On mathematical maturity

I have heard this term being thrown at students ever so often that it's entered my common vocabulary now. Nevertheless I didn't realize this loaded term had an entire page on wikipedia dedicated to it -> http://en.wikipedia.org/wiki/Mathematical_maturity In short, it's just the ability to deal with proofs. What then is a proof, I'd ask. A formal definition doesn't matter really. As Scott Aaronson of MIT likes to put it, it is sort of useless "for when you’re doing your homework...a proof is an argument that can withstand all criticism from a highly caffeinated adversary." Works!

P vs NP and Chekhov

 Just like Chekhov said, 'Every happy family is alike. Each unhappy one is unhappy in its own way.'
- Dr. Sampath Kannan (talking about P and NP class problems)