It’s a semi relative question who invented synthesizers or electronic music in general. After WW2 the Brits had formed the EMS studios, which Tristam Cary made from obsolete radio/radar equipment, tape loops, etc. But besides the theme for Dr. Who (original Black & white version), I cant verify there was a lot of music recorded for the general masses of the 50’s/60’s.
A YouTube documentary explains this in detail.
https://youtu.be/8KkW8Ul7Q1IThere is also the German Krautrock Scene which was where Kraftwerk, Can, Neu, Tangerine Dream contributed to electronic music while trying to forge ahead in a divided Germany, and appalled by the crimes their parents were involved with or did nothing to stop. Making German rock be less American influenced, but more...tribal perhaps?? But that doesn’t necessarily tell the tale
of Electronic Synthesizers beginnings. But more of the effect that Krautrock had in making the sounds that would be sampled into Africa Bambatta’s “Planet Rock” from sampling Kraftwerk’s “Trans Europe Express”, to influencing Synth Britannia in the 70’s/80’s.
https://youtu.be/ne7M63P820ghttps://youtu.be/TK1P93r9xesBut most of the history of electronic music mainly gets mentioned is the east coast/west coast synthesis. Don Buchla in the West, Bob Moog in the east. I don’t know too many west coast synth artists who used Buchla synthesizers other than Herbie Hancock, but later he switched to Moogs, Arps, Yamaha DX7s, etc.
It gets a bit confusing who really invented it all, because it kind of depends on who could think of & invent the equipment, and what could be done with them that was decades before we had MIDI, Daws, etc.
Some companies faded into obscurity, but are still highly sought after synths. (ARPs, Sequential Circuits, EMUs, etc)