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The Wikipedia page on parity currently says:

The ancient Greeks considered 1, the monad, to be neither fully odd nor fully even

Why didn't they consider 1 as odd? (I am assuming they already had the concept of odd and even numbers.) What did they consider it as?

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    $\begingroup$ Hello. Perhaps you could look the discussion about the baffling concept of "even-odd" hsm.stackexchange.com/questions/6721/… $\endgroup$
    – sand1
    Sep 9 '20 at 18:42
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    $\begingroup$ They (at least Pythagoreans and Euclid) did not consider 1 to be a number either, because number had to be a multitude of units. And since an odd had to be the unit attached to an even, and they they did not have zero, the unit by itself did not qualify. $\endgroup$
    – Conifold
    Sep 9 '20 at 21:36
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    $\begingroup$ One is the only integer that's not divisible by other integers but is not a prime number. That makes it pretty odd, so the Greeks were wrong. #itsajokedammit $\endgroup$
    – Carl Witthoft
    Sep 10 '20 at 11:55
  • $\begingroup$ Some Greek schools of thought were also a bit suspicious of $2$, on the grounds that a number had to have a beginning, a middle and an end, and $2$ lacked a middle. $\endgroup$
    – Prime Mover
    Sep 11 '20 at 5:04

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