I think the main reason people are attracted to him is because he is very similar to Gary Oak in the first games. He jumps out of nowhere and challenges you to a battle, he judges you often in his belief that he is the better one. And he becomes your final opponent in the league after becoming the champion himself.
The difference is that he's not as effective as Gary Oak, he's actually more like a cheap copycat. He tries to jump you, but he does it in all the wrong places, either in town just after you got all healed up, or at the end of the tiresome cave where he announces his presence long before you reach him. And his final battle only happens once, and it isn't the real final battle. And, to put it simply, he's just not Gary Motherfucking Oak
And the Menger Sponge does trace back to Maths, as there actually is a complex formula to determine how many cubes there are in a menger sponge. Natural Harmonia may only be holding the 1st stage sponge, but he might have more at home, used for his practice in maths.