The School of Pythagoras was originally built around 1200, before even the University of Cambridge existed. It also predates St John's College, which was founded in 1511. It was initially a private house, but over the centuries it has had many uses. For a period it was a ruin. The reason for the name is unclear.
In the 16th century, a small manor house was added to its west side. This is now used for graduate student accommodation. It is known as Merton Hall. From 1266 until 1959 the School of Pythagoras and later Merton Hall were owned by Merton College, Oxford.
The School of Pythagoras is now used as the College Archive Centre.