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Solomon Kullback

Solomon Kullback 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 Solomon Kullback rather than just read about it. In short: Solomon Kullback (April 3, 1907 – August 5, 1994) was an American cryptanalyst and mathematician, who was one of the first three employees hired by William F. Friedman at the US Army's Signal Intelligence Service (SIS) in the 1930s, along with Frank Rowlett and Abraham Sinkov.

Solomon Kullback — main illustration
Solomon Kullback — illustration

Key takeaways

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

Reference excerpt

Solomon Kullback (April 3, 1907 – August 5, 1994) was an American cryptanalyst and mathematician, who was one of the first three employees hired by William F. Friedman at the US Army's Signal Intelligence Service (SIS) in the 1930s, along with Frank Rowlett and Abraham Sinkov. He went on to a long and distinguished career at SIS and its eventual successor, the National Security Agency (NSA). Kullback was the Chief Scientist at the NSA until his retirement in 1962, whereupon he took a position at the George Washington University. The Kullback–Leibler divergence is named after Kullback and Richard Leibler.

Life and career Kullback was born to Jewish parents in Brooklyn, New York. His father Nathan had been born in Vilna, Russian Empire, (now Vilnius, Lithuania) and had immigrated to the US as a young man circa 1905, and became a naturalized American in 1911. Kullback attended Boys High School in Brooklyn. He then went to City College of New York, graduating with a BA in 1927 and an MA in math in 1929. He completed a doctorate in math from George Washington University in 1934. His intention had been to teach, and he returned to Boy's High School to do so, but found it not to his taste; he discovered his real interest was using mathematics, not teaching it. At the suggestion of Abraham Sinkov, who showed him a Civil Service flyer for "junior mathematicians" at US$2,000 per year, he took the examination. Both passed, and were assigned to Washington, D.C. as junior cryptanalysts. Upon arrival in Washington, Kullback was assigned to William F. Friedman. Friedman had begun an intensive program of training in cryptology for his new civilian employees. For several summers running, the SIS cryptanalysts attended training camps at Fort Meade until they received commissions as reserve officers in the Army. Kullback and Sinkov took Friedman's admonitions on education seriously and spent the next several years attending night classes; both received their doctorates in mathematics. Afterward, Kullback rediscovered a love of teaching; he began offering evening classes in mathematics at George Washington University from 1939. Once they had completed the training, the three were put to the work for which they had actually been hired, compilations of cipher or code material for the U.S. Army. Another task was to test commercial cipher devices which vendors wished to sell to the U.S. government. Kullback worked in partnership with Frank Rowlett against RED cipher machine messages. Almost overnight, they unravelled the keying system and then the machine pattern – with nothing but the intercepted messages in hand. Using the talents of linguist John Hurt to translate text, SIS started issuing current intelligence to military decision-makers. In May 1942, five months after attack on Pearl Harbor, Kullback, by then a Major, was sent to Britain. He learned at Bletchley Park that the British were producing intelligence of high quality by exploiting the Enigma machine. He also cooperated with the British in the solution of more conventional German codebook-based systems. Shortly after his return to the States, Kullback moved into the Japanese section as its chief. When the National Security Agency (NSA) was formed in 1952, Rowlett became chief of cryptanalysis. The primary problem facing research and development in the post-war period was development of high-speed processing equipment. Kullback supervised a team of about 60 people, including such innovative thinkers in automated data processing development as Leo Rosen and Sam Snyder. His staff pioneered new forms of input and memory, such as magnetic tape and drum memory, and compilers to make machines truly "multi-purpose". Kullback gave priority to using computers to generate communications security (COMSEC) materials. Kullback's book Information Theory and Statistics was published by John Wiley & Sons in 1959. The book was republished, with additions and corrections, by Dover Publications in 1968.

Retirement Solomon Kullback retired from NSA in 1962, and focused on his teaching at George Washington University and publishing new papers. In 1963 he was elected as a Fellow of the American Statistical Association. He reached the rank of colonel, and was inducted into the Military Intelligence Hall of Fame. Kullback is remembered by his colleagues at NSA as straightforward; one described him as "totally guileless, you always knew where you stood with him." One former NSA senior recalled him as a man of unlimited energy and enthusiasm and a man whose judgment was usually "sound and right."

References

External links Solomon Kullback at the Mathematics Genealogy Project Solomon Kullback at the NSA Hall of Fame

Illustrations

Solomon Kullback illustration

Worked examples

Example 1 — a first encounter with Solomon Kullback

Start with the simplest possible case. Write down what Solomon Kullback 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 Solomon Kullback 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 Solomon Kullback 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 Solomon Kullback

In research
Solomon Kullback 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 Solomon Kullback 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
Solomon Kullback is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1907 births, 1994 deaths, 20th-century American statisticians, so understanding it makes those chapters shorter.
In everyday life
Look for Solomon Kullback 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 Solomon Kullback in 20 minutes

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

Frequently asked questions

What is Solomon Kullback in simple terms?

Solomon Kullback (April 3, 1907 – August 5, 1994) was an American cryptanalyst and mathematician, who was one of the first three employees hired by William F. Friedman at the US Army's Signal Intelligence Service (SIS) in the 1930s, along with Frank Rowlett and Abraham Sinkov.

Why does Solomon Kullback 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 Solomon Kullback?

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 Solomon Kullback.

Tags

  • 1907 births
  • 1994 deaths
  • 20th-century American statisticians
  • American cryptographers
  • American people of Lithuanian-Jewish descent
  • Boys High School (Brooklyn) alumni
  • City College of New York alumni
  • Columbian College of Arts and Sciences alumni
  • Fellows of the American Statistical Association
  • George Washington University faculty
  • Information theorists
  • Mathematicians from New York (state)

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