To me, examples are to mathematics as experiments are to physics.
Although every example is particular in a way that a “general theory” is not, it is usually possible to “twiddle the experimental knobs” of the example such that you a feel for the more “general theory”. Related to this is solving a problem by considering a simpler sub-problem which is a particular case (i.e. a special example) of the general problem you want to solve.
For example: if you have trouble solving a geometry problem in 3D, look for similar problems in 2D and 1D. Are they easier to solve? How does the solution to the 1D and 2D problem shed light on the possible 3D solution?
But this probably also depends on which field of math you study.
To me, examples are to mathematics as experiments are to physics.
Although every example is particular in a way that a “general theory” is not, it is usually possible to “twiddle the experimental knobs” of the example such that you a feel for the more “general theory”. Related to this is solving a problem by considering a simpler sub-problem which is a particular case (i.e. a special example) of the general problem you want to solve.
For example: if you have trouble solving a geometry problem in 3D, look for similar problems in 2D and 1D. Are they easier to solve? How does the solution to the 1D and 2D problem shed light on the possible 3D solution?
But this probably also depends on which field of math you study.