Editing Enrico Bombieri

{{Short description|Italian mathematician (born 1940)}}
{{redirect|Bombieri|the theorem|Bombieri–Vinogradov theorem}}
{{use dmy dates|date=March 2024}}
{{BLP sources|date=February 2013}}
{{Infobox scientist
|name              = Enrico Bombieri
|image             = Enrico Bombieri.jpg
|caption           = 
|image_size        = 
|birth_date        = {{birth date and age|1940|11|26|df=y}}
|birth_place       = [[Milan]], Italy
|death_date        = 
|death_place       = 
|field             = [[Mathematics]]
|work_institutions = [[Institute for Advanced Study]]
|alma_mater        = [[University of Milan]]<br>[[Trinity College, Cambridge]]
|doctoral_advisor  = [[Giovanni Ricci (mathematician)|Giovanni Ricci]]
|doctoral_students = [[Umberto Zannier]]
|known_for         = [[Determinant method]]<br />[[Large sieve method]] in [[analytic number theory]] <br /> [[Glossary of arithmetic and Diophantine geometry#B|Bombieri-Lang conjecture]]<br /> [[Bombieri norm]] <br /> [[Bombieri–Vinogradov theorem]] <br /> "[[Glossary of arithmetic and Diophantine geometry#H|Heights]]" in [[Diophantine geometry]] <br /> [[Siegel's lemma]] for bases (Bombieri–Vaaler)  <br /> [[Partial differential equations]]  
|author_abbrev_bot = 
|author_abbrev_zoo = 
|influences        = 
|influenced        = 
|prizes            =1966, [[Caccioppoli Prize]]<ref>{{cite web| url = http://umi.dm.unibo.it/caccioppoli/index-en.html| title = Site of Caccioppoli Prize| access-date = 2011-12-31| archive-date = 2019-05-14| archive-url = https://web.archive.org/web/20190514091912/http://umi.dm.unibo.it/caccioppoli/index-en.html| url-status = dead}}</ref> <br /> 1974, [[Fields Medal]] <br /> 1976, [[Feltrinelli Prize]] <br /> 1980, [[Balzan Prize]] <br /> 2006, Pythagoras Prize<ref>[http://www.math.it/eventi/premiopitagora_06.htm Premio Pitagora 2006] {{in lang|it}}</ref> <br /> 2008, [[Joseph L. Doob Prize]]<ref>{{cite web| url = https://www.ams.org/profession/prizes-awards/ams-prizes/doob-prize| title = Joseph L. Doob Prize}}</ref><ref>{{cite journal|title=2008 Doob Prize|journal=Notices of the AMS|date=April 2008|volume=55|issue=4|pages=503–504|url=https://www.ams.org/notices/200804/tx080400503p.pdf}}</ref> <br /> 2010, [[King Faisal International Prize]]<br /> 2020, [[Crafoord Prize]]
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}}
'''Enrico Bombieri''' (born 26 November 1940) is an Italian [[mathematician]], known for his work in [[analytic number theory]], [[Diophantine geometry]], [[complex analysis]], and [[group theory]].<ref name=mathunion>{{cite web |url = https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/1974/index.html#0x82496a1f_0x0005ea1e |title = Fields medals 1974|website = International Mathematical Union (IMU)|language=en|access-date=2024-09-08}}</ref> Bombieri is currently professor emeritus in the School of Mathematics at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]].<ref>{{Cite web|url=https://www.ias.edu/scholars/bombieri|title=Enrico Bombieri|website=Institute for Advanced Study|language=en|access-date=2019-08-07}}</ref> Bombieri won the [[Fields Medal]] in 1974<ref name=mathunion/> for his work on the [[large sieve]] and its application to the distribution of [[prime number]]s.<ref name=ias>{{cite web
| url = https://www.ias.edu/scholars/bombieri#:~:text=Enrico%20Bombieri%2C%20a%20Fields%20Medalist%20for%20his%20work,and%20the%20partial%20differential%20equations%20of%20minimal%20surfaces.
| title = Enrico Bombieri PROFESSOR EMERITUS School of Mathematics Number Theory
| work =www.ias.edu ([[Institute for Advanced Study]])
| date = 9 December 2019
|archive-url=
|archive-date=
| access-date = 2 July 2021}}</ref>

==Career==
Bombieri published his first mathematical paper in 1957, when he was 16 years old. In 1963, at age 22, he earned his first degree (Laurea) in mathematics from the [[Università degli Studi di Milano]] under the supervision of Giovanni Ricci<ref name="MathematicalLives">{{cite book | last1=Bartocci | first1=Claudio | last2=Betti | first2=Renato | last3=Guerraggio | first3=Angelo | last4=Lucchetti | first4=Roberto | title=Mathematical Lives | publisher=Springer | date=2014-09-28 | isbn=978-3-642-44755-6 | pages=213–215}}</ref> and then studied at [[Trinity College, Cambridge]], with [[Harold Davenport]].<ref name=":0">{{Cite web |title=Professor Enrico Bombieri – King Faisal Prize |url=https://kingfaisalprize.org/professor-enrico-bombieri/ |access-date=2024-10-30 |language=en-US}}</ref>

Bombieri was an assistant professor (1963–1965) and then a full professor (1965–1966) at the [[University of Cagliari|Università di Cagliari]], at the [[Università di Pisa]] in 1966–1974, and then at the [[Scuola Normale Superiore di Pisa]] in 1974–1977. From Pisa, he emigrated in 1977 to the United States, where he became a professor at the School of Mathematics at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]]. In 2011, he became professor emeritus.<ref name=":0" />

Bombieri is also known for his ''[[pro bono]]'' service on behalf of the [[mathematics]] [[profession]], e.g. for serving on external review boards and for [[peer review|peer-reviewing]] extraordinarily complicated manuscripts (like the paper of [[Per Enflo]] on the [[invariant subspace problem]]).<ref name="Enflo 1987 pp. 213–313">{{cite journal | last=Enflo | first=Per | title=On the invariant subspace problem for Banach spaces | journal=Acta Mathematica | volume=158 | date=1987 | issn=0001-5962 | doi=10.1007/BF02392260 | pages=213–313}}</ref>

==Research==
The [[Bombieri–Vinogradov theorem]] is one of the major applications of the [[large sieve method]]. It improves [[Dirichlet's theorem on arithmetic progressions|Dirichlet's theorem]] on prime numbers in [[arithmetic progression]]s, by showing that by averaging over the modulus over a range, the mean error is much less than can be proved in a given case. This result can sometimes substitute for the still-unproved [[generalized Riemann hypothesis]].

In 1969, Bombieri, [[Ennio De Giorgi|De Giorgi]], and [[Enrico Giusti|Giusti]] solved [[Bernstein's problem]] on minimal surfaces in dimensions above eight.<ref>{{Citation | last1=Bombieri | first1=Enrico | last2=De Giorgi | first2=Ennio | last3=Giusti | first3=Enrico | title=Minimal cones and the Bernstein problem | doi=10.1007/BF01404309 | mr=0250205 | year=1969 | journal=[[Inventiones Mathematicae]] | issn=0020-9910 | volume=7 | issue=3 | pages=243–268| bibcode=1969InMat...7..243B | s2cid=59816096 }}</ref>

In 1976, Bombieri developed the technique known as the "asymptotic sieve".<ref name="asymp-sieve">E. Bombieri, "The asymptotic sieve", ''[[:it:Accademia Nazionale delle Scienze|Mem. Acad. Naz. dei XL]]'', 1/2 (1976) 243–269.</ref> In 1980, he supplied the completion of the proof of the uniqueness of [[Ree group|finite groups of Ree type]] in [[characteristic (algebra)|characteristic]] 3; at the time of its publication, it was one of the missing steps in the [[classification of finite simple groups]].<ref>{{cite journal|author=Bombieri, E.|title=Thompson's problem σ<sup>2</sup>=3. Appendices by A. Odlyzko and D. Hunt|journal=Invent. Math.|volume=58|issue=1|year=1980|pages=77–100|doi=10.1007/bf01402275|s2cid = 122867511}} (This paper completed a line of research initiated by the [[Walter theorem]].)</ref>

==Awards==
Bombieri's research in [[number theory]], [[algebraic geometry]], and [[mathematical analysis]] has earned him many international prizes — a [[Fields Medal]] in 1974 and the [[Balzan Prize]] in 1980. He was a [[List of International Congresses of Mathematicians Plenary and Invited Speakers|plenary speaker at the International Congress of Mathematicians]], which took place in 1974 in [[Vancouver]]. He is a member, or foreign member, of several learned academies, including the [[Accademia Nazionale dei Lincei]] (elected 1976), the [[French Academy of Sciences]] (elected 1984), the [[Academia Europaea]] (elected 1995),<ref>{{cite web|title=Enrico Bombieri|url=https://www.ae-info.org/ae/Member/Bombieri_Enrico|work=Member|publisher=Academia Europaea|access-date=2024-11-17}}</ref> and the [[United States National Academy of Sciences]] (elected 1996).<ref>[http://www.lincei.it/modules.php?name=Soci&file=scheda&func=Soci_scheda&Id=438 Scheda socio] {{Webarchive|url=https://web.archive.org/web/20121114214244/http://www.lincei.it/modules.php?name=Soci&file=scheda&func=Soci_scheda&Id=438 |date=2012-11-14 }}, from the website of [[Accademia Nazionale dei Lincei|Accademia dei Lincei]] (elected 1976)</ref> In 2002 he was made ''Cavaliere di Gran Croce al Merito della Repubblica Italiana''.<ref>{{cite news|author=Torno Armando|title=BOMBIERI Il re dei numeri che ha conquistato il mondo|newspaper=Corriere della Sera|date=28 May 2002|page=35|url=http://archiviostorico.corriere.it/2002/maggio/28/BOMBIERI_dei_numeri_che_conquistato_co_0_0205285644.shtml|language=it}}</ref> In 2010, he received the [[King Faisal International Prize]] (jointly with [[Terence Tao]]).<ref>[http://www.kff.com/ King Faisal Foundation], – retrieved 2010-01-11.</ref><ref>{{cite journal|title=Bombieri and Tao Receive King Faisal Prize|journal=Notices of the AMS|date=May 2010|volume=57|issue=5|pages=642–643|url=https://www.ams.org/notices/201005/rtx100500642p.pdf}}</ref> and in 2020 he was awarded the [[Crafoord Prize]] in Mathematics.<ref>{{Cite web |date=2020-01-29 |title=The Crafoord Prizes in Mathematics and Astronomy 2020 |url=https://www.crafoordprize.se/news/the-crafoord-prizes-in-mathematics-and-astronomy-2020/ |access-date=2024-10-30 |website=Crafoord Prize |language=en-GB}}</ref>

==Other interests==
Bombieri, accomplished also in the arts, explored for wild orchids and other plants as a hobby in the Alps when a young man.<ref>[http://www.italyonthisday.com/2018/11/enrico-bombieri-mathematician.html Bombieri – Mathematician] retrieved 10 February 2020</ref>

{{blockquote|With his powder-blue shirt open at the neck, khaki pants and running shoes, he might pass for an Italian film director at Cannes. Married with a grown daughter, he is a gourmet cook and a serious painter: He carries his paints and brushes with him whenever he travels. Still, mathematics never seems far from his mind. In a recent painting, Bombieri, a one-time member of the [[Cambridge University]] chess team, depicts a giant chessboard by a lake. He's placed the pieces to reflect a critical point in the historic match in which [[IBM]]'s chess-playing computers, [[Deep Blue (chess computer)|Deep Blue]], beat [[Garry Kasparov]].<ref>{{cite news|author=Birch, Douglas|title=Lifelong pursuit of mathematical pursuit Professor: At 15, Enrico Bombieri picked up a book on number theory that introduced him to the fiendishly puzzling Riemann Hypothesis. He was hooked|newspaper=The Baltimore Sun|date=30 September 1998|url=http://articles.baltimoresun.com/1998-09-30/news/1998273107_1_riemann-hypothesis-mathematician-david-hilbert|access-date=2015-10-12|archive-date=2015-10-29|archive-url=https://web.archive.org/web/20151029042833/http://articles.baltimoresun.com/1998-09-30/news/1998273107_1_riemann-hypothesis-mathematician-david-hilbert|url-status=dead}}</ref>}}

==Selected publications==
===Sole===
* E. Bombieri, ''Le Grand Crible dans la Théorie Analytique des Nombres'' (Seconde Édition). Astérisque 18, Paris 1987.

===Joint===
*{{cite journal|last = Bombieri|first = E.|author2=Vaaler, J.|title = On Siegel's lemma|journal = Inventiones Mathematicae|volume = 73|issue = 1|date = Feb 1983|pages = 11–32|doi = 10.1007/BF01393823|bibcode = 1983InMat..73...11B|s2cid = 121274024}}
*{{cite journal|last = Bombieri|first = E.|author2=Mueller, J.|title = On effective measures of irrationality for <math>{\scriptscriptstyle\sqrt[r]{a/b}}</math> and related numbers|journal = Journal für die reine und angewandte Mathematik|volume = 342|year = 1983|pages = 173–196}}
* <!-- Bernard Beauzamy -->B. Beauzamy, E. Bombieri, [[Per Enflo|P. Enflo]] and [[Hugh Montgomery (mathematician)|H. L. Montgomery]]. "Product of polynomials in many variables", ''Journal of Number Theory'', pages 219–245, 1990.

==See also==
*[[Bombieri norm]]
*[[Bombieri–Vinogradov theorem]]
*[[Glossary of arithmetic and Diophantine geometry#B|Glossary of arithmetic and Diophantine geometry – Bombieri–Lang conjecture]]

==References==
{{Reflist}}

==Sources==
*{{cite journal|last = Bombieri|first = E.|author2=Mueller, J.|title = On effective measures of irrationality for <math>{\scriptscriptstyle\sqrt[r]{a/b}}</math> and related numbers|journal = Journal für die Reine und Angewandte Mathematik|volume = 342|year = 1983|pages = 173–196}}
*{{cite journal|last = Bombieri|first = E.|author2=Vaaler, J.|title = On Siegel's lemma|journal = Inventiones Mathematicae|volume = 73|issue = 1|date = Feb 1983|pages = 11–32|doi = 10.1007/BF01393823|bibcode = 1983InMat..73...11B|s2cid = 121274024}}
* E. Bombieri, ''Le Grand Crible dans la Théorie Analytique des Nombres'' (Seconde Édition). Astérisque 18, Paris 1987.
* <!-- Bernard Beauzamy -->B. Beauzamy, E. Bombieri, [[Per Enflo|P. Enflo]] and [[Hugh Montgomery (mathematician)|H. L. Montgomery]]. "Product of polynomials in many variables", ''Journal of Number Theory'', pages 219–245, 1990.
*{{cite book|
author=Enrico Bombieri and Walter Gubler
|title=Heights in Diophantine Geometry
|publisher=Cambridge U. P.
|year=2006}}
<!-- *{{cite book
|author=Knuth, Donald E
|author-link=Donald E. Knuth
|chapter=4.6.2 [[Polynomial factorization|Factorization of Polynomials]]
|title=Seminumerical Algorithms
|series=[[The Art of Computer Programming]]
|volume=2
|edition=Third
|location=Reading, Massachusetts
|publisher=Addison-Wesley
|year=1997
|pages=439—461, 678–691   xiv+762
|isbn=0-201-89684-2}} -->
*{{cite encyclopedia
| url = https://www.britannica.com/biography/Enrico-Bombieri
| title =Enrico Bombieri Italian mathematician 
| encyclopedia =www.britannica.com ([[Encyclopedia Britannica]])
|archive-url=
|archive-date=
| access-date = 2 July 2021}}

==External links==
{{Commons category-inline}}
{{Sister project links| wikt=no | commons=no | b=no | n=no | q=Enrico Bombieri | s=no | v=no | voy=no | species=no | d=no}}

*{{MathGenealogy |id=72210}}
*{{MacTutor Biography|id=Bombieri}}
*[http://www.ias.edu/people/faculty-and-emeriti/bombieri Enrico Bombieri, Institute for Advanced Study]
*[http://www.unipi.it/ateneo/comunica/cerimonie/honoris/pubblicazioni.htm Lista delle pubblicazioni di Enrico Bombieri, University of Pisa]

{{Fields medalists}}

{{Authority control}}

{{DEFAULTSORT:Bombieri, Enrico}}
[[Category:20th-century Italian mathematicians]]
[[Category:21st-century Italian mathematicians]]
[[Category:1940 births]]
[[Category:Fields Medalists]]
[[Category:Institute for Advanced Study faculty]]
[[Category:Living people]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Number theorists]]
[[Category:Partial differential equation theorists]]
[[Category:Scientists from Milan]]
[[Category:University of Milan alumni]]
[[Category:Alumni of Trinity College, Cambridge]]
[[Category:Members of the Royal Swedish Academy of Sciences]]
[[Category:Members of Academia Europaea]]