He was born Isidore Jacob Gudak, in a Jewish family in London. He read mathematics at Jesus College, University of Cambridge, graduating in 1983. He did research work under G. H. Hardy and Besicovitch, before moving to Bletchley Park in 1941 on completing his doctorate.
At Bletchley Park he was in initially in Hut 8 under Alan Turing; he worked with Donald Michie in Max Newman’s group on the Fish codes, leading to the development of the Colossus machine.
After the war ended he worked at Manchester University and then GCHQ. (to 1959). He then had a variety of defence, consulting and academic positions. He was a prolific author of technical papers.
In 1967 he moved to the United States. He is a University Distinguished Professor at Virginia Tech, where his "vanity" car license plate, hinting at his spy-like wartime work, is 007 IJG.
He is known for his work on Bayesian statistics. He has published a number of books on probability theory.
He played chess to county standard, and helped to popularise go by a 1965 article in New Scientist (he had learned the rules from Turing).