Ramble, Part 0: Prologue

[stoutfellow]

The oldest branches of mathematics, most likely, are arithmetic (construed broadly as the study of numbers) and geometry (broadly, the study of shapes). That they are two branches of one subject is widely accepted. But what does that mean? Certainly their subject matters are quite different. What justifies lumping them together in this way?

A first response might be that they both have to do with numbers. It's true, of course, that geometers do work a good deal with numbers - lengths, areas, volumes, angle measures, and so on. But there are many other fields that are equally involved with numbers; I invite you to tell a statistician or an engineer that what they do is a branch of mathematics. (I advise you to duck quickly.)

The relationship between arithmetic and geometry is actually rather complex, and a good deal of mathematical history is tied up in the various ways people have tried to make them fit together. That will be the subject of the first couple of posts in this series, and of at least two more later on. (If anyone would like to offer their own thoughts on the question I've just raised, well, that's what comments are for...)

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Comments

[stoutfellow.livejournal.com]

I dunno; I've known a burly statistician or two...