I have heard (I have no citation and it’s probably apocryphal, but I found the anecdote enlightening) that Enrico Fermi’s way of reading articles was to read the abstract, put the paper away, do the maths by himself and once he was done, compare his results with the article. That’s probably a bit hardcore, but you should be able to start from somewhere in the paper’s reasoning and do a few steps forward.
But where are you in your paper reading at the moment ? Is there a particular problem that spurred this question ?
That technique would be beyond me at this stage—I have done courses in Calculus, Linear Algebra and Logic and can finally understand most of the syntax and flow in research papers, though I still don’t feel at all competent, seeing that I feel I could not recreate the proofs they come up with.
I think that is my issue—I can read lots of maths, I can do the exercises but I am not sure how to go about ‘doing something real’ - ask me to write any software you can think of and I can do that, but I feel I am missing some fundamental point / learning in maths. Or maybe I am over thinking this, and haven’t had a concrete problem to play with.
I have heard (I have no citation and it’s probably apocryphal, but I found the anecdote enlightening) that Enrico Fermi’s way of reading articles was to read the abstract, put the paper away, do the maths by himself and once he was done, compare his results with the article. That’s probably a bit hardcore, but you should be able to start from somewhere in the paper’s reasoning and do a few steps forward.
But where are you in your paper reading at the moment ? Is there a particular problem that spurred this question ?
That technique would be beyond me at this stage—I have done courses in Calculus, Linear Algebra and Logic and can finally understand most of the syntax and flow in research papers, though I still don’t feel at all competent, seeing that I feel I could not recreate the proofs they come up with.
I think that is my issue—I can read lots of maths, I can do the exercises but I am not sure how to go about ‘doing something real’ - ask me to write any software you can think of and I can do that, but I feel I am missing some fundamental point / learning in maths. Or maybe I am over thinking this, and haven’t had a concrete problem to play with.
Try taking a thing you know how to do, and figure out why it works.
Why does integration-by-parts work, say?