Georg Kreisel
Encyclopedia
Georg Kreisel FRS
(born September 15, 1923 in Graz
) is an Austria
n-born mathematical logic
ian who has studied and worked in Great Britain
and America
. Kreisel came from a Jewish background; his family sent him to England
before the Anschluss
, where he studied mathematics at Trinity College, Cambridge
and then, during World War II
, worked on military
subjects. After the war he returned to Cambridge and received his doctorate
. He taught at the University of Reading
until 1954 and then worked at the Institute for Advanced Study
from 1955 to 1957. Subsequently he taught at Stanford University
and the University of Paris
. 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 proof
s.
Kreisel was elected to the Royal Society
in 1966; Kreisel remained a close friend of the late Francis Crick
who he had met in the Royal Navy during WWII.
While a student at Cambridge, Kreisel was the student most 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
.*
Kreisel currently lives in retirement in Salzburg
, Austria. He has written several biographies of high profile mathematicians including Kurt Godel
, Bertrand Russell
and Luitzen Egbertus Jan Brouwer
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
(born September 15, 1923 in Graz
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...
) is an Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
n-born mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
ian who has studied and worked in Great Britain
Great Britain
Great Britain or Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island, as well as the largest of the British Isles...
and America
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
. Kreisel came from a Jewish background; his family sent him to England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
before the Anschluss
Anschluss
The Anschluss , also known as the ', was the occupation and annexation of Austria into Nazi Germany in 1938....
, where he studied mathematics at Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
and then, during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, worked on military
Military
A military is an organization authorized by its greater society to use lethal force, usually including use of weapons, in defending its country by combating actual or perceived threats. The military may have additional functions of use to its greater society, such as advancing a political agenda e.g...
subjects. After the war he returned to Cambridge and received his doctorate
Doctorate
A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder to teach in a specific field, A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder...
. He taught at the University of Reading
University of Reading
The University of Reading is a university in the English town of Reading, Berkshire. The University was established in 1892 as University College, Reading and received its Royal Charter in 1926. It is based on several campuses in, and around, the town of Reading.The University has a long tradition...
until 1954 and then worked at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
from 1955 to 1957. Subsequently he taught at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
and the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
. Kreisel was appointed a professor at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
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
Proof theory
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...
, where he is known for his so-called "unwinding" program, whose aim was to extract constructive
Constructivism (mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption, one still has not found the object and therefore not proved its...
content from superficially non-constructive proof
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
s.
Kreisel was elected to the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
in 1966; Kreisel remained a close friend of the late Francis Crick
Francis Crick
Francis Harry Compton Crick OM FRS was an English molecular biologist, biophysicist, and neuroscientist, and most noted for being one of two co-discoverers of the structure of the DNA molecule in 1953, together with James D. Watson...
who he had met in the Royal Navy during WWII.
While a student at Cambridge, Kreisel was the student most respected by Ludwig Wittgenstein
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
. Ray Monk
Ray Monk
Ray Monk is a Professor of Philosophy at the University of Southampton, where he has taught since 1992.He won the Mail on Sunday/John Llewellyn Rhys Prize and the 1991 Duff Cooper Prize for Ludwig Wittgenstein: The Duty of Genius. His interests lie in the philosophy of mathematics, the history of...
writes, "In 1944--when Kreisel was still only twenty-one--Wittgenstein shocked Rush Rhees
Rush Rhees
Rush Rhees was a philosopher at Swansea University from 1940 to 1966Rhees is principally known as a student, friend, and literary executor of the philosopher Ludwig Wittgenstein. With G. E. M. Anscombe, he edited Wittgenstein's posthumous Philosophical Investigations , a highly influential work...
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
Iris Murdoch
Dame Iris Murdoch DBE was an Irish-born British author and philosopher, best known for her novels about political and social questions of good and evil, sexual relationships, morality, and the power of the unconscious...
. 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
Nuns and Soldiers
Nuns and Soldiers is a 1980 novel by Iris Murdoch. The setting is England and two of the main characters are Gertrude, a widow, and Anne, an ex-nun.- Plot :...
.*
Kreisel currently lives in retirement in Salzburg
Salzburg
-Population development:In 1935, the population significantly increased when Salzburg absorbed adjacent municipalities. After World War II, numerous refugees found a new home in the city. New residential space was created for American soldiers of the postwar Occupation, and could be used for...
, Austria. He has written several biographies of high profile mathematicians including Kurt Godel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
, Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
and Luitzen Egbertus Jan Brouwer
Luitzen Egbertus Jan Brouwer
Luitzen Egbertus Jan Brouwer FRS , usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, a graduate of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis.-Biography:Early in his career,...
External links and further reading
- Kreiseliana: About and Around George Kreisel, Piergiorgio Odifreddi, ed., Wellesley, Massachusetts: A. K. Peters, 1996. ISBN 156881061X.
- [ftp://ftp.cs.ru.nl/pub/CompMath.Found/kr.ps Kreisel, lambda calculus, a windmill and a castle] Contains personal recollections about Kreisel by his student Henk BarendregtHenk BarendregtHendrik Pieter Barendregt is a Dutch logician, known for his work in lambda calculus and type theory.Barendregt studied mathematical logic at Utrecht University, obtaining his Masters in 1968 and his Ph.D. in 1971, both cum laude, under Dirk van Dalen and Georg Kreisel...
.