For his discovery, Dr. Klitzing was awarded the Nobel Prize in 1985.
Theoreticians wanted to explain Dr. Klitzing’s discovery mathematically, so Dr. Thouless, working with three research assistants, applied topology to the problem. This led to a landmark paper in 1982 that linked Dr. Klitzing’s discovery to the so-called Chern numbers — named after the mathematician Shiing-Shen Chern — which are used to characterize topological shapes.
It was for this mathematical insight, as well as his earlier work with Dr. Kosterlitz, that Dr. Thouless received half the Nobel Prize.
David James Thouless was born on Sept. 21, 1934, in Bearsden, Scotland, to Robert and Priscilla (Gorton) Thouless, both of whom were originally from England. (He said his surname was a variation on Thewless and Thewlis.) His mother taught English in Manchester, England, before she gave birth to Dr. Thouless’s oldest sister, Susan, in 1925. Dr. Thouless’s father was a psychology professor at the University of Glasgow and familiar to radio audiences for his programs on thinking critically. He drew on those programs to write the book “Straight and Crooked Thinking” (published in the United States as “How to Think Straight”), which became required reading for students of rhetoric.
Dr. Thouless pursued his undergraduate education at the University of Cambridge before earning his Ph.D. at Cornell University. He studied there under Hans Bethe, who received the Nobel Prize in Physics in 1967.
While at Cornell, Dr. Thouless met and married Margaret Scrase. His wife, who is now a professor emeritus of pathobiology at the University of Washington, survives him. His survivors also include their three children, Michael, Christopher and Helen.
After graduating from Cornell in 1958, Dr. Thouless spent a year at the Lawrence Berkeley National Laboratory in California before joining the department of mathematical physics at the University of Birmingham, where he worked under Rudolf Peierls, another world-renowned physicist.
Dr. Thouless remained at Birmingham until 1978. He then taught at Yale University for two years before the appointment at the University of Washington, in Seattle, where he worked until 2014. He then returned to Cambridge.
Dr. Thouless was awarded the prestigious Wolf Prize in physics and the Dirac Medal, named for Paul Dirac, one of the fathers of quantum physics, in 1993.