Did the ancient Greeks know that $\pi$ was not algebraic ( did they know it was not the root of some polynomial? )
If not could they have possibly deduced such a thing with their level of understanding of mathematics? (what I mean in conjecture it)
I realize this may be considered off topic but i think its an interesting intellectual exercise. I realize they couldn't have easily proved such a result as it took us forever whilst trying to prove it but many conjectures have a solid basis for themselves with no proof could they have been inclined to believe such a result?