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It's a commonplace to state that while other sciences (like biology) may always need the newest books, we mathematicians also use to use older books. While this is a qualitative remark, I would like to get a quantitative result. So what are "old" books still used?

Coming from (algebraic) topology, the first things which come to my mind are the works by Milnor. Frequently used (also as a topic for seminars) are his Characteristic Classes (1974, but based on lectures from 1957), his Morse Theory (1963) and other books and articles by him from the mid sixties.

An older book, which is sometimes used, is Steenrod's The Topology of Fibre Bundles from 1951, but this feels a bit dated already. Books older than that in topology are usually only read for historic reasons.

As I have only very limited experience in other fields (except, perhaps, in algebraic geometry), my question is:

What are the oldest books regularly used in your field (and which don't feel "outdated")?

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I think this should be Community Wiki. – Alberto García-Raboso Dec 28 '12 at 16:28
Please don't call "Characteristic Classes" old or I will have to call myself old, being born in the same year as the lectures :-/ – Lee Mosher Dec 28 '12 at 18:28
@Lee Mosher: Would you prefer to call yourself "classical"? :) – user29720 Dec 29 '12 at 0:08
Timeless . . . . – Rodrigo A. Pérez Dec 29 '12 at 3:08
E. Spanier "ALgebric TOpology", "Eilenberg Steenrod "ALgebric TOpology", GOdement "Topologie Algébrique et Théorie des Faisceaux ", COurant-Hilbert "Methods of Mathematical Physics"... "the problem of contemporary authors, is to being con-temporary" (Ennio Flaiano) – Buschi Sergio Dec 29 '12 at 10:45

66 Answers 66

Daniel Quillen's "Homotopical algebra", 1967.

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O. Kellogg, Foundation of Potential Theory

The first edition of Kellogg's Foundation of Potential Theory was published in 1929. Btw he was a student of David Hilbert.

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I'm surprised that no one has mentioned Emil Artin's beautiful monograph on the Gamma Function. The economy and elegance are unsurpassed.

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Bonnesen and Fenchel, "Theorie Der Konvexen Korper" Springer, Berlin 1934 not available in English translation until 1987 although Eggleston's "Convexity" 1958 draws heavily on it.

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For ordinary differential equations there is:

  • Theory of ordinary differential equations by Coddington and Levinson, McGraw-Hill Book Company, 1955

I'm not sure it is used in courses, but it is certainly still cited frequently, for example as a reference for Carathéodory type differential equations where the vector field is only integrable in time.

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Nathaniel Bowditch is generally regarded as a nineteenth century American mathematician . His American Practical Navigator has been in continous print since 1804. It is still in use today judging from the comments on Amazon. But perhaps this isn't what was meant by a mathematics book and perhaps navigation isn't to be considered applied mathematics.

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According to wikipedia (see the book has been continually revised since 1804 and at this point contains essentially none of the 19th century content. – Andy Putman Feb 6 '13 at 16:58
Apart from the details of its revision, I think historically "navigation" was very much a topic in mathematics: spherical trigonometry and all that! Bowditch was certainly a mathematician by U.S. standards, such as they were! :) – paul garrett May 17 '15 at 21:55

protected by Scott Morrison Oct 12 '13 at 11:46

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