Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I was wondering if mathematics learning process require the use of textbooks.

When I was a high school student, I read as a preparation for university, Legendre book on Elements of geometry and trigonometry, I notice the power of that style of teaching mathematics: propositions lead to theorems, then I read old books on the foundations of geometry such as Russell's, Hilbert's and Coxeter's. In order to learn some arithmetic, I tried to read Dedekind's Essays on the theory of numbers, off course that was just a big fail, I had to run straight to Niven's book.

I was wondering if a person is capable to substitute textbooks in order to learn directly from the source of Knowledge and creativity, I mean replace a normal HS algebra book with a modern edition of Cardano, Wallis, Vietè, Descartes, etc. Analytical geometry with Descartes, Learn arithmetic with Disquisitiones Arithmeticae; Abstract algebra with Cayley, Dedekind, Galois, Noether, etc; Switch Munkres to Cantor, Poincaré, Hadamard, Borel, etc.

I do not think you can learn Calculus without Spivak's or Hardy's or Rudin's because original calculus was develop for applied purposes and real analysis do require a pedagogical treatment (I think), and those books are really great; but books on Algebra, Topology, Number theory, analytic number theory,categories, representation, even homotopy books are just compiling work and providing useful exercises.

The question is, reading the master, you think yourself capable of learn math without reading the pupils, and instead of that reading the masters, or you think that modern and contemporary math require a depth pedagogical treatment to translate you ideas?, if you think your capable, what articles, books would you read.

I would read Grothendieck, Shannon, Knuth and Mirsky stuff

Note: That is constructional, I want to teach algorithms next term using not textbooks, but old papers, I need an opinion (would it be a waste of time, or inspirational)

Thank you very much

share|improve this question
Of note is that the notation used by the masters is not necessarily the same as, or even compatible with, currently accepted notation. You might want to keep this in mind. –  J. M. Apr 4 '13 at 6:02
Yeah, i mentioned modern edition of Cardano,..., etc, but the question is anyway for modern and contemporary math, i don't thing Atiyah notation would differ that much from the one we learned as graduates. –  Sebastian Griotberg Apr 4 '13 at 6:04
Original material tends to ne difficult. The exceptions are mainly books written by the masters but intended as textbooks. –  André Nicolas Apr 4 '13 at 6:29
Well, that's basically the only way to do it... once you have your PhD. Before that it's a good idea to read more recently written things. It's not easy to read Principia when you ain't ever done any calculus before. –  Alexander Gruber Apr 5 '13 at 5:16
Obstacles to reading the masters include: papers written in Latin, French, German , Italian, Russian, Japanese, Hugarian or other languages; papers not being readily available - either not online or behind paywalls. –  Snor Apr 6 '13 at 12:04

1 Answer 1

André Weil wrote:

... our students of mathematics would profit much more from a study of Euler's Introductio in analysin infinitorum, rather than of the available modern textbooks.

(André Weil, 1979; quoted by J.D. Blanton, 1988, p. xii)

Blanton's translation has made this wonderful 1748 work available to English-speaking audiences. Once you have mastered the Introductio you can go on to Euler's Institutiones of 1755, similarly available in Blanton's translation.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.