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I think it's intriguing that they took an experimental approach to what is originally a theoretical problem: Generate lots of examples with a computer and see if you notice any patterns.

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We do that all the time in mathematics though; generate some random examples of the phenomena you're investigating to see if there are any "easy" counterexamples. If not, try to visualize them and see if patterns emerge. This is an easy way to build up intuition on a problem: seeing "how" something behaves gives you clues about where to look when you go to prove it.

Not only for the easy counterexamples, also to check whether the things you are studying actually exist.

Once the stuff you think about is abstract enough, you may start thinking of objects with properties P, Q, and R, showing all kinds of wonderful results before somebody else shows that there are no objects having properties P, Q, and R, or that there only are trivial ones.

Some of the first code I ever wrote outside of a classroom was in Mathematica to generate examples that would later fuel the results in a set of two papers (in pure mathematics).

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