I love this quote:
In college my honors math professor would go over unsolved math problems. He would explain math is a science and not an art and that many proofs which were unsolvable were later solved. He then gave a math problem which had been unsolvable as an example and taught the lecture. This was a double period class with a break and I stayed in seat entire time. At end of class when class had exited Professor came to me.
Professor: "Class is over and you have not paid attention the whole class."
Me: "I read the chapter already and did all of the problems but I could not get my mind off the first problem."
Professor: "The first problem was simple."
Me: "No, the unsolved problem. I solved it.
Professor: "It seems deceptively simple but it is not."
Me: "Yes I saw that but I took another approach and able to prove it." I handed him my notepad.
Professor: "Yes. I have seen this approach before but not how you did it. Some of your assumptions are not proved yet however. Complete the proof and I will back it as part of your thesis."
I changed degrees in last year of school but I gave him my proof before I graduated with CS degree.
He said "I will examine the proof and if it is complete I will use it as an example in class. Contact me if you go to grad school."
I got a very strong reference letter as person who solves problems.