For more than two decades, Zbigniew Błocki has been sharing the story of the Polish codebreakers who helped crack Nazi Germany’s Enigma machine—with math.

What was the turning point that led the Allies to victory in World War II? Some might cite a particular battle or army, but University of Maryland Mathematics Visiting Professor Zbigniew Błocki offered another perspective during a Department of Mathematics colloquium in February.

“Some people say that mathematicians won the Second World War,” said Błocki, a mathematics professor from Jagiellonian University in Krakow, Poland. “Maybe that is exaggerated, but I would argue not that much.”

Periodically over the last 24 years, Błocki has given talks on the lesser-publicized role that Polish mathematicians played in decrypting Enigma, the typewriter-like machine that Nazi Germany used to conceal its communications. English mathematician Alan Turing is widely credited for cracking the code, but few know that Marian Rejewski from Poland’s Cipher Bureau laid the foundation.

“When it comes to Enigma, people outside of Poland have usually heard about Alan Turing but rarely about Marian Rejewski,” Błocki said. “I am still surprised how little in general people know about the story.”

A cryptologic bomb

For decades after World War II ended, Rejewski’s role in cracking Enigma—along with the contributions of his colleagues Jerzy Różycki and Henryk Zygalski—was classified. This information wasn’t made public until the 1970s, and Błocki only learned about it in the mid-1980s while reading a book on the subject.
As a lover of math and history, Błocki was impressed to learn how these cryptologists used a mix of math, mainly permutation group theory, and human psychology to capitalize on the Germans’ mistakes. At the time, Enigma was considered virtually unbreakable because of its complex network of rotating wheels and plugboard connections that scrambled the letters each time a key was pressed.

However, these encrypted messages followed a predictable format, providing the Polish mathematicians with clues. By December 1932, Rejewski’s team had leveraged crucial intelligence obtained by the French to figure out Enigma’s internal wiring pattern. When coding procedures were overhauled in September 1938, making their decoding efforts much harder, the Poles built a device dubbed a “bomba,” or bomb, that automated the process of determining Enigma’s daily settings. 

Coupled with earlier developments that allowed the Poles to keep pace with German improvements, the bomba—an early precursor to computing—enabled the Polish to read intercepted German communications from 1933 to 1939. After handing these findings off to the British, Turing and mathematician Gordon Welchman designed the Bombe machine that greatly advanced the Allies’ decryption efforts and helped them win key battles.
“The breaking of the Enigma code had an incredible impact on the outcome of the Second World War,” Błocki said. “It was important everywhere the Allies were fighting the Germans, including the Battle of Britain, where, thanks to decoded Enigma messages, the British knew quite in advance where the attacks would be.”

Setting the record straight

Błocki noted that despite garnering some international attention, Poland’s role in cracking the Enigma code remained a footnote in history for many years—or worse, the subject of misinformation.

“Twenty years ago, the item on Enigma in Encyclopedia Britannica didn't mention Poles at all,” Błocki said. “The problem culminated in 2014 with the Hollywood blockbuster on Alan Turing, ‘The Imitation Game’ starring Benedict Cumberbatch. In it, the role of Polish cryptologists was again missing and the totally false story of a Pole who stole an Enigma machine from the Germans was repeated.”

Since then, Błocki has been committed to setting the record straight. The first time he gave his talk on Enigma was for his habilitation defense—a postdoctoral presentation on a subject separate from one’s research—at Jagiellonian University in 2001.

“It was very crowded with well over 100 people,” Blocki said of his audience. “The atmosphere was pretty patriotic, and by the end of it, they seemed almost ready to sing the Polish national anthem.”

Błocki has since adapted his presentation for a range of audiences, including scientific institutions, universities, high schools and even his son’s elementary school class. When he left his position with Poland’s National Science Centre, where he served as director from 2015 to 2023, Błocki received a unique parting gift from his colleagues: an electronic copy of Enigma. 

After joining UMD, Błocki shared the story of Enigma with Mathematics Professor Yanir Rubinstein, who encouraged Błocki to present the topic at a department colloquium. While reflecting on the story’s reach since it was uncovered in the ’70s, Błocki feels encouraged by recent efforts to portray this chapter of history more accurately.
“Fortunately, a lot has changed. For example, the Encyclopedia Britannica entry about Enigma has been completely revised,” he said. “I think the 2018 publication of ‘X, Y & Z: The Real Story of How Enigma Was Broken,’ a book by Alan Turning’s nephew, Dermot Turing, was very important. This is probably the first British publication of its kind where the critical role of Polish mathematicians in this story is presented.”

For Błocki, this lecture is also a fun way to teach mathematical and computing concepts through history.
“I gave this talk at the University of Bonn in Germany in 2001, and the professor who organized it said he had been to several talks on Enigma, but mine was the only one that explained the mathematics,” Błocki said. “Although from today's viewpoint the mathematics behind Enigma is fairly elementary, it turned out to be crucial for the future development of computer science.”

Written by Emily Nunez