Ramble, Part 7: Uncertainties
Dec. 8th, 2006 10:37 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowSome years ago, I read a book entitled Ancient History: Evidence and Models, by M. I. Finley. The main lesson I took away from that reading was just how little we know, with any certainty, about the classical world. So much material was simply lost, and so much of what survived is unreliable. (The case of Thucydides, who freely confesses to making up many of the speeches he presents, is notorious, but he was far from alone.) In reference to classical mathematics, one might point to the fact that Archimedes' letter to Eratosthenes, mentioned in the last Ramble, was not only lost but forgotten (if it was ever widely known) for more than two thousand years, and there are many other important works that we know to be lost.
The next mathematician I want to take up is Diophantus of Alexandria, and the problem I just mentioned is rather severe here. He stands outside the Euclidean tradition, interested neither in geometry nor, even, in the definition-theorem-proof mode of presentation. He seems like an outlier, almost, but he can't have been. Some of his work definitely seems to be derived from the Pythagorean tradition, though without the "all is number" triumphalism of that school. More strikingly, there are similarities of style and technique between Diophantus and the mathematicians of ancient Mesopotamia. It seems clear that there was at least one flourishing mathematical tradition, outside what we see as the main line, that stretched across millennia from Babylon to Alexandria - but we know next to nothing about the means of transmission.
Thus, I want to raise a cautionary flag. When I speak of mathematics in the classical era, for the most part I mean as it had impact on latter-day mathematics - not, primarily, what it was like in itself. There were mathematical schools other than the one that runs through Euclid, but the Euclidean tradition is the primary one which survived and nourished post-classical mathematics.
Not everything is simple, though. In theearly late seventeenth century, Diophantus' Arithmetica was translated from the Arabic (in which it had survived) into Latin from Greek, and a copy found its way into the hands of a fellow by the name of Pierre de Fermat...
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The next mathematician I want to take up is Diophantus of Alexandria, and the problem I just mentioned is rather severe here. He stands outside the Euclidean tradition, interested neither in geometry nor, even, in the definition-theorem-proof mode of presentation. He seems like an outlier, almost, but he can't have been. Some of his work definitely seems to be derived from the Pythagorean tradition, though without the "all is number" triumphalism of that school. More strikingly, there are similarities of style and technique between Diophantus and the mathematicians of ancient Mesopotamia. It seems clear that there was at least one flourishing mathematical tradition, outside what we see as the main line, that stretched across millennia from Babylon to Alexandria - but we know next to nothing about the means of transmission.
Thus, I want to raise a cautionary flag. When I speak of mathematics in the classical era, for the most part I mean as it had impact on latter-day mathematics - not, primarily, what it was like in itself. There were mathematical schools other than the one that runs through Euclid, but the Euclidean tradition is the primary one which survived and nourished post-classical mathematics.
Not everything is simple, though. In the
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