I know it is hard to ask for the perfect method for doing mathematics, but I hope there are some paths that are more preferable over others. I am a engineering student who has switched to mathematics but I still only have experience with very calculation heavy subjects like differential equations, calculus 1 and 2, ... Today I thought the following, is there a good method to tackle all problems? Reductionism works well in many areas of life, is it a good strategy in mathematics? Or is it a good strategy to always strive for a higher degree of abstraction? Things always seems harder when it is abstract but I think this is the place where relationships between various things are understood.

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    $\begingroup$ I’m skeptical of the idea that much of anything is always a good strategy. In practice I may find myself working from either end, or from both. $\endgroup$ – Brian M. Scott Apr 28 '13 at 13:42
  • $\begingroup$ @user29163 Your question is probably appropriate for the nearly-in-beta-SE area51.stackexchange.com/proposals/64216/…. Check out the proposal and commit to it if you're interested. Then we can get it off the ground and get the site in beta! $\endgroup$ – Xoque55 Mar 3 '14 at 4:52

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