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Ramble, Part 31: The Need for Narrowing
Sep. 5th, 2007 06:55 pmPopular histories of classical civilization sometimes rhapsodize about the brief but brilliant light of the Greek golden age. At least as far as mathematics is concerned, though, that's misleading. The heyday of Greek mathematics begins with Thales, sometime around 600 BC, and lasts until sometime after the death of Archimedes in 212 or 211 BC - a span of about four centuries.
The modern era in mathematics, in my view, begins with Descartes's publication of La Géométrie in 1637. That is, you may note, less than four centuries ago. It may not be meaningful to compare the Greek era with the modern, but it is hard to dispute that mathematics since Descartes has undergone another golden age. (Whether we are still in that golden age is doubted by some; I am not among them.)
Unfortunately, this presents a problem for me in writing the Ramble. After the development of calculus, mathematics begins to ramify in many directions - too many to recap in any reasonable span of words. Beyond that, many of the new developments are too abstruse or simply too complicated to synopsize easily. From this point on, then, I'm going to have to be very selective. Some mathematicians - even some of the greats - will simply be passed by, and even of those that I do talk about, I will concentrate on particular achievements rather than try to indicate the fullness of their work.
When I began writing this series of posts, I intended to talk primarily about issues of philosophy and methodology. I've done somewhat more than that, I think, but for the remainder of the Ramble I will have to narrow the focus. I think that there's enough meat there to be of interest, but if not, well... choices have to be made, and these are mine.
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The modern era in mathematics, in my view, begins with Descartes's publication of La Géométrie in 1637. That is, you may note, less than four centuries ago. It may not be meaningful to compare the Greek era with the modern, but it is hard to dispute that mathematics since Descartes has undergone another golden age. (Whether we are still in that golden age is doubted by some; I am not among them.)
Unfortunately, this presents a problem for me in writing the Ramble. After the development of calculus, mathematics begins to ramify in many directions - too many to recap in any reasonable span of words. Beyond that, many of the new developments are too abstruse or simply too complicated to synopsize easily. From this point on, then, I'm going to have to be very selective. Some mathematicians - even some of the greats - will simply be passed by, and even of those that I do talk about, I will concentrate on particular achievements rather than try to indicate the fullness of their work.
When I began writing this series of posts, I intended to talk primarily about issues of philosophy and methodology. I've done somewhat more than that, I think, but for the remainder of the Ramble I will have to narrow the focus. I think that there's enough meat there to be of interest, but if not, well... choices have to be made, and these are mine.
Previous Next
Ramble Contents
