In 1895, Wilhelm Konrad Rontgen discovered x-rays. These X-rays could be used to produce images of the interior of the human body! Naturally the scientific community was impressed and Rontgen received the Nobel Prize for Physics in 1901.
Wilhelm K. Rontgen
In 1917, a mathematician named Johann Radon worked out the mathematics of reconstructing a function from a set of projections. This decomposition of a function is now called the Radon transform, and it plays a large role in computed tomography.
Johann Radon
In the early 1960s, the quality of the X ray images being produced were similar to the ones seen by Rontgen at the beginning of the century. At this time, Allan Cormack began to popularize and extend Radon's work.
Allan Cormack
In the early 1970s, Godfrey Hounsfield directed a project to combine X-ray scanning and digital computer technology. This work gave birth to computed tomography. In 1979, both Alan Cormack and Godfrey Hounsfield received the Nobel Prize for Physiology and Medicine.