Arne Beurling

Arne Beurling was a very prominent Swedish mathematician and cryptologist. He received his doctorate from Uppsala University in 1933, and after a few years as an associate professor, he was a professor at the Department of Mathematics from 1937 to 1954.

Beurling worked mainly on harmonic analysis, complex analysis and potential theory. He made several important scientific contributions and is known for Beurling’s theorem on invariant subspaces, Beurling-Ahlfors’ theorem on quasiconformal mappings and Beurling-Malliavin’s theorem in function theory.

He became even more widely known for his significant contributions to cryptography, and in particular for his success in deciphering the G-schreiber. It was Germany’s most advanced encryption machine during World War II.

He left Uppsala in 1954 for an honorary professorship at the Institute for Advanced Study at Princeton University. There he later took over Albert Einstein's office. He remained at Princeton and at the same post until his retirement in 1973. He lived there with his family until his death in 1986.

Many have described him as a genius. He had a dimension to his thinking that was not logical but guided by intuition, feeling and aesthetics. For him, the world of mathematics seemed to be integrated with the real world and with life itself. He never built on what others had done, but always approached new problems in his own way.

As a person, Arne Beurling was very charismatic and for his friends he had an unquestionable loyalty and boundless generosity. At the same time, he was known for his explosive temperament, which he inherited from his father, who was a sea captain, as well as his interest in outdoor life, adventure, hunting and sailing.

His doctoral thesis became one of the most influential mathematical publications of its time. However, it was delayed five years because his father took him on a hunting trip to South America to hunt alligators just before he finished. In the meantime, the same results were published by another researcher, Lars Ahlfors from Finland, who later became Arne Beurling’s best friend.

The G-schreiber

Alongside his professorship at Uppsala University, Arne Beurling worked for the Swedish Defence Cryptography Agency (now FRA) during World War II. After the German invasion of Norway in the spring of 1940, German telegram traffic began to be sent via Swedish telegraph cables. The messages were encrypted with the so-called G-schriber, der Geheimschreiber. The G-schriber was Germany’s most advanced encryption machine and was considered impossible to crack. Its ten wheels allowed for almost a quintillion different combinations.

In two weeks, with just pen and paper, Beurling managed to figure out how the G-schriber’s crypto worked. This incredible feat made it possible, in collaboration with others, to crack the entire crypto and construct a forcing device that from autumn 1940 was used to continuously decode German telegram traffic. Thanks to Beurling, Sweden gained insight into German communications, which helped keep Sweden out of the war.