Abel remarked that he attributed his profound knowledge of mathematics to the fact that he read the masters, rather than the pupils.
Are you better off reading the Masters or the pupils? This of course depends on the masters and the pupil and other factors.
- I have heard that Godel's original papers (even when translated) are well written and show a profound understanding of the subject and why its important.
- However, we now have a better understanding of what Godel did and better ways to express it.
- The Masters may include the motivation which may be lost in later papers.
- Often the first proof of anything is ugly or odd and later proofs really clean it up.
- Often the first proof of anything uses only basic concept- later abstractions may hide the heart of the proof.
- As a practical matter sometimes the early papers are not available (thanks to paywalls or obscurity) or in a language you do not read.
- If Lance and I ever do a book-of-blog-posts I will clean up some of the spelling, make some of the arguments more clear (perhaps indicate where I am being sarcastic in cases where it was not understood), improve the writing. This will make it better than the blog but less authentic.
Here are examples where the Masters papers may not be worth reading:
- Recursion theory in the early 1960's had several infinite injury arguments. I have heard that they were known to work only because the lemmas and proofs worked out. Only after Bob Soare's excellent article on the topic were they really understood. For 0''' priority arguments it is also true that the early papers are not the ones to read.
- Example (and the real motivation for this post). I have tried to read Ramsey's original article. I knew that his goal was a problem in logic, and I wanted to know what that problem was. I had a hard time reading the paper. (I did my own writeup.) Why was his version so hard to read? (1) He never uses the words coloring or graph or hypergraph. He doesn't mention that if you have six people at a party either three of them know each other or three of them don't know each other. Perhaps he didn't go to many parties. (2) He uses odd terms at time. (3) His paper is rather abstract. If he had just proven a simple case then it would be obvious how to proceed to his abstract case. This is true for both his combinatorial theorem--- he only proves (what we would call) the hypergraph version, and also the Logic theorem.
- The Cliff notes for Atlas Shrugged are far better than the book. Shorter too. They are online for free here which makes sense since Ayn Rand was known for her altruism.
SO- what do you think? Examples of cases where the Master is better to read?
Examples of cases where the Pupil (or more generally later summaries, surveys, expositions) is better to read?