He first noted that the cells of all living things contain atoms taken in from the organism's environment, including carbon; all organic compounds contain carbon.
Thus the less of it that remained in an object, in proportion to normal carbon, the older the object was.
The amount of carbon-14 gradually decreases through radioactive beta decay with a half-life of 5,730 years.
So, scientists can estimate the age of the fossil by looking at the level of decay in its radioactive carbon.
Other corrections must be made to account for the proportion of throughout the biosphere (reservoir effects).
Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the 1950s and 1960s.
An example of the ingenious technical work and hard-fought debates underlying the main story is the use of radioactive carbon-14 to assign dates to the distant past.