Mobius strips out of wood don't require carving... *grin*... just the right kind of wood cut into a thin strip and twisted and the ends reglued.
Nope.. a Klein bottle is a different matter. If I want one, I can

As to genius in math, it varies from 'idiot savant' to the Indian you mention to the guy (John Von Neumann) who was visited by some computer folks a number of years ago. They were hoping he could design a program to help their computers solve some arcane problem. He asked them to show them the problem and the parameters. When they finished, he gazed at the ceiling for awhile, then said, "You don't need a program... here's your answer." He was right.
"Von Neumann believed that much of his mathematical thought occurred intuitively; he would often go to sleep with a problem unsolved and know the answer upon waking up."

   I think that synesthesia might be a form of genius, though not in the common sense.