[atrettel]

I agree completely. There always has been too much to read, and the best strategy remains to read what you can while recognizing that you may be missing something. I make every effort to find as much related literature as possible but I am continually amazed by some of the work that I find years afterwards that I missed the first time around.

On a similar note, I remember reading a biography of physicist Lev Landau years ago (Dorozynski's The Man They Wouldn't Let Die). If I recall correctly --- and please correct if I am wrong --- there was a part where the author described Landau's intentional reluctance to read papers, at least early on in the research process. Landau wanted to formulate original approaches to problems, so he did not want his thinking influenced by how things were previously done. I do not agree with the idea but I do find it interesting that some researchers in the past have valued the opposite of reading widely.

[impendia]

My postdoctoral mentor didn't go that far. But he did say that when he read a book, and encountered the statement of some lemma or theorem, he liked to try to figure out how to prove it himself instead of reading the proof there.

There is also the infamous "exercise" in Serge Lang's algebra book (scroll to the bottom):

https://drive.google.com/file/d/0B_pEp00B111JYWU1NmY4MjktZTN...

[atrettel]

I think your mentor strikes the right balance between awareness and originality. My criticism of Landau's idea is that it's a great way to make you think you have an original idea when you actually don't. Only a detailed literature search will verify its originality. I think that any attempt to "isolate" your thinking from others' thinking will fail because you cannot live in a total vacuum. At least some external thinking will influence you no matter what and we must acknowledge that. "Multiple independent discovery" happens all the time in science, and it's because everyone tends to operate in a similar environment.

I do agree with Landau that occasionally knowing how things are previously done could limit how you approach the problem, but that can be fixed by systematically reproducing or falsifying the previous results and drawing your own conclusions (trust but verify). You gotta get your hands dirty. It's slow and difficult but the right way in the long term.