I remember learning that the inventor of polymerase chain reaction (PCR) was Kary Mullis, who was awarded the Nobel prize in chemistry in 1993. I recently learned that there is some controversy about this due to the fact that his idea may not have been entirely original.
The first actual written description of it was a 1971 paper by Norwegian biochemist Kjell Kleppe. IIRC the paper was theoretical and didn't have any experimental demonstration of DNA amplification. Part of the problem was that it wouldn't be until 1976 that the Taq polymerase enzyme was isolated which is used in the PCR. So Mullis seems to have proven experimentally that Kleppe's idea worked. He also was able to optimize the process using thermal cycling and make use of the heat stable Taq polymerase enzyme.
Part of what led me to doubt Mullis' claims was this article about the PCR story.
Who actually invented PCR?