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Judging by posts and comments by graduate students in math.stackexchange.com and mathoverflow.net, I have come to the conclusion that a large part of their knowledge comes from SE sites and the Wikipedia, as opposed to traditional publications such as books and papers.

I was deeply shocked the first time I heard of a student researching the literature through Google, which spits out at least as many SE and Wikipedia answers as references to books and journals. But, of course, nowadays I do the same, certainly more often than going to the library!

Are traditional publication forms becoming obsolete, in the face of purely electronic forms? Or, contrariwise, do younger people who ignore traditional forms miss out on essential information?

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    What you learn from SE or Wikipedia does not really have much to do with what you learn from the latest journal publications. There is a lot of background information researchers need here and there, and in the old days one might go over to the library and find an advanced textbook or a monograph to catch up on things. – Jon Custer Oct 6 '20 at 16:42
  • Interesting - I voted to close this question, it was closed, then reopened, but I cannot vote to close it again. Is that a bug because it was anonymized? Or is that intended? – Azor Ahai -him- Oct 7 '20 at 20:14
  • @AzorAhai--hehim It's intended: you cannot revote to close the same post. – Massimo Ortolano Oct 7 '20 at 20:19
  • @AzorAhai--hehim, also, the question has been changed from the original, hopefully making it reasonable and answerable here. – paul garrett Oct 7 '20 at 20:32
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    @AzorAhai--hehim Yep, you can only vote to close once per question. It essentially avoids open/close wars. – Massimo Ortolano Oct 7 '20 at 20:48
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I think wikipedia is good for mathematics topics that are fairly settled. There are few errors and the ones that do appear (I've found some) tend to disappear quickly. You can get a good overview and if you follow up on the sources provided you can get a more complete view. So, I hope students use this for background on things they need to study.

But, by its nature, it is less useful to bring you to the state of the art: stuff that isn't yet "settled".

I think SE is the opposite, in some ways. You might find answers to contemporary questions, but the sources may be less reliable. Wikipedia has many editors (formal and informal) keeping things right, SE, less so and not everyone commenting really has a good answer. So, again, I hope that grad students use it when necessary, but with caution.

If the alternative is to set for ten hours at a time in a library, pulling older and older books from the shelves, it is no contest.

But reading things and being given answers isn't the best way to gaining insight into a mathematics problem. Not deep insight, anyway. For that you need to do some work yourself.

And, as you say yourself, it is a professional approach to use such resources. You do it yourself. And, I would say "to the detriment", actually. It is a supplement and/or a place to start.

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  • I have seen PhDs be done through a list of mathoverflow questions. – FourierFlux Oct 6 '20 at 18:25
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    @FourierFlux, anything is possible, I suppose. – Buffy Oct 6 '20 at 18:28
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    @Buffy, could you please read the comments in the original post? Thanks. – anon Oct 7 '20 at 18:40
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    @anon SE is like an eternal coffee break with a bunch of knowledgeable people across the planet. You get the informal background information, hidden tricks etc., but not the solidity of textbooks or the depth of properly vetted publications. It has its role, but it's only one part of the game. – Captain Emacs Oct 8 '20 at 1:07
  • @FourierFlux sounds like a topic for a PhD on its own. Or for a self-help book: "how to do a PhD in math in 100 SE questions". – Captain Emacs Oct 8 '20 at 1:08

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