The first calculators were arguably Avebury stone circle, Stonehenge and their allies, solid state technology designed to solve a single problem. These were therefore not programmable calculators.
Babbage designed the difference and analytic engines, generally identified as the birth of computing as a mechanical process. Ada, Countess Lovelace is generally credited with being the first programmer and she also sponsored Babbage,
The Analytic engine (1833-1837) was not completed. It had storage for 1000 numbers and punched card control: the stored program concept- first true computer design.
In World-War II ballistics calculations, code-breaking etc inspired various relay/valve machines in the UK, the USA and Germany. The immediate results were various large calculators (e.g. USA Electronic Numerical Integrator and Computer: ENIAC) and the First stored program electrnic machine, the Manchester Mark 1 (1948).
Transistor technology allowed greater reliability and closer packing, but its most important contribution was that it lead to the integrated circuit, eventually giving us the first microprocessr, the Intel 4004 (USA).
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