from the Greek Anthology

The fourteenth book of the Greek Anthology is mainly made up of puzzles and riddles.
The mathematical conundrum freely translated here is attributed to Socrates.

14: 1.

Polycrates speaks:

    Pythagoras, wise and so discerning
    Your house is well known for its learning.
    How many are there there who choose
    To follow the discipline of a Muse?

Pythagoras answers:

    Within my mansion, half are men
    Whose mission is to use the pen
    In order that the words they write
    May furnish wisdom or delight.

    Another quarter studiously
    Through science or geometry
    Research this world in which our fate
    Condemns us to be animate.

    One seventh of them do not write
    But sit in silence day and night
    Discovering introspectively
    The deep truths of philosophy.

    All these are men but there are three
    Women here too, as there should be.
    They know the female mysteries.
    Theano is the Queen of these.

    The wise now have the means of telling
    How many thinkers are in this dwelling.

Socrates (maybe)

Some manuscripts of the Greek Anthology attribute this versified maths problem to Socrates. Others suggest Metrodorus, who lived several centuries later.
Such questions of authorship are often doomed to remain murky, but the answer to the riddle is not so tricky for someone with basic algebra skills. If you want to check that you've got it right, the solution can be found by clicking here.

Neither Socrates nor Metrodorus  have a current email address, but if you have any thoughts about this poem,  its translator, George Simmers,  would be pleased to hear them