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I was thinking about Abel's advice to read the masters, yet many people claim that reading the old masters (Euclid, Archimedes, Newton, Euler, Gauss, Lagrange, and so on) is not a good idea today, for various reasons. However, if one were to read, or at least have reference to, the most often cited, and original, books in mathematics, wouldn't there be much to gain?

For example, I expect Euclid's Elements to be on the list. Newton's Principia, particularly his Treatise on Fluxions, is valuable historically, rightly as the origins of calculus, but never cited for a reference in modern calculus texts, thus would not be on the list. Gauss's Disquisitiones Arithmeticae, should be on the list. Dickson's Histories of the Theory of Numbers is a nice reference to have as well... it's very often cited.

So what are the most referenced works in Mathematics? Which works would be "the base of the reference tree"?

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    $\begingroup$ This question seems to broad and opinion-based for this site. Could you narrow it down and make it more straightforward? $\endgroup$ Jan 2, 2016 at 16:07

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The notion that Euclidean geometry is "still the same" is a bit naive. A pass through Moise's book "Elementary Geometry from an Advanced Standpoint" will convince you of this. In particular, modern Euclidean geometry relies pretty solidly on the notion of measure -- the length of a line, the measure of an angle -- rather than on ideas of proportion as an abstract way of comparing things. This modern approach allows one to use algebraic methods to prove many things more easily.

In much the same way, learning projective geometry from Hartshorne's little book shows you the connections between various geometric things (Fano's Axiom, for instance, or Pappus' Theorem) and the underlying algebraic properties of an algebraic entity $F$ that's associated to a (rich enough) projective geometry (e.g., for geometries that satisfy Pappus' Theorem, the associated $F$ might have a commutative multiplication operation, although I may be misremembering this -- it might be that the operation is associative). You can read a lot of early but well-developed projective geometry texts that will not tell you about this because the formal notions of abstract algebra hadn't yet been developed.

I'm definitely keen on reading older texts, but there's a lot to be said for modern "revisionist" views as well. I'd prefer to read Milnor and Stasheff's Characteristic Classes to anything Whitney wrote, despite my huge admiration for Witney's work on sphere bundles (and almost anything else, too!).

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    $\begingroup$ I stand by my claim that I would prefer to read Milnor and Stasheff rather than Whitney. But I bow to your superior knowledge. I probably don't know which one led me to greater understanding. $\endgroup$ Jan 3, 2016 at 21:57

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