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'''Adrian Richard David Mathias''' (born 12 February 1944) is a British mathematician working in [[set theory]].
'''Adrian Richard David Mathias''' (born 12 February 1944) is a British mathematician working in [[set theory]].
The [[forcing_(mathematics)|forcing]] notion [[List_of_forcing_notions#Mathias_forcing|Mathias forcing]] is named for him.
The [[forcing (mathematics)|forcing]] notion [[List of forcing notions#Mathias forcing|Mathias forcing]] is named for him.


==Career==
==Career==
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studied with [[Ronald Jensen]], visiting [[UCLA]], [[Stanford University|Stanford]], the [[University of Wisconsin]], and [[Monash University]] during that period.
studied with [[Ronald Jensen]], visiting [[UCLA]], [[Stanford University|Stanford]], 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]] from 1972 to 1974, spent one academic year (1978/79) as ''Hochschulassistent'' to Jensen in [[University of Freiburg|Freiburg]] and another year (1989/90) at the [[Mathematical Sciences Research Institute|MSRI]] in [[Berkeley, California|Berkeley]]. After leaving Peterhouse in 1990, Mathias had visiting positions in [[University of Warsaw|Warsaw]], at the [[Mathematisches Forschungsinstitut Oberwolfach]], at the [[Centre de Recerca Matemàtica|CRM]] in [[Barcelona]], and in [[Universidad de los Andes (Colombia)|Bogotá]], 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]] at the [[University of Cambridge]] in 2015.<ref>{{cite journal |last1=Kanamori |first1=Akihiro|date=2016|title=Mathias and Set Theory|journal=Mathematical Logic Quarterly|volume=62:3|pages=278-294}}</ref>
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]] from 1972 to 1974, spent one academic year (1978/79) as ''Hochschulassistent'' to Jensen in [[University of Freiburg|Freiburg]] and another year (1989/90) at the [[Mathematical Sciences Research Institute|MSRI]] in [[Berkeley, California|Berkeley]]. After leaving Peterhouse in 1990, Mathias had visiting positions in [[University of Warsaw|Warsaw]], at the [[Mathematisches Forschungsinstitut Oberwolfach]], at the [[Centre de Recerca Matemàtica|CRM]] in [[Barcelona]], and in [[Universidad de los Andes (Colombia)|Bogotá]], 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]] at the [[University of Cambridge]] in 2015.<ref>{{cite journal |last1=Kanamori |first1=Akihiro|date=2016|title=Mathias and Set Theory|journal=Mathematical Logic Quarterly|volume=62:3|pages=278–294}}</ref>


==Work==
==Work==
Mathias became mathematically active soon after the introduction of [[forcing_(mathematics)|forcing]] by [[Paul Cohen]], and Kanamori<ref>{{cite book |last=Kanamori |first=Akihiro |date=2003 |title=The Higher Infinite|title-link= The Higher Infinite |location=Berlin|publisher=Springer |page=117 |isbn=3-540-00384-3}}</ref> credits his survey of forcing that was eventually published as ''Surrealist landscape with figures''<ref>{{cite journal |last1=Mathias |first1=Adrian|title=Surrealist landscape with figures|journal=Periodica Hungarica|volume=10|pages=109-175}}</ref> as being a "vital source" on forcing in its early days.
Mathias became mathematically active soon after the introduction of [[forcing (mathematics)|forcing]] by [[Paul Cohen]], and Kanamori<ref>{{cite book |last=Kanamori |first=Akihiro |date=2003 |title=The Higher Infinite|title-link= The Higher Infinite |location=Berlin|publisher=Springer |page=117 |isbn=3-540-00384-3}}</ref> credits his survey of forcing that was eventually published as ''Surrealist landscape with figures''<ref>{{cite journal |last1=Mathias |first1=Adrian|title=Surrealist landscape with figures|journal=Periodica Hungarica|volume=10|pages=109–175}}</ref> as being a "vital source" on forcing in its early days.


His paper ''Happy families'',<ref>{{cite journal |last1=Mathias |first1=Adrian|date=1977|title=Happy Families|journal=Annals of Mathematical Logic |volume=12|pages=59-111}}</ref> extending his 1968 Cambridge thesis, proves important properties of the forcing now known as [[List_of_forcing_notions#Mathias_forcing|Mathias forcing]]. In the same paper he shows that no (infinite) [[Almost disjoint sets|maximal almost disjoint family]] can be [[Analytic set|analytic]].
His paper ''Happy families'',<ref>{{cite journal |last1=Mathias |first1=Adrian|date=1977|title=Happy Families|journal=Annals of Mathematical Logic |volume=12|pages=59–111}}</ref> extending his 1968 Cambridge thesis, proves important properties of the forcing now known as [[List of forcing notions#Mathias forcing|Mathias forcing]]. In the same paper he shows that no (infinite) [[Almost disjoint sets|maximal almost disjoint family]] can be [[Analytic set|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 [[Total order|linearly ordered]], does not imply the [[Boolean prime ideal theorem|Boolean Prime Ideal Theorem]].<ref>{{cite book |last=Jech |first=Thomas |date=2008 |title=The Axiom of Choice |location=Mineola, New York|publisher=Dover |page=117 |isbn=978-0-486-46624-8}}</ref>
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 [[Total order|linearly ordered]], does not imply the [[Boolean prime ideal theorem|Boolean Prime Ideal Theorem]].<ref>{{cite book |last=Jech |first=Thomas |date=2008 |title=The Axiom of Choice |location=Mineola, New York|publisher=Dover |page=117 |isbn=978-0-486-46624-8}}</ref>


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
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.<ref>{{cite journal |last1=Mathias |first1=Adrian|date=2015|title=Provident sets and rudimentary set forcing|journal=Fundamenta Mathematicae|volume=230|pages=99-148}}</ref>
construction to proceed.<ref>{{cite journal |last1=Mathias |first1=Adrian|date=2015|title=Provident sets and rudimentary set forcing|journal=Fundamenta Mathematicae|volume=230|pages=99–148}}</ref>


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 [[Nicolas Bourbaki|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 [[Zermelo–Fraenkel set theory|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.<ref>{{cite journal |last1=Mathias |first1=Adrian|date=2001|title=The Strength of Mac Lane Set Theory|journal=Annals of Pure and Applied Logic |volume=110|pages=107-234}}</ref>
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 [[Nicolas Bourbaki|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 [[Zermelo–Fraenkel set theory|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.<ref>{{cite journal |last1=Mathias |first1=Adrian|date=2001|title=The Strength of Mac Lane Set Theory|journal=Annals of Pure and Applied Logic |volume=110|pages=107–234}}</ref>


==References==
==References==
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{{Authority control}}
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{{DEFAULTSORT:Mathias, Adrian}}
{{DEFAULTSORT:Mathias, Adrian}}
[[Category:20th-century English mathematicians]]
[[Category:20th-century English mathematicians]]
[[Category:21st-century English mathematicians]]
[[Category:21st-century English mathematicians]]
[[Category:1944 births]]
[[Category:1944 births]]
[[Category:Living people]]
[[Category:Living people]]

Latest revision as of 18:34, 21 January 2024

Adrian Mathias
Mathias in London, February 2020
Born (1944-02-12) 12 February 1944 (age 80)
NationalityBritish
Alma materTrinity College, Cambridge
Scientific career
FieldsMathematics
InstitutionsUniversity of Cambridge
Université de la Réunion
Doctoral advisorRonald Jensen
John Horton Conway
Doctoral studentsAkihiro Kanamori, Thomas Forster

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

Career

[edit]

Mathias was educated at Shrewsbury 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, 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 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. After leaving Peterhouse in 1990, Mathias had visiting positions in Warsaw, at the Mathematisches Forschungsinstitut Oberwolfach, at the CRM in Barcelona, and in Bogotá, 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 at the University of Cambridge in 2015.[1]

Work

[edit]

Mathias became mathematically active soon after the introduction of forcing by Paul Cohen, and Kanamori[2] credits his survey of forcing that was eventually published as Surrealist landscape with figures[3] as being a "vital source" on forcing in its early days.

His paper Happy families,[4] 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.

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.[5]

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.[6]

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.[7]

References

[edit]
  1. ^ Kanamori, Akihiro (2016). "Mathias and Set Theory". Mathematical Logic Quarterly. 62:3: 278–294.
  2. ^ Kanamori, Akihiro (2003). The Higher Infinite. Berlin: Springer. p. 117. ISBN 3-540-00384-3.
  3. ^ Mathias, Adrian. "Surrealist landscape with figures". Periodica Hungarica. 10: 109–175.
  4. ^ Mathias, Adrian (1977). "Happy Families". Annals of Mathematical Logic. 12: 59–111.
  5. ^ Jech, Thomas (2008). The Axiom of Choice. Mineola, New York: Dover. p. 117. ISBN 978-0-486-46624-8.
  6. ^ Mathias, Adrian (2015). "Provident sets and rudimentary set forcing". Fundamenta Mathematicae. 230: 99–148.
  7. ^ Mathias, Adrian (2001). "The Strength of Mac Lane Set Theory". Annals of Pure and Applied Logic. 110: 107–234.
[edit]
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