{{short description|American mathematician}} {{Infobox scientist | image = Robert Griess.jpg <!-- only free-content images are allowed for depicting living people – see WP:NONFREE --> | image_size = 200px | name = Robert Griess | birth_date = {{Birth date and age|1945|10|10|mf=y}} | birth_place = Savannah, Georgia | field = Mathematics | work_institution = University of Michigan | alma_mater = University of Chicago (B.S., 1967; M.S., 1968; Ph.D., 1971) | doctoral_advisor = John Griggs Thompson | doctoral_students = | thesis_title = Schur Multipliers of the Known Finite Simple Groups |thesis_year = 1971 | thesis_url = https://www.proquest.com/docview/302625511 | website = {{URL|http://www.math.lsa.umich.edu/~rlg/}} | awards = Leroy P. Steele Prize (2010) | known_for = Classification of sporadic groups (Happy Family and pariahs)<br /> Construction of the Fischer–Griess Monster group<br />Gilman–Griess theorem<br />Griess algebra }}
'''Robert Louis Griess Jr.''' (born 1945) is a mathematician working on finite simple groups and vertex algebras.<ref>{{Cite book |last=Griess |first=Robert L. Jr. |chapter=Research topics in finite groups and vertex algebras |title=Vertex Operator Algebras, Number Theory and Related Topics |series=Contemporary Mathematics |publisher=American Mathematical Society |location=Providence, Rhode Island |year=2020 |volume=753 |pages=119–126 |doi=10.1090/CONM/753/15167 |arxiv= 1903.08805 |isbn=978-1-4704-4938-4 |zbl=1490.17034 |s2cid=126782539 }}</ref> He is currently the John Griggs Thompson Distinguished University Professor of mathematics at University of Michigan.<ref>{{Cite web |url=https://lsa.umich.edu/math/news-events/all-news/search-news/griess-named-distinguished-university-professor.html |title=Griess Named Distinguished University Professor |website=University of Michigan College of Literature, Science, and the Arts |publisher=University of Michigan |date=May 20, 2016 |access-date=2023-01-02 }}</ref>
== Education == Griess developed a keen interest in mathematics prior to entering undergraduate studies at the University of Chicago in the fall of 1963.<ref>{{Cite interview |subject-last=Griess |subject-first=Robert L. Jr. |interviewer=Shun-Jen Cheng and company |title=Interview with Prof. Robert Griess |work=Interviews in English |date=2010-08-18 |publisher=Institute of Mathematics, Academia Sinica |location=New Taipei |url=https://web.math.sinica.edu.tw/mathmedia/interviewE.jsp?mID=35402 |access-date=2023-01-07 }}</ref> There, he eventually earned a Ph.D. in 1971 after defending a dissertation on the Schur multipliers of the then-known finite simple groups.<ref>{{Cite journal |last=Griess |first= Robert L. |url=https://www.ams.org/journals/bull/1972-78-01/S0002-9904-1972-12855-6/S0002-9904-1972-12855-6.pdf |title=Schur Multipliers of the Known Finite Simple Groups |journal=Bulletin of the American Mathematical Society |volume=78 |number=1 |year=1972 |pages= 68–71 |doi=10.1090/S0002-9904-1972-12855-6 |doi-access=free |jstor=1996474 |mr=2611672 |zbl=0263.20008 }}</ref>
== Career == Griess' work has focused on group extensions, cohomology and Schur multipliers, as well as on vertex operator algebras and the classification of finite simple groups, with emphasis on constructions of the monster group.<ref>{{Cite journal |url=https://web.math.sinica.edu.tw/bulletin_ns/20184/2018401.pdf |title=A Survey: Bob Griess' work on Simple Groups and their Classification |last=Smith |first=Stephen D. |journal=Bulletin of the Institute of Mathematics |publisher=Academia Sinica (New Series)|volume=13 |number=4 |year=2018 |pages=365–382 |doi=10.21915/BIMAS.2018401 |doi-access=free |zbl=1482.20010 }}</ref><ref>{{Cite journal |last=Griess |first=Robert L. Jr. |url=https://www.intlpress.com/site/pub/pages/journals/items/iccm/content/vols/0009/0001/a002/index.php?mode=ns|title=My life and times with the sporadic simple groups |journal=Notices of the International Consortium of Chinese Mathematicians |volume=9 |number=1 |year=2021 |pages=11–46 |archive-url=https://web.archive.org/web/20230122215947/https://www.intlpress.com/site/pub/files/_fulltext/journals/iccm/2021/0009/0001/ICCM-2021-0009-0001-a002.pdf |archive-date=2023-01-22 |url-status=live |doi=10.4310/ICCM.2021.v9.n1.a2 |zbl=1537.20002 |issn=2326-4810 |url-access=subscription }}</ref>
=== Friendly Giant === In 1982, Robert Griess published the first construction of the largest sporadic group, the monster group <math>\mathbb M</math> (or <math>F_1</math>).<ref name="FG" /> He first successfully constructed this group while at the Institute for Advanced Study (1979–80, 1981, and later in 1994), through rotations of an object in 196,883-dimensional space.<ref name="Roberts">{{Cite web |author=Siobhan Roberts |author-link=Siobhan Roberts |title=Curiosities: Pursuing the Monster |url=https://www.ias.edu/ideas/2013/roberts-monster |website=IAS (Ideas) |publisher=Institute for Advanced Study |date=2013 }}</ref>
Originally, Griess called the monster group the '''"Friendly Giant"''';<ref name="FG" /> however, a paper published in 1979 by John Horton Conway and Simon P. Norton in the ''Bulletin of the London Mathematical Society'' titled "Monstrous Moonshine" formally coins the term.<ref>{{Cite journal |last=Conway |first=John H. |author-link=John H. Conway |author2-first=Simon P. |author2-last=Norton |author2-link=Simon P. Norton |title=Monstrous Moonshine |journal=Bulletin of the London Mathematical Society |url=https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/blms/11.3.308 |url-access=subscription |publisher=London Mathematical Society |volume=11 |issue=3 |year=1979 |pages=308-339 }} Quote: ''We proposed to call this group the MONSTER and conjectured that it had a representation of degree 196883''... (p. 308).</ref> Bernd Fischer and Griess independently predicted the existence of the monster group earlier in the decade, by 1973.<ref name="Roberts" />
Conway, speaking about the monster group on one occasion (in 2011), expressed Griess' dissatisfaction with his choice in naming the Fischer-Griess 196,883-dimensional group, as the "Monster group":<ref>{{Cite AV media |people=Alex Ryba, with John H. Conway (interviewee) (May 12, 2011). Siobhan Roberts, ed. |type=Video interview |language=en |publisher=Simons Foundation |location=New York City |title=19. The Monster |series=John Conway (1937 - 2020) (''ScienceLives'') |url=https://www.simonsfoundation.org/2014/04/04/john-conway/ |time=05:07 − 05:58 |access-date=2025-11-20 }} YouTube:[https://www.youtube.com/watch?v=lbN8EMcOH5o ...McOH5o]</ref>
:By the way, Griess criticized me very strongly for using the term ''monster'' for it, ... I wrote a postcard to Fischer, who is the first discoverer of the Monster, saying something like, "I've been thinking a lot about your monster group"... he liked that name, and ever since then, it's been called ''the Monster'' <nowiki>[</nowiki>...<nowiki>]</nowiki> Griess made the point — and I... I agree with him in a way — that to call it a monster suggests it's sort of ugly, or frightening, or something; and I wasn't thinking of that at all, I was just thinking of it as being ''tremendously big''. You know, maybe a 'bit <nowiki>[</nowiki>''sic''<nowiki>]</nowiki> frightening in a way, but not ugly, really a beautiful thing...
In the same landmark 1982 paper where he published his construction, Griess detailed an organization of the twenty-six sporadic groups into two general families of groups (the Happy Family and the pariahs).<ref name="FG">{{Cite journal |last = Griess |first = Robert L. Jr. |title = The Friendly Giant |url=https://www.digizeitschriften.de/dms/img/?PPN=PPN356556735_0069&DMDID=dmdlog7 |journal = Inventiones Mathematicae |volume=69 |year=1982 |page = 91 |doi=10.1007/BF01389186 |bibcode = 1982InMat..69....1G |hdl = 2027.42/46608 |hdl-access = free |mr= 671653 }}</ref>
=== Recognition === In 1983 Griess was an invited speaker at the International Congress of Mathematicians in Warsaw to give a lecture on the sporadic groups and his construction of the monster group, as the largest of these geometric groups.<ref>{{Cite web |url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1983.1/ICM1983.1.ocr.pdf |title=Proceedings of the International Congress of Mathematicians, August 16-24, 1983, Warszawa |website=International Mathematical Union |publisher=IMU |pages=369–384 |access-date=2023-01-02 }} Lecture on "The sporadic simple groups and construction of the monster."</ref> In 2010, he was awarded the AMS Leroy P. Steele Prize for Seminal Contribution to Research for his construction of the monster group.<ref>{{Cite journal |url=https://www.ams.org/notices/201004/rtx100400510p.pdf |title=2010 Steele Prizes |journal=Notices of the American Mathematical Society |date=April 2010 |volume=57 |number=4 |pages=511–513 |issn= 0002-9920 }} :"To Robert L. Griess Jr. for his construction of the 'Monster' sporadic finite simple group, which he first announced in 'A construction of F1 as automorphisms of a 196,883-dimensional algebra' (Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 2, part 1, 686-691) with details published in 'The friendly giant' (Invent. Math. 69 (1982), no. 1, 1-102)."</ref><ref name="FG" />
He became a member of the American Academy of Arts and Sciences in 2007, and a fellow of the American Mathematical Society in 2012.<ref>{{Cite web |url=https://www.amacad.org/person/robert-l-griess |title=Robert L. Griess (Member) |website=American Academy of Arts & Sciences |access-date=2023-01-02 }}</ref><ref>{{Cite web |title=List of Fellows of the American Mathematical Society |url=https://www.ams.org/profession/fellows-list |website=American Mathematical Society |access-date=2013-01-19 }}</ref> In 2020 he became a member of the National Academy of Sciences.<ref>{{Cite web |url=https://www.nasonline.org/news-and-multimedia/news/2020-nas-election.html |title=National Academy of Sciences Elects New Members |website=National Academy of Sciences |date=April 27, 2020 |access-date=2023-01-02 }}</ref> Since 2006, Robert Griess has been an editor for Electronic Research Announcements of the AIMS (ERA-AIMS), a peer-review journal.<ref>{{Cite web |url=http://eramath.s3-website-us-east-1.amazonaws.com/EditorialBoard.html |title=Editorial Board |website=Electronic Research Announcements |publisher= American Institute of Mathematical Sciences |issn=1935-9179 |access-date=2023-01-07 }}</ref>
== Selected publications == {{Scholia}} === Books === *{{cite book |last= Griess |first= Robert L. Jr. |title= Twelve Sporadic Groups |publisher= Springer-Verlag |location= Berlin |year= 1998 |isbn= 978-3-540-62778-4 |mr= 1707296 |oclc= 38910263 |zbl= 0908.20007}}<ref>{{Cite journal |last=Conder |first=Marston |url=https://nzmathsoc.org.nz/downloads/newsletters/NZMSnews89_Dec2003.pdf?1262333312 |title=Review: ''Twelve Sporadic Groups'', by Robert L. Griess, Jr.. |journal=Newsletter of the New Zealand Mathematical Society |volume=89 |date=December 2003 |pages=44–45 |issn=0110-0025 }}</ref> *{{cite book |last= Griess |first= Robert L. Jr. |title= An Introduction to Groups and Lattices: Finite Groups and Positive Definite Rational Lattices |series= Advanced Lectures in Mathematics |volume= 15 |publisher= International Press |location= Somerville, MA |year= 2011 |isbn= 978-1-57146-206-0 |oclc= 702615699 |mr= 2791918 |zbl= 1248.11048 }}
=== Journal articles === *{{Cite journal |last= Griess |first= Robert L. Jr. |url= https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46608/222_2005_Article_BF01389186.pdf?sequence=1 |title= The Friendly Giant |journal= Inventiones Mathematicae |volume= 69 |date= 1982 |pages= 1–102 |doi= 10.1007/BF01389186 |bibcode= 1982InMat..69....1G |hdl= 2027.42/46608 |mr= 671653 |zbl= 0498.20013 }}
* {{Cite journal |last2=Griess |first2=Robert L. Jr. |last1=Gilman |first1=Robert H. |url=https://deepblue.lib.umich.edu/bitstream/2027.42/25314/1/0000759.pdf |title=Finite groups with standard components of Lie type over fields of characteristic two |journal=Journal of Algebra |volume=80 |issue=2 |year=1983 |pages=383–516 |doi=10.1016/0021-8693(83)90007-8 |hdl=2027.42/25314 |hdl-access=free |mr=691810 |zbl= 0508.20010 }}
*{{Cite journal |last1= Griess |first1= Robert L. Jr. |last2= Ryba |first2= A. J. E. |url= https://www.ams.org/journals/bull/1999-36-01/S0273-0979-99-00771-5/S0273-0979-99-00771-5.pdf |title= Finite Simple Groups which Projectively Embed in an Exceptional Lie group are Classified! |journal= Bulletin of the American Mathematical Society |volume= 36 |issue= 1 |date= 1999 |pages= 75–93 |doi= 10.1090/S0273-0979-99-00771-5 |mr=165317 |zbl= 0916.22008 }}
*{{Cite journal |last1= Griess |first1= Robert L. Jr. |url= http://www.math.lsa.umich.edu/~rlg/researchandpublications/pdffiles1/uniqe8.pdf |title= Positive definite lattices of rank at most 8 |journal= Journal of Number Theory |volume= 103 |issue= 1 |date= 2003 |pages= 77–84 |doi= 10.1016/S0022-314X(03)00107-0 |doi-access= free |mr=2008067 |zbl= 1044.11014 }}
*{{Cite journal |last1= Griess |first1= Robert L. Jr. |last2= Lam |first2= Ching Hung |url= http://www.math.lsa.umich.edu/~rlg/researchandpublications/pdffiles/moonshinepath13oct09.pdf |title= A moonshine path from E8 to the Monster |journal= Journal of Pure and Applied Algebra |volume= 215 |issue= 5 |year= 2011 |pages= 927–948 |doi= 10.1016/j.jpaa.2010.07.001 |doi-access= free |mr= 2747229 |zbl= 1213.17028 }}
*{{Cite book |last= Griess |first= Robert L. Jr. |url= http://www.ams.org/books/pspum/086/ |url-access= subscription |title= Recent developments in Lie algebras, groups and representation theory |chapter= Moonshine paths and a VOA existence proof of the Monster |series= Proc. Sympos. Pure Math. |publisher= Amer. Math. Soc. |location= Providence, RI |year= 2012 |volume= 86 |pages= 165–172 |doi= 10.1090/pspum/086 |isbn= 978-0-8218-6917-8 |mr= 2977002 |zbl= 1320.20018 }}
*{{Cite journal |last2= Griess |first2= Robert L. Jr. |last1= Dong |first1= Chongying |title= Integral forms in vertex operator algebras which are invariant under finite groups |url=https://www.sciencedirect.com/science/article/pii/S0021869312002517 |journal= Journal of Algebra |volume= 365 |issue= 3 |year= 2012 |pages= 184–198 |mr= 2928458 |zbl= 0613.17012 |arxiv= 1201.3411 }}
== References == {{Reflist}}
== External links == *{{MathGenealogy|id=6646}} *{{YouTube|id=Zynb7VKRr-U|title=Robert Griess: My life and times with the sporadic simple groups}} for the Mathematical Science Literature lecture series, Harvard University (2020)
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{{DEFAULTSORT:Griess, Robert L.}} Category:Living people Category:20th-century American mathematicians Category:21st-century American mathematicians Category:Group theorists Category:University of Michigan faculty Category:University of Chicago alumni Category:Fellows of the American Mathematical Society Category:1945 births