On September 12, 1958, Jack Kilby of Texas Instruments connected a germanium transistor and some resistors and capacitors on one sliver of semiconductor, about the size of a paper clip. He hooked it to an oscilloscope. It produced a sine wave. It was the first working integrated circuit. He was 34 and had been at TI for three months, and most of the senior staff were on holiday.
The problem he was solving had a name, the tyranny of numbers. As circuits grew, the number of components and the number of hand-soldered connections between them grew faster, and the connections were where things broke. Every element of the circuit already existed in semiconductor form by the late 1950s; what nobody had done was make them all out of the same material and in the same piece of it, so that the interconnections were part of the device rather than something added to it. Kilby's demonstration circuit was a phase-shift oscillator, and its components were formed in germanium and wired together with fine gold wires.
Nine months later, in 1959, Robert Noyce at Fairchild Semiconductor arrived at a better version. Where Kilby's device used external gold wires to connect the parts, Noyce used the planar process developed by Jean Hoerni, putting a layer of aluminium directly on an oxide surface to make the connections, and built it in silicon rather than germanium. Silicon won. It forms a stable oxide, and it works at higher temperatures. Both men's companies knew about the other's work, and the litigation was settled by cross-licensing; the two firms effectively split the industry for a decade.
Kilby kept going at TI. He led the team that built the first handheld calculator in 1967, a machine that existed largely to prove that the integrated circuit could be put into something a person would buy, and he took out more than sixty patents. He was awarded the Nobel Prize in Physics in 2000, 42 years after the demonstration and ten years after Noyce's death, which is why Noyce never shared it.
The reason any of this compounds is that making a circuit in one piece of material means that making it smaller is not harder, it is cheaper. That inversion is the whole basis of the industry that followed, and it is why the phrase associated with it, Moore's law, described an economic expectation rather than a physical one.