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
Best Answer
You may find the following website interesting/useful: Teaching with Original Historical Sources in Mathematics
Use of original historical sources in lower and upper division university courses is discussed. Reinhard Laubenbacher and David Pengelley were inspired by William Dunham to cover "mathematical masterpieces from the past, viewed as works of art." However, "Whereas Dunham presents his students with his own modern rendition of these masterpieces, [their] idea was to use the original texts themselves." They have authored at least two books intended for this purpose:
Mathematical Expeditions: Chronicles by the Explorers.
Mathematical Masterpieces: Further Chronicles by the Explorers
As I recall, the books use excerpts from the original sources, liberally augmented with modern explanation/analysis.
Assuming you are a student and not a mathematics researcher, my own personal opinion is that for a first reading it is better to use a (good) contemporary author writing for a student at roughly your level. He or she will have the benefit of history's digestion, simplification, and further development of the subject and, when applicable, will be able to translate outmoded notation into modern notation. If the original source is more recent and has been written at roughly your level then it may be superior. Otherwise, I think original sources are best for second readings and/or supplements.