This is a biography of Alan MacLeod Cormack, a physicist who (together with Godfrey Hounsfield) won the Nobel Prize in Medicine in 1979 for the discovery of the diagnostic technique of x-ray computed tomography. Cormack was born in South Africa to Scottish emigrant parents. He attended schools in South Africa and studied at the University of Cape Town where he earned B.Sc. and M. Sc. degrees in physics. Later, he did additional graduate work in nuclear physics at Cambridge University but he never completed a Ph.D. He returned to South Africa where he lectured for several years before eventually moving to Tufts University.
The title, Imagining the Elephant, was inspired by A. A. Milne:
I think I am an Elephant,
Behind another Elephant
Behind another Elephant who isn’t really there…
and by the story of the blind men trying to imagine an elephant when each can touch only one part, a whimsical precursor of the reconstruction of an elephant from slices.
Cormack worked actively in particle physics most of his professional life. His interest in imaging was, in a certain sense, an avocation. He worked briefly in crystallography for his M.Sc. thesis, but passed up an opportunity to work with the crystallographer Lawrence Bragg at the Cavendish laboratory where x-ray diffraction was a very hot topic. Yet, although nuclear physics was his career, he never entirely let go of an interest in imaging. As the only nuclear physicist in South Africa at one time, Cormack was required to supervise the clinical administration of radioactive isotopes. That got him interested in the question of differential absorption of x-rays by human tissue. Beginning in South Africa and continuing at Tufts, entirely as a spare-time pursuit, Cormack worked on what his colleagues came to call “Allan’s line integral problem”. He was convinced that the problem must have been solved by Riemann, Cauchy or someone of their ilk, but he found nothing in the literature. It was only later that he discovered Radon’s work from 1914.
In 1963 and 1964 Cormack published two papers in the Journal of Applied Physics, “Representation of a function by its line integrals, with some radiological applications”, Parts I and II. He received a total of three requests for reprints. When Godfrey Hounsfield and his colleagues built the first CT scanner in 1971, they brought Cormack’s theoretical results from utter obscurity to prominence.
For mathematicians this biography offers little in the way of explicit mathematics. It does, however, offer something quite important — an inspiring picture of an applied mathematician at work. Allan Cormack had an excellent mathematical background and considerable determination. He recognized that the problem of obtaining precise values for the tissue-density distribution with the body was a mathematical one. He worked his way to a solution via analysis of special cases and was able, in model experiments, to reconstruct an accurate cross-section of an irregularly shaped object. His “computer” for these initial CT scans was a desktop calculator. Cormack’s work was truly remarkable.
Bill Satzer (email@example.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.