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I shall take away all the mathematical jargon and explain it not-very-accurately. P and NP are sets of optimization problems, or problems in which you minimize or maximize something. P = NP? asks whether having a (fairly efficient) method to solve a problem is equivalent to having a (fairly efficient) method to check if there really is a solution when you know that there is a solution.
P = NP? is one of the seven Millennium Prize Problems which were proposed as the few most important questions in maths. Some of them, including P = NP?, haven't been solved and there's a $1 000 000 award for the first person who solves each question.
My interest in this question wasn't because of the solution to it, but because of the nature of the question. It doesn't sound entirely mathematical, does it? My search of this question on Wikipedia brought me to another theorem which, together with P = NP?, was mentioned in Basics of Maths - Gödel's first incompleteness theorem. This theorem suggests that there are things in maths that cannot be proven.
I thought to myself, the things mathematicians do at higher levels are really mind-boggling. But somehow, the theories they prove come to find use in today's techonology. Sugoi.
There was a question from yesterday's tutorial where the lecturer went around to ask if anyone knew how to do it. Everyone was shaking his/her head, but when the lecturer finished his round of asking, he said,
"That guy knows the answer." Wah..
Then the guy spoke. "I don't know." ?!
The lecturer explained, "The correct answer is, there is no answer. Don't write anything else if you're asked this question in the exam. You'll be marked wrong."
This is.. maths?