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

forcing Forcing may refer to: Mathematics and science * Forcing (mathematics), a technique for obtaining independence proofs for set theory *Forcing (recursion theory), a modification of Paul Cohen's original set theoretic technique of forcing to deal with ...

notion

Mathias forcing In mathematics, forcing is a method of constructing new models ''M'' 'G''of set theory by adding a generic subset ''G'' of a poset ''P'' to a model ''M''. The poset ''P'' used will determine what statements hold in the new universe (the 'extension ...

is named for him.

Career

Mathias was educated at

Shrewsbury Shrewsbury ( , also ) is a market town, civil parish, and the county town of Shropshire, England, on the River Severn, north-west of London; at the 2021 census, it had a population of 76,782. The town's name can be pronounced as either 'Sh ...

and Trinity College, Cambridge, where he read mathematics and graduated in 1965. After graduation, he moved to Bonn in Germany where he studied with Ronald Jensen, visiting UCLA,

Stanford Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considere ...

, the University of Wisconsin, and Monash University during that period. In 1969, he returned to Cambridge as a research fellow at Peterhouse 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 a ...

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

. After leaving Peterhouse in 1990, Mathias had visiting positions in Warsaw, at the

Mathematisches Forschungsinstitut Oberwolfach The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekl ...

, at the CRM in Barcelona, and in

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

, before becoming Professor at the

Université de la Réunion The University of Reunion Island (''Université de la Réunion'') is a French university in the Academy of Réunion. It is the first and only European university in the Indian Ocean. Established in 1982, it has grown steadily over the years in t ...

. He retired from his professorship in 2012 and was admitted to the higher degree of Doctor of Science at the University of Cambridge in 2015.

Work

Mathias became mathematically active soon after the introduction of

by Paul Cohen, 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

. In the same paper he shows that no (infinite) maximal almost disjoint family can be analytic. Mathias also used forcing to separate two weak forms of the Axiom of choice, showing that the ''ordering principle'', which states that any set can be linearly ordered, does not imply the Boolean Prime Ideal Theorem. 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'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 {{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