What problem in math had the longest time between POSING IT and SOLVING it? This might not be a well defined question since the notion of when was it posed? might be murky. For some problems even when it was solved? might be murky. Nevertheless I have a candidate:
Is there a straight-edge and compass construction that will, given a square, produce a circle with the same area. (This problem is often called Squaring the circle..)
Wikipedia says that Oenopides was the first person to pose construction problems and that he posed this one. He was born in roughly 500 BC. Even back then there were people who thought it could not be done. However, it was proven impossible when pi was shown to be transcendental in 1882 by Lindemann. (This was one of the motivations for Lindemann.)
This problem was open for roughly 2300 years.
- Is there any solved problem that was open for longer?
- Is there any open problem that has been opened for that longer?
- If you polled people in 400 BC what they would have guessed for which way it would go and when it would be solved?
Will P vs NP take that long?