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Jan 22, 2020 at 21:40 comment added Sebastian Bechtel @mlk good point! To stay at the state of the art even the word published needs further specification. I was once in the situation that I waited for a paper to appear on ArXiv to be able to submit my own paper to the journal because I already used the result while being personal communication (of course I checked the result really carefully).
Jan 21, 2020 at 15:33 comment added mlk Maybe to add to my last comment. Things are also source dependent. As a student, papers generally get recommended to you. Assuming the recommender knows what they are doing, those will be relevant and worth a detailed reading. As an active researcher trying to stay at the "state of the art" (whatever that may be), most of the papers you read are whatever just has been published, which as said often have a promising abstract but then turn out to be less relevant after a few pages.
Jan 21, 2020 at 15:24 comment added mlk @Jim In most cases most academics just skim the paper and skip large parts of it. However asking for the average is highly misleading. Perhaps 90% of the papers I'll read, I'll never use. And in general those are the papers I skim. In theory I could move the average to reading all papers in detail by simply not looking at those 90% at all and still do the same mathematics as before. It's just that the best way to gauge if a paper is worth reading in detail and has results or techniques that can be used, is skimming it first.
Jan 21, 2020 at 15:10 comment added Buffy Not for a serious mathematician. Maybe it is a bit flip but: Theorems are boring. Proofs are interesting. The most interesting part of my doctoral work was one of the proofs, which broke new ground. The statements were fun, but that one proof is what gave it value. Don't assume reviewers never make mistakes. See this recent question, for example: academia.stackexchange.com/q/143215/75368
Jan 21, 2020 at 15:04 comment added Michael @xLeitix if something is published in peer reviewed journal, I think assessing correctness is the last objective of the reader, is not it?
Jan 21, 2020 at 15:00 comment added xLeitix @Jim But rarely is one interested in the results without also getting a feeling for how trustworthy these results are. If your question is "how often does a mathematician read the results without caring whether they are right or wrong", my assumption is that the answer is "basically never".
Jan 21, 2020 at 14:54 comment added Michael Please note that my issue is not whether the proof is correct or not, I want to know what most academic do in the most of the cases when a result is published in a journal pepper? Do they read and understand the proof or they just skip the proof and remember the result (provided that the proof technique is not out of the box)?
Jan 21, 2020 at 14:49 history answered Buffy CC BY-SA 4.0