Comment by seanhunter

I don’t think that’s true. Lots of mathematicians excel at (and revel in) finding weird counterexamples and love the strangeness of it all. John H Conway being my favourite- Look up the Conway knot[1] or the Conway base 13 function[2] for famous examples.

Ugliness is in the eye of the beholder. Lots of counterexamples are very beautiful. For example, the Dirichlet function (f(x) = 1 if x is rational, 0 otherwise) is a source of very beautiful counterexamples. Eg it is discontinuous everywhere but f restricted to only rational numbers is continuous on all rationals and likewise f restricted to irrationals is continuous on the set of irrationals (R-Q).

[1] The Conway knot has 11 crossings yet shares the same Alexander polynomial as the “unknot” which has no crossings at all. It took 50 years to decide the question of whether it has a basic property known as “sliceness” https://en.wikipedia.org/wiki/Conway_knot

[2] Conway’s base 13 function Was invented as a counterexample to the converse of the intermediate value theorem. That is, it satisfies the intermediate value property while being everywhere discontinuous (which breaks my brain completely) https://digitalresearch.bsu.edu/mathexchange/wp-content/uplo...