The tradition says that this phrase was recorded at the entrance of the Academy of Plato.

This tradition is transmitted by several commentators of Aristotle, as Elias in his "Commentary on the Categories, XVIII, 118, 18-19:

"In Plato's Academy, before the temple of the Muses was written: '  Let None But Geometers Enter Here',

καὶ διὰ Πλατὁνα ἐπιγράψαντα πρὸ τοῦ μουσείου ἀγεωμέτρητος μέδεις εἰσίτω (" kai dia Platona epigrápsanta pro tou mouseíou ageométretos médeis eisíto ")

and John Philoponus on 'Commentary on the soul, XV, 117.27, with a slight variation:

" Let None But Geometers Enter Here",

"ageometretos me eisito" ἀγεωμέτρητος μὴ εἰσίτω.

Diogenes Laertius in IV, 10 has an anecdote that shows the importance of geometry in Plato's teaching:

"Xenocrates wanted to study with him without knowing music or geometry or astronomy, and Plato said," Go, because you do not have the handholds of philosophy ".

But what was Plato's Academy? The name, which comes from the Latin Academy and this from Greek akademeia, Ἀκαδημία, defines the institution, school or philosophical-political corporation founded by Plato in the outskirts of the city of Athens, near the walls, which receives the name of the place where it was built, a space in which there was a shrine to the mythical hero attic Academo (minor in Greek mythology who revealed to the Dioscuri the place where Helena was hiding). So etymologically it means "the garden or field of Academos".

Although the news is scarce, we must assume that this center would continue the educational program that Plato disclosed in the "Republic" dialogue. Mathematics and geometry had a specific gravity in it, as I said at the beginning of this article. Music is also essential  in the sense of "arts" inspired by the Muses.

But the essential purpose of the Academy was to prepare men for the service of the state. From it  many statesmen came out, educated by the dialectical method, by which students were discovering the truth in coexistence with other members of the institution. Alongside philosophical activity an intense scientific reflection on mathematics was also developped on music, astronomy, division and classification. His teaching was based on lessons and dialogues. It also produced a lot of comments on Plato and Aristotle which have provided us with valuable information.

The Academy is thus one of the oldest institutions of higher education; it must have been founded around 387 BC He continued actively to the death of Plato (347 BC), when his nephew Speusippus took it, although it certainly had other major philosophers. It is somewhat curious that who demanded choose the best for the city government, he did not follow the same principle to guide your institution, a clear example of nepotism. Among these best was precisely Aristotle, who created his school which is known as the Lyceum;  I will talk some other time on it.

Note: it's called nepotism the granting of appointments and public employments to relatives and own family members. It derives from the Latin word nepos, -tis which means grandson, nephew.

The Academy received a mortal blow when in 86 BC the Roman general Sulla captured and destroyed Athens. The director of the Academy, Philo of Larissa, left Athens the following year and he died leaving no successor, what resulted in the death of the institution.

Centuries later, in the V of Christ Neoplatonic philosophers resurrected the Academy, but without the splendor and future of the first. However it survived until 529, when Justinian closed it for religious reasons, rather than philosophical, because Neoplatonism continued to influence in Byzantine era. From this time the institution was running out by starvation. So the Academy came to last more than nine hundred years.

Regarding the closure by Justinian, it seems that no formal abolition, but it was a result of its legislation to suppress paganism.

One of the main measures to prevent the spread of paganism was the prohibition that  pagan philosophers and teachers could teach, establishing harsh penalties for those who infringe these laws.

During the consulate of Decius, the emperor sent an order to Athens that stipulates that no one could teach philosophy or interpret the law. This order is placed in relation to the law of the Code of Justinian I, tit. XI, 10, 2 which among other things says:

Moreover, we forbid the teaching of any doctrine by those who labor under the insanity of paganism, so that they may not in that manner pretend to instruct those coming to see them in a way to excite pity, while in fact they corrupt the souls of their disciples. Nor shall they receive any salary (annona) in as much as they are not permitted to claim anything of the kind pursuant to a rescript or pragmatic sanction. (Translated by  Fred H. Blume)

Omnem autem doctrinam ab  iis, qui impiorum paganorum furore laborant, doceri prohibemus, ut ne hoc modo simulent, se  eos, qui misera sorte ad ipsos veniant, erudire, sed revera ánimos erudiendorum corrumpant,  neque magis aliquid annonae ex publico percipiant, non habentes licentiam, ne ex divinis  quidem rescriptis vel pragmaticis sanctionibus eiusmodi ius sibi vindicandi (1.11.10) . 

The law, it appears that not formally closes the Academy, but requires teachers to be baptized or exile. This situation and the economic hardships would end up ruining it. But there is no absolute agreement among historians about it.

Platonic Academy (1): “Let none but geometers enter here.”

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