[3] Crombie undertook postgraduate study at Jesus College, the University of Cambridge, receiving his doctorate in 1942 in the area of population dynamics.
He undertook research at the Cambridge Zoological Laboratory for the British Ministry of Agriculture and Fisheries from 1941 until he was appointed as lecturer at University College London in 1946.
[5] Crombie was one of the founders of the review journal History of Science in 1962, and was awarded the Galileo Prize by the Domus Galileana in Pisa in 1964.
He received the Forschungspreis (Research Award) of the Alexander von Humboldt Foundation, honorary doctorates from Durham (1978), Paris, X-Nanterre and Sassari, and the European Premio Dondi (1995).
He published his ideas in 1994 in a definitive 3-volume work, entitled, Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation especially in the Mathematical and Biomedical Sciences and Arts.