Mathematical literature to lose yourself in

H.M. Edwards in the preface to his book on the Riemann Zeta Function, summarises his philosophy on learning Mathematics:

...I have tried to say to students of mathematics that they should read the classics and beware of secondary sources

In trying to learn more, I feel that I have accumulated a bookshelf full of secondary sources which I have left largely unread. So I would like to take heed of Edwards's advice and read some classics for the wonderment of it and for the respect I would gain for mathematicians of the past. I would like to exercise creativity over rigour, at least for a little while.

But this begs the question: what are the classics? And this is what I hoped to ask about.

Which primary sources do you feel are suitable for self-study? Naturally this is a broad question, but people must have their favourites, and I am hoping for some recommendations on the basis of these personal preferences.

Solution 1:

For introductory Number Theory, you could go with Gauss, Disquisitiones Arithmeticae. Don't worry, you don't have to read Latin, it is available in English and other living languages.

Solution 2:

Three books: Euler's Introduction to the Analysis of the Infinite and Foundations of the Differential Calculus both translated by JD Blanton and published by Springer, also the very informative Analysis by its History by Hairer and Wanner. There are always the original papers by the biggies which are more often than not very interesting, illuminating and convey a sense of a firsthand encounter with the author(s).

Solution 3:

Euclid's "The Elements". Greek. Old. It doesn't get much more classic than that. As well as his other writings. http://en.wikipedia.org/wiki/Euclid#Other_works

Also, the Principia Mathematica by Newton. As well as his other writings. http://en.wikipedia.org/wiki/Isaac_Newton#Mathematics

Archimedes probably deserves a mention as well. You know, pi and circles and all that. http://en.wikipedia.org/wiki/Archimedes#Writings

Also I've seen Gödel, Escher, Bach mentioned on this page several times. Perhaps not canonically 'classic'. But really an excellent book. Changed the way I've thought about life, science, philosophy, CS, and many other things. It's also probably a good gateway into Gödel's incompleteness theorem.

Solution 4:

There are several Source Books that have made nice selections for you to pick from, e.g., Smith, Struik, Fauvel and Gray, Stedall. But for an extended read, you can do nothing wrong by immersing yourself in Gauss' Disquisitiones.