Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils

Solution 1:

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.

Solution 2:

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.

Solution 3:

I'd oppose that idea. What later refiners and lately textbook writers did was to select material, clean it up, simplify and systematize notation, select understandable proofs, add modern extensions and applications. A selection of exercises that challenge and help deepen understanding is a valuable resource. A peek at the history is valuable, but should not be the principal source (unless it is a very new area, but that is another kettle of fish).

Granted, not all textbooks are excellent, but I'd wager most are a step nearer the "average interested student"'s understanding than any random "original source". Besides, some of the towering historical (or contemporary) figures were also accomplished writers (like Euler or Russell), a few were very good teachers too, but most wrote/write opaque gibberish.