Born at Leipzig in Germany, Katz received his MD from the university there in 1934 and his PhD, under Archibald Hill, from the University of London in 1938. He spent the war in Australia first working with John Eccles and later in the Royal Australian Air Force as a radar operator. Katz returned to London in 1946 to University College and in 1952 became professor of biophysics, a post he retained until he retired in 1978.

In 1936 Henry Dale demonstrated that peripheral nerves act by releasing the chemical acetylcholine in response to a nerve impulse. To find how this secretion takes place Katz, working in collaboration with the British biophysicist, Paul Fatt, inserted a micropipette at a neuromuscular junction to record the ‘end-plate potential’ or EPP. He noted a random deflection on the oscilloscope with an amplitude of about 0.5 millivolt even in the absence of all stimulation. At first he assumed such a reading to be interference arising from the machine but the application of curare, an acetylcholine antagonist, by abolishing the apparently random EPPs, showed the activity in the nerves is real.

Consequently Katz proposed his quantum hypothesis. He suggested that nerve endings secrete small amounts of acetylcholine in a random manner in specific amounts (or quanta). When a nerve is stimulated it does not begin secreting but instead enormously increases the number of quanta of acetylcholine released. Katz was able to produce a good deal of evidence for this hypothesis, which he later presented in his important work Nerve, Muscle and Synapse (1966).

It was mainly for this work that Katz shared the 1970 Nobel Prize for physiology or medicine with Julius Axelrod and Ulf von Euler.