can automatically tell different numbers of objects apart only up to about 5. Everything after that is learned, not in the unconscious way we assimilate new words but through deliberate effort, the way we learn to read. Any mathematical skill, whether counting or a complicated method of proof, has to be learned, practiced, and, often, failed at before it can be used. Even the most accomplished and brilliant mathematicians learn their craft step by step. Their astonishing insights are supported by a background of patient and diligent study-- and that background, at least, we can all imitate if we want to.