Adrian Richard David Mathias (born 12 February 1944) is a British mathematician working in

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

. The forcing notion Mathias forcing is named for him.

Career

Mathias was educated at

Shrewsbury Shrewsbury ( , ) is a market town and civil parish in Shropshire (district), Shropshire, England. It is sited on the River Severn, northwest of Wolverhampton, west of Telford, southeast of Wrexham and north of Hereford. At the 2021 United ...

and

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

, where he read mathematics and graduated in 1965. After graduation, he moved to

Bonn Bonn () is a federal city in the German state of North Rhine-Westphalia, located on the banks of the Rhine. With a population exceeding 300,000, it lies about south-southeast of Cologne, in the southernmost part of the Rhine-Ruhr region. This ...

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

where he studied with

Ronald Jensen Ronald Björn Jensen (born April 1, 1936) is an American mathematician who lives in Germany, primarily known for his work in mathematical logic and set theory. Career Jensen completed a BA in economics at American University in 1959, and a Ph.D. ...

, visiting

UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school then known as the southern branch of the C ...

Stanford Leland Stanford Junior University, commonly referred to as Stanford University, is a private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth governor of and th ...

, the

University of Wisconsin A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Uni ...

, and

Monash University Monash University () is a public university, public research university based in Melbourne, Victoria (state), Victoria, Australia. Named after World War I general Sir John Monash, it was founded in 1958 and is the second oldest university in the ...

during that period. In 1969, he returned to Cambridge as a research fellow at

Peterhouse Peterhouse is the oldest Colleges of the University of Cambridge, constituent college of the University of Cambridge in England, founded in 1284 by Hugh de Balsham, Bishop of Ely. Peterhouse has around 300 undergraduate and 175 graduate stud ...

and was admitted to the Ph.D. at Cambridge University in 1970. From 1969 to 1990, Mathias was a fellow of Peterhouse; during this period, he was the editor of the

Mathematical Proceedings of the Cambridge Philosophical Society ''Mathematical Proceedings of the Cambridge Philosophical Society'' is a mathematical journal published by Cambridge University Press for the Cambridge Philosophical Society. It aims to publish original research papers from a wide range of pure ...

from 1972 to 1974, spent one academic year (1978/79) as ''Hochschulassistent'' to Jensen in

Freiburg Freiburg im Breisgau or simply Freiburg is the List of cities in Baden-Württemberg by population, fourth-largest city of the German state of Baden-Württemberg after Stuttgart, Mannheim and Karlsruhe. Its built-up area has a population of abou ...

and another year (1989/90) at the MSRI in

Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California *George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer to ...

. After leaving Peterhouse in 1990, Mathias had visiting positions in

Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...

, at the

Mathematisches Forschungsinstitut Oberwolfach The Oberwolfach Research Institute for Mathematics () is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and ...

, at the CRM in

Barcelona Barcelona ( ; ; ) is a city on the northeastern coast of Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second-most populous municipality of Spain. With a population of 1.6 million within c ...

, and in

Bogotá Bogotá (, also , , ), officially Bogotá, Distrito Capital, abbreviated Bogotá, D.C., and formerly known as Santa Fe de Bogotá (; ) during the Spanish Imperial period and between 1991 and 2000, is the capital city, capital and largest city ...

, before becoming Professor at the Université de la Réunion. He retired from his professorship in 2012 and was admitted to the higher degree of

Doctor of Science A Doctor of Science (; most commonly abbreviated DSc or ScD) is a science doctorate awarded in a number of countries throughout the world. Africa Algeria and Morocco In Algeria, Morocco, Libya and Tunisia, all universities accredited by the s ...

at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

in 2015.

Work

Mathias became mathematically active soon after the introduction of forcing by

Paul Cohen Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician, best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was awarded a F ...

, and Kanamori credits his survey of forcing that was eventually published as ''Surrealist landscape with figures'' as being a "vital source" on forcing in its early days. His paper ''Happy families'', extending his 1968 Cambridge thesis, proves important properties of the forcing now known as Mathias forcing. In the same paper he shows that no (infinite) maximal almost disjoint family can be

analytic Analytic or analytical may refer to: Chemistry * Analytical chemistry, the analysis of material samples to learn their chemical composition and structure * Analytical technique, a method that is used to determine the concentration of a chemical ...

. Mathias also used forcing to separate two weak forms of the

Axiom of choice In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of non-empty sets, it is possible to construct a new set by choosing one element from e ...

, showing that the ''ordering principle'', which states that any set can be

linearly ordered In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation \leq on some set X, which satisfies the following for all a, b and c in X: # a \leq a ( re ...

, does not imply the

Boolean Prime Ideal Theorem In mathematics, the Boolean prime ideal theorem states that Ideal (order theory), ideals in a Boolean algebra (structure), Boolean algebra can be extended to Ideal (order theory)#Prime ideals , prime ideals. A variation of this statement for Filte ...

. His more recent work on forcing includes the study of the theory PROVI of ''provident sets'', a minimalist axiom system that still allows the forcing construction to proceed. Mathias is also known for his writings around sociological aspects of logic. These include ''The ignorance of Bourbaki'' and ''Hilbert, Bourbaki and the scorning of logic'', in which Mathias criticises Bourbaki's approach to logic; in ''A Term of Length 4,523,659,424,929'' he shows that the number in the title is the number of symbols required for Bourbaki's definition of the number 1. Mathias has also considered claims that standard ZFC is stronger than necessary for "mainstream" mathematics; his paper ''What is Mac Lane missing?'' on this topic appeared alongside

Saunders Mac Lane Saunders Mac Lane (August 4, 1909 – April 14, 2005), born Leslie Saunders MacLane, was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near w ...

's response ''Is Mathias an ontologist?''. Mathias also conducted a detailed study of the strength of a weakened system suggested by Mac Lane.

References

External links

Home page

Adrian Richard David Mathias
at the

Mathematics Genealogy Project The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. it contained information on 300,152 mathematical scientists who contributed to research-level mathematics. For a typical mathematicia ...

{{DEFAULTSORT:Mathias, Adrian 20th-century English mathematicians 21st-century English mathematicians 1944 births Living people Mathematical logicians Set theorists Fellows of Peterhouse, Cambridge Alumni of Trinity College, Cambridge Cambridge mathematicians