Origin of the concept of types
Depends on how deep you want to go.  I believe Russell was the guy who introduced the concept in a specifically set-theoretic context, but the concept itself is as old as the hills, it's really the notion of universals and particulars expressed in a modern mathematical / computational form.  I wouldn't be surprised if Liebniz did something vaguely like types, if you look at his stuff in the right way.

You might have better luck at the History of Math and Science exchange.