Emotions are what enable us to judge something as right vs. wrong. This has been conjectured philosophically since forever, and has recently been proven to be true by scanning a brain while it solves mathematical questions. Every right step evokes emotional center of the brain, qed.

EDIT: This fact has been used to argue against the 'enlightenment' era approach to solving problems. Unfortunately I am unable to find the relavant talk on youtube right now, since all the results for 'enlightenment' return mystic sadhu bs.