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Marian Rejewski

Marian Rejewski is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Marian Rejewski rather than just read about it. In short: Marian Adam Rejewski (Polish: [ˈmarjan rɛˈjɛfskʲi] ; 16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen German military Enigma cipher machine. Over the next nearly seven years, Rejewski and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski, working at the Polish General Staff's Cipher Bureau, developed techniques and equip…

Marian Rejewski — main illustration
Marian Rejewski — illustration

Key takeaways

  • Marian Rejewski belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Marian Rejewski to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Marian Rejewski from memory before moving on to harder problems.

Reference excerpt

Marian Adam Rejewski (Polish: [ˈmarjan rɛˈjɛfskʲi] ; 16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen German military Enigma cipher machine. Over the next nearly seven years, Rejewski and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski, working at the Polish General Staff's Cipher Bureau, developed techniques and equipment for decrypting the Enigma ciphers, even as the Germans introduced modifications to their Enigma machines and encryption procedures. Rejewski's contributions included the cryptologic card catalog and the cryptologic bomb. Five weeks before the outbreak of World War II in Europe, the Poles shared their achievements with French and British counterparts who had made no progress, enabling Britain to begin reading German Enigma ciphers. The intelligence gained by the British from Enigma decrypts formed part of what they code-named Ultra and contributed—perhaps decisively—to the defeat of Nazi Germany. Soon after the outbreak of war, the Polish cryptologists were evacuated to France, where they continued breaking Enigma ciphers. After the fall of France in June 1940, they and their support staff were evacuated to Algeria in North Africa; a few months later, they resumed work clandestinely in southern Vichy France. After the Vichy "Free Zone" was occupied by Nazi Germany in November 1942, Rejewski and Zygalski escaped via Spain (and Spanish imprisonment), Portugal, and Gibraltar to Britain. There they enlisted in the Polish Armed Forces and were put to work solving low-grade German ciphers. After the war, Rejewski returned to Poland and his family. For two decades, he remained silent about his prewar and wartime work so as to avoid the attention of Poland's Soviet-dominated government. In 1967, he broke his silence, providing Poland's Military Historical Institute his memoirs of work at the Cipher Bureau.

Early life

Marian Rejewski was born 16 August 1905 in Bromberg in the Prussian Province of Posen (now Bydgoszcz, Poland) to Józef and Matylda, née Thoms. After completing secondary school, he studied mathematics at Poznań University's Mathematics Institute, housed in Poznań Castle. In 1929, shortly before graduating from university, Rejewski began attending a secret cryptology course which opened on 15 January, organized for select German-speaking mathematics students by the Polish General Staff's Cipher Bureau with the help of the Mathematics Institute's Professor Zdzisław Krygowski. The course was conducted off-campus at a military facility and, as Rejewski would discover in France in 1939, "was entirely and literally based" on a 1925 book by French colonel Marcel Givierge, Cours de cryptographie (Cryptography Course). Rejewski and fellow students Henryk Zygalski and Jerzy Różycki were among the few who could keep up with the course while balancing the demands of their normal studies. On 1 March 1929, Rejewski graduated with a Master of Philosophy degree in mathematics. A few weeks after graduating, and without having completed the Cipher Bureau's cryptology course, he began the first year of a two-year actuarial statistics course at Göttingen, Germany. He did not complete the statistics course, because while home for the summer of 1930, he accepted an offer, from Professor Krygowski, of a mathematics teaching assistantship at Poznań University. He also began working part-time for the Cipher Bureau, which by then had set up an outpost at Poznań to decrypt intercepted German radio messages. Rejewski worked some twelve hours a week near the Mathematics Institute in an underground vault referred to puckishly as the "Black Chamber". The Poznań branch of the Cipher Bureau was disbanded in the summer of 1932. In Warsaw, on 1 September 1932, Rejewski, Zygalski, and Różycki joined the Cipher Bureau as civilian employees working at the General Staff building (the Saxon Palace). Their first assignment was to solve a four-letter code used by the Kriegsmarine (German Navy). Progress was initially slow, but sped up after a test exchange—consisting of a six-group signal, followed by a four-group response—was intercepted. The cryptologists guessed correctly that the first signal was the question, "When was Frederick the Great born?" followed by the response, "1712." On 20 June 1934 Rejewski married Irena Maria Lewandowska, daughter of a prosperous dentist. The couple eventually had two children: a son, Andrzej (Andrew), born in 1936; and a daughter, Janina (Joan), born in 1939. Janina would later become a mathematician like her father.

Enigma machine

The Enigma machine was an electromechanical device, equipped with a 26-letter keyboard and 26 lamps, corresponding to the letters of the alphabet. Inside was a set of wired drums (rotors and a reflector) that scrambled the input. The machine used a plugboard to swap pairs of letters, and the encipherment varied from one key press to the next. For two operators to communicate, both Enigma machines had to be set up in the same way. The large number of possibilities for setting the rotors and the plugboard combined to form an astronomical number of configurations, and the settings were changed daily, so the machine code had to be "broken" anew each day. Before 1932, the Cipher Bureau had succeeded in solving an earlier Enigma machine that functioned without a plugboard, but had been unsuccessful with the Enigma I, a new standard German cipher machine that was coming into widespread use. In late October or early November 1932, the head of the Cipher Bureau's German section, Captain Maksymilian Ciężki, tasked Rejewski to work alone on the German Enigma I machine for a couple of hours per day; Rejewski was not to tell his colleagues what he was doing.

Solving the wiring

To decrypt Enigma messages, three pieces of information were needed: (1) a general understanding of how Enigma functioned; (2) the wiring of the rotors; and (3) the daily settings (the sequence and orientations of the rotors, and the plug connections on the plugboard). Rejewski had only the first at his disposal, based on information already acquired by the Cipher Bureau.

… excerpt ends here. Continue reading the full article.

Illustrations

Marian Rejewski illustration
Marian Rejewski: Rejewski's birthplace
Rejewski's birthplace
Marian Rejewski: Rejewski studied mathematics at Poznań University.
Rejewski studied mathematics at Poznań University.
Marian Rejewski: Rejewski laid flowers on Gauss's grave (Göttingen).[7]
Rejewski laid flowers on Gauss's grave (Göttingen).[7]
Marian Rejewski: Enigma machine, solved by Rejewski in 1932
Enigma machine, solved by Rejewski in 1932

Worked examples

Example 1 — a first encounter with Marian Rejewski

Start with the simplest possible case. Write down what Marian Rejewski claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Marian Rejewski before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Marian Rejewski ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Marian Rejewski

In research
Marian Rejewski appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Marian Rejewski in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Marian Rejewski is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1905 births, 1980 deaths, 20th-century Polish inventors, so understanding it makes those chapters shorter.
In everyday life
Look for Marian Rejewski outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Marian Rejewski in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Marian Rejewski means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Marian Rejewski out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Marian Rejewski in simple terms?

Marian Adam Rejewski (Polish: [ˈmarjan rɛˈjɛfskʲi] ; 16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen German military Enigma cipher machine. Over the next nearly seven years, Rejewski and fellow mathematician-cryptologist…

Why does Marian Rejewski matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Marian Rejewski?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Marian Rejewski.

Tags

  • 1905 births
  • 1980 deaths
  • 20th-century Polish inventors
  • 20th-century Polish mathematicians
  • 20th-century cryptographers
  • Adam Mickiewicz University in Poznań alumni
  • Cipher Bureau (Poland)
  • Enigma machine
  • Grand Crosses of the Order of Polonia Restituta
  • People from Bydgoszcz
  • People from the Province of Posen
  • Polish Army officers

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