The Mortaboard, Square Cap, Corner Cap, Oxford Cap
The Mortarboard cap named after bricklayers tool for holding mortar or perhaps it was the other way round not sure.
This style of cap dates back at least as far 16th Century where it was used in the uniform of those attending universities in Europe, forms of this hat go back even further were its seen in Italian paintings of 15th Century.
In the past, this form of hats was the default hat for the teaching profession and mandatory uniform at Oxford University. Now the mortarboard is seen across the worlds colleges and university, mostly in graduation ceremonies, were once the ceremony is over its thrown into the air.