In Conjecture and Proof:
* Define something that prevents.
* Consider something smallest.
* Consider something largest.
* Find a clever coloring.
* Try using a Hamel basis.
* Try following paths.
* Count things.
In Geometric Graph Theory:
* Turn the edges into rubber bands.
* Draw circles around *everything*.
* Apply Euler’s formula.
* Pass a line across it.
* Color the edges red and blue and find the vertex where the red edges are together
* Use physics.
In Set Theory:
* Use the sandwich theorem.
* Use ridiculous seeming approximations.
* Look at the cardinality of the sets.
* Order the sets and compare ordinals.
* Consider a representative set.
* Draw the diagrams.
* Remember that everything is a set - unless it isn’t.
In Topics in Geometry:
* Try stringing definitions together.
* Try looking at equivalent definitions.
* Play with the geometry, convert to algebra, play with the algebra, convert back to geometry, repeat.
* Look for eigenvectors/values.
* Draw pictures.
* Use symmetry.
* Look at subgroups.