The method was developed by Willard Libby in the late 1940s and soon became a standard tool for archaeologists.
Libby received the Nobel Prize for his work in 1960.
For an example, when they tried to get the carbon dating for presence of Aboriginal people in Australia they get to the number 40,000. Why is that 40,000 years limit for carbon dating methods?
The older a sample is, the less (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by radiocarbon dating are around 50,000 years ago, although special preparation methods occasionally permit dating of older samples.
The idea behind radiocarbon dating is straightforward, but years of work were required to develop the technique to the point where accurate dates could be obtained.
This isn't a fundamental limit as more accurate measurements could go further back, but at some point you'd simply run out of C-14 atoms.
With our current kit 40-50K years is about the limit.
Libby and James Arnold proceeded to test the radiocarbon dating theory by analyzing samples with known ages.