The Hall of the Philosophers is one of the first buildings encountered when visiting Hadrian's Villa.
The main entrance is on the north side and had two large columns that disappeared. On the west side is another entrance with twin staircases ascending from the double portico of the Poecile. Finally, on the east side was a corridor closed by a large door, leading to the Maritime Theater and the private area of the Villa.
The building was therefore located midway between the "public" part of the Villa, namely the large squale or the Poecile, and the "private" part, namely the Maritime Theater and the Imperial Palace.
The Hall of the Philosophers owes its name to the seven niches in the apse, as many as the Seven Sages. For centuries, it was mistakenly thought that it was a library, and that the seven niches contained wooden cabinets for storing papyrus and parchments. But it was not so.
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This hypothesis does not work, because the niches are too high from the ground, 1.60 meters, making them uncomfortable and difficult to access (with a ladder?). To prove this, a comparison with the small library in the Imperial Palace, also at Hadrian's Villa, is sufficient: there, the cabinet niches were at eye level, easily accessible.
In the seven niches of the Hall of the Philosophers, the imprints of marble slabs can still be seen in the mortar, and there are no signs of shelving. So they were made to house large statues, about which Pirro Ligorio, however, says nothing.
The statues could be those discovered by the Michilli family in the nearby Cento Camerelle (Hundred Chambers), including the statue of Flora, now in the Capitoline Museums in Rome. Alternatively, they could have been statues of members of the Imperial House.
The earliest description of this building dates back to the 16th century and was made by Pirro Ligorio, the great architect and antiquarian who first made large-scale excavations at Hadrian's Villa on behalf of Cardinal Ippolito II d'Este, Governor of Tivoli.
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Ligorio called it the "Temple of the Stoics," and in his Codices describes the decoration he found during his excavations. There were alabaster columns, which he claimed were reused in Tivoli's churches, and marble floors, especially red porphyry, the imperial stone par excellence due to its purple color. (It was used for the sarcophagi of emperors such as Nero and Hadrian, of Constance and Helena, and for the statues of Diocletian's Tetrarchs.)
Nothing of that marble remains in place, except the holes for the clamps that held the slabs to the walls- The floor is buried, but it's likely that the traces of the opus sectile described by Ligorio remain in the mortar.
Since this was not a Library, considering the precious red porphyry decoration, the presence of statues, and the imposing architecture, the Hall of the Philosophers it was a majestic Audience Hall, a Throne room where the emperor could receive important figures.
The Maritime Theater was nearby: as we know, it was Hadrian's very private "villa within the Villa," and was separated from the rest of the Villa by a particularly large door. It protected the emperor's safety and privacy, but he was nearby and could grant audiences at any time.
See: Marina De Franceschini, Villa Adriana. Mosaici, pavimenti, edifici. Roma 1991, pp. 199-201 e 487-491.