Mathematicians often find minimal counterexamples easier to work with because they can focus on those parts of the graph that are relevant to the problem at hand and temporarily ignore the rest.
He thought the five-cycle case, in particular, would be the counterexample demonstrating that very point.
So one immediate question is whether there are counterexamples to be found using other number systems such as the real or complex numbers.
For Gardam, his discovery is the culmination of years spent hunting for intriguing counterexamples in algebra.
Gardam’s discovery of a counterexample to the unit conjecture is oddly reassuring, Kropholler said, because it suggests that this hard work was really needed.