"Authentic Maths" (...and proofs)

A sort of fun read from the week, "The Time I 'Nearly' Solved the Twin Prime Conjecture":

https://medium.com/@fjmubeen/the-time-i-nearly-solved-the-twin-prime-conjecture-8f033030fe90#.itcm4ftbq

With some important points toward the end, including:

a)  recognizing "failure" as "an inevitable part of the problem-solving process," and experiencing math "in a manner that engenders the learner’s sense of identity as a problem-solver."

and

b) "Authentic maths relies on having students develop and confront their intuitions as they straddle the lines between truth and uncertainty."