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Paul Cohn

Paul Cohn 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 Paul Cohn rather than just read about it. In short: Paul Moritz Cohn FRS (8 January 1924 – 20 April 2006) was Astor Professor of Mathematics at University College London, 1986–1989, and author of many textbooks on algebra. His work was mostly in the area of algebra, especially non-commutative rings.

Paul Cohn — main illustration
Paul Cohn — illustration

Key takeaways

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

Reference excerpt

Paul Moritz Cohn FRS (8 January 1924 – 20 April 2006) was Astor Professor of Mathematics at University College London, 1986–1989, and author of many textbooks on algebra. His work was mostly in the area of algebra, especially non-commutative rings.

Early life Cohn was the only child of Jewish parents, James (or Jakob) Cohn, owner of an import business, and Julia (née Cohen), a schoolteacher. Both of his parents were born in Hamburg, as were three of his grandparents. His ancestors came from various parts of Germany. His father fought in the German army in World War I; he was wounded several times and awarded the Iron Cross. A street in Hamburg is named in memory of his mother. When he was born, his parents were living with his mother's mother in Isestraße. After her death in October 1925, the family moved to a rented flat in a new building in Lattenkamp, in the Winterhude quarter. He attended a kindergarten then, in April 1930, moved to Alsterdorfer Straße School. After a while, he had a new teacher, a National Socialist, who picked on him and punished him without cause. Thus in 1931, he moved to the Meerweinstraße School where his mother taught. Following the rise of the Nazis in 1933, his father's business was confiscated and his mother dismissed. He moved to the Talmud-Tora-Schule, a Jewish school. In mid-1937, the family moved to Klosterallee. This was nearer the school, the synagogue and other pupils, being in the Jewish area. His German teacher was Dr. Ernst Loewenberg, the son of the poet Jakob Loewenberg. On the night of 9/10 November 1938 (Kristallnacht), his father was arrested and sent to Sachsenhausen concentration camp. He was released after four months but told to emigrate. Cohn went to Britain in May 1939 on the Kindertransport to work on a chicken farm, and never saw his parents again. He corresponded regularly with them until late 1941. At the end of the War, he learned that they were deported to Riga on 6 December 1941 and never returned. At the end of 1941, the farm closed. He trained as a precision engineer, acquired a work permit and worked in a factory for 4½ years. He passed the Cambridge Scholarship Examination, and won an exhibition to Trinity College, Cambridge.

Career He received a B.A in mathematics from Cambridge University in 1948 and a Ph.D. (supervised by Philip Hall) in 1951. He then spent a year as a Chargé de Recherches at the University of Nancy. On his return, he became a lecturer in mathematics at Manchester University. He was a visiting professor at Yale University in 1961–1962, and for part of 1962 was at the University of California at Berkeley. On his return, he became Reader at Queen Mary College. He was a visiting professor at the University of Chicago in 1964 and at the State University of New York at Stony Brook in 1967. By then, he was regarded as one of the world's leading algebraists. Also in 1967, he became head of the Department of Mathematics at Bedford College, London. He held several visiting professorships, in America, Paris, Delhi, Canada, Haifa and Bielefeld. He was awarded the Lester R. Ford Award from the Mathematical Association of America in 1972 and the Senior Berwick Prize of the London Mathematical Society in 1974. In the early 1980s, funding cuts caused the closure of the small colleges of the University of London. Cohn moved to University College London in 1984, together with the two other experts at Bedford on ring theory, Bill Stephenson and Warren Dicks. He became Astor Professor of Mathematics there in 1986. He continued to be a visiting professor, for example to the University of Alberta in 1986 and to Bar Ilan University in 1987. He retired in 1989, but remained active as professor emeritus and honorary research fellow until his death. He was president of the London Mathematical Society, 1982–1984, having been its secretary, 1965–1967 and a council member in 1968–1971, 1972–1975 and 1979–1982. He was editor of the society's monographs in 1968–1977 and 1980–1993. He was elected a Fellow of the Royal Society in 1980 and was on its council, 1985–1987. He was a member of the Mathematical Committee of the Science Research Council, 1977–1980. He chaired the National Committee for Mathematics, 1988–1989.

… excerpt ends here. Continue reading the full article.

Illustrations

Paul Cohn illustration

Worked examples

Example 1 — a first encounter with Paul Cohn

Start with the simplest possible case. Write down what Paul Cohn 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 Paul Cohn 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 Paul Cohn 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 Paul Cohn

In research
Paul Cohn 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 Paul Cohn 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
Paul Cohn is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1924 births, 2006 deaths, 20th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Paul Cohn 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 Paul Cohn in 20 minutes

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

Frequently asked questions

What is Paul Cohn in simple terms?

Paul Moritz Cohn FRS (8 January 1924 – 20 April 2006) was Astor Professor of Mathematics at University College London, 1986–1989, and author of many textbooks on algebra. His work was mostly in the area of algebra, especially non-commutative rings.

Why does Paul Cohn 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 Paul Cohn?

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 Paul Cohn.

Tags

  • 1924 births
  • 2006 deaths
  • 20th-century British mathematicians
  • 20th-century German mathematicians
  • 21st-century British mathematicians
  • Academics of Queen Mary University of London
  • Academics of University College London
  • Algebraists
  • Alumni of Trinity College, Cambridge
  • British fellows of the Royal Society
  • German emigrants to the United Kingdom
  • German fellows of the Royal Society

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