Who do you think is going to be more motivated to think about math: someone who feels it is their duty to become smarter, or a naive student who believes he or she has the answer to some mathematical problem and is only lacking a proof?
Or, how about the student who believes they may have the answer, and has a burning itch to know whether this is the case? Or the one with something to protect?
Or, how about the student who believes they may have the answer, and has a burning itch to know whether this is the case? Or the one with something to protect?