# What is the oldest open question solved in mathematics?

In mathematics, 1760 Plateau's problem were solved, but it was only in 1930 that general solutions were found in the context of mappings (immersions) independently by Jesse Douglas and Tibor Radó.

1760 - 1930 = 170 years.

What is the oldest open question solved in mathematics?

1. Is $$\pi$$ rational? The squaring of circle was already mentioned. But people (Egyptians and Babylonians) tried to calculate $$\pi$$ long before invention of ruler-and-compass constructions. Even if they didn't know the notion of irrational numbers, they probably would be interested in a problem whether a circumference of a unit circle could be described as "number" (e.g. sexagesimal number for Babylonians). So, you can argue that this problem is much older than squaring a circle. And, even if irrationality of $$\pi$$ was proved earlier (in 1760s) than transcendence of $$\pi$$ and impossibility of squaring a circle (in 1882), the irrationality of $$\pi$$ was probably much older open problem.
2. But maybe the oldest open problem was a very simple one. For example, how to calculate the area of a given quadrilateral? Babylonians used an incorrect formula $$\frac{a+c}2 \cdot \frac{b+d}2$$, where $$a$$, $$b$$, $$c$$ and $$d$$ are the sides. I'm not sure when the correct formula was discovered, but it needs trigonometry, which was invented about 2nd century BC (depending on definition of invention of trigonometry). It's impossible to say when people first interested in calculating area of quadrilateral, but it is possible that it was more than two milleniums before asking a question about $$\pi$$. So it may be the oldest open question at the time when it was solved.