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What I want to ask is: can I use the results of others when doing scientific research, whether it is math, physics or other science, without trying to prove them myself or try to verify them? For example results like theorems, proofs, definitions, abstract mathematical objects in math or results in physics. Should I refer to them in the end of the research and tell the literature I used, for example which books or notes? What results whether older or more modern could I use? They should be verified I suppose?

Could I try to answer my own problems or questions or already known problems? Should I communicate with scientists from the university I study at? Could they help me to tackle the problems i want and read the things I want to read?If the math or physics I want to use for the problems are not already discovered should I try to discover them myself?

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    $\begingroup$ 1) This looks more relevant to Academia SE, there's nothing here about education. 2) There's a lot of questions here, which makes it impossible to answer. 3) You're mixing "doing research" with "writing scientific articles" and also with some personal advice issues. $\endgroup$
    – Michał Miśkiewicz
    Commented Dec 17, 2022 at 23:21
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    $\begingroup$ I’m voting to close this question because it does not seem to be about mathematics education. $\endgroup$
    – JRN
    Commented Dec 18, 2022 at 0:39

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  1. This is not a formed question. You ask at least two different things (is it trustworthy to use others results--and--should you try to prove missing things yourself.) There's also a question about attribution.

  2. You should start capitalizing I (i). Was giving you some leeway based on likely foreign language. But English is the lingua franca (haha) of technical work. As a young student, just buckle down and learn it. It comes off as lazy if you don't. I'm sure you'll still have some minor errors, I do, and fine. But the i thing just irks like crazy. You won't get help from others if you are so lazy yourself.

  3. (Content) By and large yes, you can use known results (e.g. physical constants in physics, molar masses in chemistry, and character tables of point groups). For math, it's probably pretty normal that you would be able to, or at least once have, prove(ed) the tools you are using. In chemistry/physics/bio, it is normal to use some well known results without checking them. Of course, if it is a sketchy phenomenon (new report, e.g. "stripy nanoparticles"), you should verify the basis, before building further. Attributions via citations are normal for relatively new phenomena (BOTH to give credit and to direct readers for more info), but not required for well known results. The decision of where to draw the line is a judgment call, but not hard as a practitioner. (Instead of trying to anticipate how to do this, get some "practitioner" work. There are many things actually getting your hands dirty with real research will teach you...and you will ask better questions as a result.)

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