The mathematician Jack Good played a key role among the codebreaking team at Bletchley Park during the Second World War. He went on to help to build one of the first computers, was the father of a branch of modern statistics and contributed to the development of artificial intelligence.

Good was born Isidore Jacob Gudak to a Polish-Jewish family in London in 1916; his father was a watchmaker and well known in Yiddish literary circles. Isidore later anglicised his name to Irving John Good but he was always known as Jack. Good was slow to learn to read, but partly as a result of being bed-bound with diphtheria at the age of 9 — when he began to discover mathematics for himself — his extraordinary intelligence became clear to his teachers.

From Haberdashers’ Aske’s School he won a mathematics scholarship to Jesus College, Cambridge, where he graduated with a first in 1938. He won the Smith’s Prize in 1940 and did postgraduate work under A. S. Besicovitch and G. H. Hardy; he was awarded his PhD in 1941 for a thesis on topological dimension. Meanwhile, Good had also established himself as a chess player of county standard.

He was recruited in 1941 by Hugh Alexander, the reigning British chess champion, to work in the Government Code and Cipher School (GCCS — known to its staff as the Golf Club and Chess Society) in Bletchley Park in Buckinghamshire.

There he was put to work in Hut 8, under Alexander and Alan Turing (1912-54), on deciphering German military and naval radio traffic. This was encoded on Enigma machines, thought by the Germans to be undecipherable. To attack the Enigma codes, special machines called Bombes were developed. With the war in the Atlantic and the threat posed by U-boats, naval Enigma became a top priority.

So too did work on German teleprinter-enciphering machine systems, a project known in Bletchley Park as Fish. Turing provided the mathematical leadership here, using statistical techniques that he developed for himself; Good became Turing’s statistical assistant.

The two men remained close for the rest of Turing’s short life. They played chess together — Good was much the stronger player — and discussed the possibilities of mechanisation of chess playing.

In return, Turing taught Good the Japanese board game Go, which is even harder than chess and which Good later helped to popularise.

In 1943 Good transferred to the Newmanry — the group working under the mathematician Max Newman. Here he was involved in the development of machines — precursors of the modern computer, using vast arrays of vacuum tubes and paper tape — such as the “Heath Robinson” and the Colossus.

After the war GCCS became the Government Communications Headquarters, or GCHQ. Good followed Turing and Newman to the University of Manchester in 1947, where he was involved in work on the first computer (in the modern sense, of having an internally stored program), the Manchester Mark 1.

In 1948 Good went to GCHQ, where his work remained classified. But he continued to develop the statistical ideas he had worked on with Turing during the war . The result was his first book, Probability and the Weighing of Evidence (1950), in which the author appears on the title page as “I. J. Good, MA, PhD, former lecturer in mathematics at the University of Manchester” (GCHQ was never mentioned publicly in those days — the site it occupied was not even marked on Ordnance Survey maps). He left GCHQ for the Admiralty Research Laboratory in 1959.

Other books included The Estimation of Probablilities: An Essay of Modern Bayesian Methods (1965) and Good Thinking: The Foundations of Probability and its Applications (1983).