Beurling was born in Gothenburg, Sweden and was the son of the landowner Konrad Beurling and baroness Elsa Raab. After graduating in 1924, he was enrolled at the Uppsala University where he received a Bachelor of Arts degree in 1926 and two years later a Licentiate of Philosophy degree. Beurling was assistant teacher at Uppsala University from 1931 to 1933. He received his doctorate in mathematics in 1933 for his dissertation Études sur un problème de majoration. Beurling was a docent of mathematics at Uppsala University from 1933 and then professor of mathematics from 1937 to 1954. He was visiting professor at Harvard University from 1948 to 1949. From 1954 he was professor at the Institute for Advanced Study at Princeton University, United States, where he took over Albert Einstein's office.
In the summer of 1940 he single-handedly deciphered and reverse-engineered an early version of the Siemens and Halske T52 also known as the Geheimfernschreiber used by Nazi Germany in World War II for sending ciphered messages. The T52 was one of the so-called "Fish cyphers", that, using transposition, created nearly one quintillion different variations. It took Beurling two weeks to solve the problem using pen and paper. Using Beurling's work, a device was created that enabled Sweden to decipher German teleprinter traffic passing through Sweden from Norway on a cable. In this way, Swedish authorities knew about Operation Barbarossa before it occurred. Since the Swedes would not reveal how this knowledge was attained, the Swedish warning was not treated as credible by Soviets. This became the foundation for the Swedish National Defence Radio Establishment. The cypher in the Geheimfernschreiber is generally considered to be more complex than the cypher used in the Enigma machines.
Beurling was in his first marriage married 1936-40 with the licentiate in medicine Britta Östberg, daughter of lector Henrik Östberg and Ph.D. Gerda Nilsson. He remarried in 1950 with a M.Phil. Karin Lindblad, daughter of ironmonger Henric Lindblad and Wanja Bengtsson. Karin was a distinguished Ph.D student from Uppsala University. When they lived in Princeton, she worked in a biochemistry lab at Princeton University. Beurling was in the first marriage the father of Pehr-Henrik and Jane. Beurling died in 1986 and was buried at Norra begravningsplatsen in Stockholm. Beurling's great-grandfather was Per Henric Beurling, who founded a high quality clock factory in Stockholm in 1783.
In popular culture
Beurling's prowess as a cryptanalysist is the subject of the 2005 short opera Krypto CEG by Jonas Sjöstrand and Kimmo Eriksson.