Just in case, year zero does not exist, after 1 B.C. follows 1 A.D. in standard calendar

]]>Fun!

]]>Then there’s the origin story of the trisection of the angle 😉

]]>Thanks for digging into the history of “doubling the cube”. So that problem was open for at least 432 + 1837 – 1 = 2268 years!

]]>That’s an interesting contender. Thanks! I hadn’t thought of ‘proving the parallel postulate from other axioms’ as a problem the Greeks contended with… but it probably *was*, at some point. Didn’t Euclid introduce that postulate after the rest, in his *Elements*?

Artusartos wrote:

Puzzle. Why did I subtract 1 here? The question was not posed in the beginning of the year or not settled at the end the year?

Actually I did it because there was no “year zero”. But yes: if someone formulated a math problem at the very end of 1 BC and someone solved it at the very start of 1 AD, it would have been open for just one day!

I’m somewhat confused with the last problem. How can 2^(p-1) be prime when it’s divisible by 2?

That was a typo, which I’ve now fixed.

]]>Right!

]]>I don’t know of the earliest known account of the problem, but it had to be known to whoever wrote the 5 axioms in Elements that the fifth one stands out. From a little digging it seems that book 1, which contains the axioms, was thought to mostly come from Pythagoras (c. 570–495 BC) . However, while Pythagoras (or his school) provided the proofs it’s not clear to me that anyone before Euclid explicitly stated the axioms as assumptions.

Also unclear to me is how would one consider it solved? Yes, Gauss and others worked on non-Eulcidean geometry but as far as I can tell they didn’t prove anything about the equiconsistency between non-Euclidean and Eulcidean geometries. The earliest proof of that I can find was by Beltrami in 1868.

]]>In terms of age, a quick wikipedia lookup suggests that the Egyptians understood about the existence of prime numbers circa 1550 BC (of which we have historical evidence via the Rhind Mathematical Papyrus). It is a small inference to posit that they understood about the difficulty of factoring, too, though they evidently would not have been interested in numbers much larger than several tens of thousands.

So that would make the above problem upwards of 3500 years old, and possibly closer to 4000 years old.

]]>