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Georg Kreisel

Georg Kreisel 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 Georg Kreisel rather than just read about it. In short: Georg Kreisel FRS (September 15, 1923 – March 1, 2015) was an Austrian-born mathematical logician who studied and worked in the United Kingdom and America. Biography Kreisel was born in Graz and came from a Jewish background; his family sent him to the United Kingdom before the Anschluss in 1938.

Key takeaways

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

Reference excerpt

Georg Kreisel FRS (September 15, 1923 – March 1, 2015) was an Austrian-born mathematical logician who studied and worked in the United Kingdom and America.

Biography Kreisel was born in Graz and came from a Jewish background; his family sent him to the United Kingdom before the Anschluss in 1938. He studied mathematics at Trinity College, Cambridge, and then, during World War II, worked on military subjects. Kreisel never took a Ph.D., though much later, in 1962, he was awarded the Cambridge degree of Sc.D., a 'higher doctorate' given on the basis of published research. He taught at the University of Reading from 1949 until 1954 and then worked at the Institute for Advanced Study from 1955 to 1957. He returned to Reading in 1957, but then taught at Stanford University from 1958 to 1959. Then back at Reading for the year 1959–1960, and then the University of Paris 1960–1962. Kreisel was appointed a professor at Stanford University in 1962 and remained on the faculty there until he retired in 1985. Kreisel worked in various areas of logic, and especially in proof theory, where he is known for his so-called "unwinding" program, whose aim was to extract constructive content from superficially non-constructive proofs. Kreisel was elected to the Royal Society in 1966; Kreisel remained a close friend of Francis Crick whom he had met in the Royal Navy during WWII. While a student at Cambridge, Kreisel's philosophical abilities were highly respected by Ludwig Wittgenstein. Ray Monk writes, "In 1944—when Kreisel was still only twenty-one—Wittgenstein shocked Rush Rhees by declaring Kreisel to be the most able philosopher he had ever met who was also a mathematician." Kreisel was also a close friend of the Anglo-Irish philosopher and novelist Iris Murdoch. They met at Cambridge in 1947 during Murdoch's year of study there. Peter Conradi reports that Murdoch transcribed Kreisel's letters into her journals over the next fifty years. According to Conradi, "For half a century she nonetheless records variously Kreisel's brilliance, wit and sheer 'dotty' solipsistic strangeness, his amoralism, cruelty, ambiguous vanity and obscenity." Murdoch dedicated her 1971 novel An Accidental Man to Kreisel and he became a (partial) model for several characters in other novels, including Marcus Vallar in The Message to the Planet and Guy Openshaw in Nuns and Soldiers. After retirement Kreisel lived in Salzburg, Austria. He wrote several biographies of mathematicians including Kurt Gödel, Bertrand Russell and Luitzen Egbertus Jan Brouwer. He died in Salzburg, aged 91.

Anecdotes When Kreisel was teaching at the University of Reading he would frequently take the train into London. There was a particularly fast train that was timed just right for the shows in London, and he would go to the station at that time. He checked the timetable one day, and that train was canceled. But out of habit one day he showed up at the station at the usual time and the train was there. It seems that it was going from Bristol to London, stopping at Reading only to get water. He got on the train anyway, and from then on took that train regularly. One day he was accosted by the conductor after he got on. "The train doesn't stop here sir!" "In that case I didn't get on here."

See also Kreisel–Putnam logic

References

External links Piergiorgio Odifreddi (ed.), Kreiseliana: About and Around George Kreisel, Wellesley, Massachusetts: A. K. Peters, 1996. ISBN 1-56881-061-X. Kreisel, lambda calculus, a windmill and a castle Contains personal recollections about Kreisel by his student Henk Barendregt. Georg Kreisel at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Georg Kreisel

Start with the simplest possible case. Write down what Georg Kreisel 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 Georg Kreisel 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 Georg Kreisel 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 Georg Kreisel

In research
Georg Kreisel 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 Georg Kreisel 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
Georg Kreisel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1923 births, 2015 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Georg Kreisel 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 Georg Kreisel in 20 minutes

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

Frequently asked questions

What is Georg Kreisel in simple terms?

Georg Kreisel FRS (September 15, 1923 – March 1, 2015) was an Austrian-born mathematical logician who studied and worked in the United Kingdom and America. Biography Kreisel was born in Graz and came from a Jewish background; his family sent him to the United Kingdom before the Anschluss in 1938.

Why does Georg Kreisel 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 Georg Kreisel?

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 Georg Kreisel.

Tags

  • 1923 births
  • 2015 deaths
  • 20th-century American mathematicians
  • 20th-century British mathematicians
  • 21st-century American mathematicians
  • 21st-century British mathematicians
  • Academics of the University of Reading
  • Alumni of the University of Cambridge
  • American fellows of the Royal Society
  • Austrian emigrants to the United Kingdom
  • Austrian logicians
  • Austrian mathematicians

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