Comment by markisus
1 day ago
It’s interesting that the conjecture was proven via case by case analysis, with each case demanding different techniques. It’s almost a coincidence that all finite groups have this property, since each group has the property because of a different “reason”.
But the article says that mathematicians are now searching for a deeper “structural reason” why the conjecture holds. Now that the result is known to be true, it’s giving more mathematicians the permission to attack it seriously.
I don't think that is that unusual in group theory proofs to be honest. You often break things down into related things and then prove for each collection of related things. And some of those proofs might be straightforward and some might be open problems for years requiring much more advanced techniques.