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Obviously anyone can publish anything at certain places, so I'm speaking in the purview of writing something that wouldn't make you look bad or is in an academic setting of some sort. Anyway would what I described be a bad idea? Also how would one even do that? Write seperate papers for each individual niche/tidbid/identity they found?

It seems like it would be easier to sort of bumble around in the dark so to speak when trying to find stuff in mathematics, rather then sort of brutishly attacking particular problems head on. Or is this not how mathematical research is performed? Do most people start out with the goal in mind? Can one just sort of bumble around like I described? Or is that "bad" so to speak.

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closed as primarily opinion-based by Rene Schipperus, Xander Henderson, user99914, Delta-u, GNUSupporter 8964民主女神 地下教會 May 1 '18 at 14:01

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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What you describe is just really unlikely to accomplish anything as far as research goes.

If you find a bunch of random identities, why would a journal want to publish it? They are likely to have already been found by someone, and just don't appear in literature because they haven't yet proven useful for anything.

The problems you solve don't need to be huge, Fermat's Last Theorem type of problems. But you want them to be standing open problems that some part of the community has an interest in, or to make progress towards some huge problem, or have some sort of interest for the mathematical community.

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  • $\begingroup$ How is any new math ever developed then if people are just working on stuff others are currently interested in? Or is it just by small deviations/generalizations of past stuff which over time creates the new stuff? Also how does it all get put into a "theory" so to speak, I mean say the study of knots or something, I don't think that was originally considered topological in nature or studied in such a frame work. I mean at what point in time, does some topic/field come into existence and books start getting written about it etc. $\endgroup$ – user3865123 Apr 30 '18 at 14:21
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    $\begingroup$ @user3865123 Did Columbus discover the americas by randomly sailing around ? $\endgroup$ – Rene Schipperus Apr 30 '18 at 14:22
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    $\begingroup$ @user3865123 Why dont you actually study some history to see how things evolved the way they did. $\endgroup$ – Rene Schipperus Apr 30 '18 at 14:23
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    $\begingroup$ No. For groups the primary motivation was the permutations of roots of algebraic equations. $\endgroup$ – Rene Schipperus Apr 30 '18 at 14:27
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    $\begingroup$ People didn't just randomly come across the idea of a group, they came across it as a tool for studying problems that they hadn't been unable to solve for a long time. $\endgroup$ – Morgan Rodgers Apr 30 '18 at 15:08
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Mathematicians do mathematics because they're curious. Some just want to understand how these interesting (to them) abstract objects behave. Some want to see how the abstractions match real world phenomena (that's applied mathematics).

Some mathematicians try to solve known open problems (what you call "brutishly attacking"). Some just explore things they find puzzling (what you call "bumbling around").

When they find new theorems they look for a way to publish them so that other equally curious mathematicians can see what they've done, perhaps extend it. If a journal's editor and referees agree that the new mathematics is correct and potentially interesting to readers of that particular journal then the work is published there.

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