Names, naming and terminology

Mathematicians use people’s names as terminology on an astonishingly regular basis. Names pepper mathematical discourse, like little nuggets of history, popping up to point to a certain kind of a thing worked on by a certain person in history: Duhamel’s formula, Cauchy data, Willmore energy.

It’s made even more interesting by the famous tendency in mathematics for a particular discovery to be named after somebody who came some time after the person who initially discovered it. This may, perhaps, be that the person who gets that particular honour is the one who brought it to widespread attention first, made it most coherent, expressed it most accessibly. This needs some research. But it highlights the strange historical situation involved in this naming.

The use of a name connects a piece of mathematics, that operates in this strange abstracted imaginary world, with a particular historical period of something probably around 70 years. It refers to a person, but particularly to that person’s life as a mathematician; it isn’t normally taken to refer to someone’s eating habits. The context will suggest which parts of their work are in question, a famous paper perhaps; this paper may have been surrounded by debate and conflict, collaboration and discourse. A lot is contained within that piece of terminology.

A computer scientist once pointed out to me the emphasis put on hierarchy and respect for history in pure mathematics, as compared to his field; whereas computer scientists would look for verification, mathematicians he knew would assert that something was true simply because somebody well known said that it was, probably because of how difficult it is even for a specialist in a field to truly understand the work of others, a problem that I have referred to elsewhere in these posts.

These names clothe mathematics in the historicity of its structure. These abstracted objects are people, just as a urinal is now Duchamp and the turn of the last century and the age of mechanical reproduction. Even on a page of black-and-white symbols, those names are inescapable reminders of the hands that have previously written those symbols and given them their meaning.

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