The Apple-1 Registry, currently maintained by Achim BaquƩ, has used handwriting analysis to solve the mystery of who hand wrote serial numbers on the first Apple-I motherboards [apple1registry.com]. Photos of many boards and several actual boards were examined. One reason for the investigation not happening earlier is that the investigation required writing samples. Achim goes through that and other aspects of the investigation. After two forensic handwriting analyses, the result was clear.
Not on every Apple-1 computer is a serial number!
Some (not all!) Apple-1 of the 1st batch [apple1registry.com] have a handwritten number on the back which is obviously a serial number. None of the 2nd batch (also called 'NTI' Apple-1) have a serial number.
List [apple1registry.com] of all known serial numbers on the back of some 1st batch Apple-1.There were many theories surrounding this number. Only Apple-1 computers sold by the Byte Shop [apple1registry.com] seems to have this number. But nobody remembers where the number really comes from. Steve Wozniak [wikipedia.org], Steve Jobs [wikipedia.org], Daniel Kottke [wikipedia.org], Paul Terrell [wikipedia.org], the board manufacturer etc. all say that they didn't put the number on the mainboard. For a factory it would be very unusual to write a serial number magic marker on a pcb. Usually it was printed on the board or a label was used.
The Apple-1 Registry is an online museum of the first model of Apple. Only 200 were made and fewer survived. Only 29 are known to have such serial numbers.