my first modem was 300 baud (or maybe 150 baud) built into a Decwriter printer/terminal. The modem was acoustic, so it literally listened to the sound coming from the telephone handset, since metallic connections to phone company wiring was not allowed. I proved that it worked once, by having a friend call me and send me something to print.
Later modems were allowed to connect to phone company wiring, the rest is history (but wouldn't the old part be the actual history?).
JR