The quality of ideas seems to play a minor role in mass movement leadership. What counts is the arrogant gesture, the complete disregard of the opinion of others, the singlehanded defiance of the world.
Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses and then start to reason. What you do is trial and error, experimentation, guesswork.