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William F. Friedman

William F. Friedman 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 William F. Friedman rather than just read about it. In short: William Frederick Friedman (September 24, 1891 – November 2, 1969) was a US Army cryptographer who ran the research division of the Army's Signal Intelligence Service (SIS) in the 1930s, and parts of its follow-on services into the 1950s. In 1940, subordinates of his led by Frank Rowlett broke Japan's PURPLE cipher, thus disclosing Japanese diplomatic secrets before America's entrance into World War II.

William F. Friedman — main illustration
William F. Friedman — illustration

Key takeaways

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

Reference excerpt

William Frederick Friedman (September 24, 1891 – November 2, 1969) was a US Army cryptographer who ran the research division of the Army's Signal Intelligence Service (SIS) in the 1930s, and parts of its follow-on services into the 1950s. In 1940, subordinates of his led by Frank Rowlett broke Japan's PURPLE cipher, thus disclosing Japanese diplomatic secrets before America's entrance into World War II.

Early life Friedman was born Wolf Friedman (Yiddish: װאָלף פֿרידמאַן, Russian: Вольф Ф. Фридман), in Kishinev, Bessarabia, the son of Frederick Friedman, a Jew from Bucharest who worked as a translator and linguist for the Russian Postal Service, and the daughter of a well-to-do wine merchant. Friedman's family left Kishinev in 1892 on account of anti-Semitic persecution, ending up in Pittsburgh, Pennsylvania. Three years later, his first name was changed to William. As a child, Friedman was introduced to cryptography in the short story "The Gold-Bug" by Edgar Allan Poe. He studied at the Michigan Agricultural College (known today as Michigan State University) in East Lansing and received a scholarship to work on genetics at Cornell University. Meanwhile, George Fabyan, who ran a private research laboratory to study any personally interesting project, decided to set up his own genetics project and was referred to Friedman. Friedman joined Fabyan's Riverbank Laboratories outside Chicago in September 1915. As head of the Department of Genetics, one of the projects he ran studied the effects of moonlight on crop growth, and so he experimented with the planting of wheat during various phases of the moon.

Initial work in cryptology

Another of Fabyan's pet projects was research into secret messages which Sir Francis Bacon had allegedly hidden in various texts during the reigns of Elizabeth I and James I. The research was carried out by Elizabeth Wells Gallup. She believed that she had discovered many such messages in the works of William Shakespeare, and convinced herself that Bacon had written many, if not all, of Shakespeare's works. Friedman had become something of an expert photographer while working on his other projects, and was asked to travel to England on several occasions to help Gallup photograph historical manuscripts during her research. He became fascinated with the work as he courted Elizebeth Smith, Gallup's assistant and an accomplished cryptographer. They married, and he soon became director of Riverbank's Department of Codes and Ciphers as well as its Department of Genetics. During this time, Friedman wrote a series of eight papers on cryptography, collectively known as the "Riverbank Publications", including the first description of the index of coincidence, an important mathematical tool in cryptanalysis.

With the entry of the United States into World War I, Fabyan offered the services of his Department of Codes and Ciphers to the government. No Federal department existed for this kind of work (although both the Army and Navy had had embryonic departments at various times), and soon Riverbank became the unofficial cryptographic center for the US Government. During this period, the Friedmans broke a code used by German-funded Indian radicals in the US who planned to ship arms to India to gain independence from Britain. Analyzing the format of the messages, Riverbank realized that the code was based on a dictionary of some sort, a cryptographic technique common at the time. The Friedmans soon managed to decrypt most of the messages, but only long after the case had come to trial did the book itself come to light: a German-English dictionary published in 1880.

Signals Intelligence Service The United States government decided to set up its own cryptological service, and sent Army officers to Riverbank to train under Friedman. To support the program, Friedman wrote a series of technical monographs, completing seven by early 1918. He then enlisted in the Army and went to France to serve as the personal cryptographer for General John J. Pershing. He returned to the US in 1920 and published an eighth monograph, "The Index of Coincidence and its Applications in Cryptography", considered by some to be the most important publication in modern cryptography to that time. His texts for Army cryptographic training were well thought of and remained classified for several decades. In 1921 he became chief cryptanalyst for the War Department and later led the Signals Intelligence Service (SIS)—a position he kept for a quarter century. In 1929, after the American Black Chamber in New York City was disbanded, its files were entrusted to SIS, and the cryptographic and intelligence services was reorganized to suit its new position at the War Department. Friedman coined several terms, including "cryptanalysis", and wrote many monographs on cryptography. One of these (written mostly in his spare time) was the first draft of his Elements of cryptanalysis, which later was expanded to four volumes and became the U.S. Army's cryptographic main textbook and reference. Realizing that mathematical and language skills were essential to SIS's work, Friedman managed to get authority to hire three men with both mathematical training and language knowledge. They were Solomon Kullback, Frank Rowlett and Abraham Sinkov, each of whom went on to distinguished service for decades. In addition he also was finally able to hire a man fluent in Japanese, John Hurt. During this period Elizebeth Smith Friedman continued her own work in cryptology, and became famous in a number of trials involving rum-runners and the Coast Guard and FBI during Prohibition.

Solution of cipher machines

… excerpt ends here. Continue reading the full article.

Illustrations

William F. Friedman illustration
William F. Friedman: William and Elizebeth Friedman, recently married, at Riverbank in 1917
William and Elizebeth Friedman, recently married, at Riverbank in 1917
William F. Friedman: Riverbank Laboratories
Riverbank Laboratories
William F. Friedman: W. F. Friedman in 1924
W. F. Friedman in 1924
William F. Friedman: Friedman with an AT&T cipher machine
Friedman with an AT&T cipher machine

Worked examples

Example 1 — a first encounter with William F. Friedman

Start with the simplest possible case. Write down what William F. Friedman 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 William F. Friedman 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 William F. Friedman 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 William F. Friedman

In research
William F. Friedman 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 William F. Friedman 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
William F. Friedman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1891 births, 1969 deaths, 20th-century people from Washington, D.C., so understanding it makes those chapters shorter.
In everyday life
Look for William F. Friedman 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 William F. Friedman in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what William F. Friedman 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 William F. Friedman out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is William F. Friedman in simple terms?

William Frederick Friedman (September 24, 1891 – November 2, 1969) was a US Army cryptographer who ran the research division of the Army's Signal Intelligence Service (SIS) in the 1930s, and parts of its follow-on services into the 1950s. In 1940, subordinates of his led by Frank Rowlett broke Japa…

Why does William F. Friedman 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 William F. Friedman?

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 William F. Friedman.

Tags

  • 1891 births
  • 1969 deaths
  • 20th-century people from Washington, D.C.
  • American cryptographers
  • American people of Moldovan-Jewish descent
  • American people of World War II
  • Baconian theory of Shakespeare authorship
  • Bessarabian Jews
  • Burials at Arlington National Cemetery
  • Cornell University alumni
  • Emigrants from the Russian Empire to the United States
  • Mathematicians from Illinois

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