I wondered how the rather odd mortar board hat became standard attire for graduation ceremonies and found this on Wikipedia:

“The mortarboard is generally believed by scholars[who?] to have developed from the biretta, a similar-looking hat worn by Roman Catholic (and High Church Anglican) clergy. The biretta itself may have been a development of the Roman pileus quadratus, a type of skullcap with superposed square and tump (meaning small mound). A reinvention of this type of cap is known as the Bishop Andrewes cap.[7]:22–23 The Italian biretta is a word derived from the Medieval Latin birretum from the Late Latin birrus "large hooded cloak", which is perhaps of Gaulish origin, or from Ancient Greek πυρρός pyrrhos "flame-colored, yellow".[8]”

Interesting and timely topic!

Found a good article on the origins of the ceremonial academic hats from the archives of the Yale alumni magazine: "Old Hat: The Evolution of your Mortarboard"

Virtually all of our "academic dress" comes from clerical clothing or practical considerations of being a) poor and b) working in cold, austere rooms while being poor. Religion and medieval scholarship was pretty much inseparable.

I am a nerd, in case that's not completely obvious.