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{{short description|Canadian-American mathematician}}
{{short description|Canadian-American mathematician (born 1974)}}
{{Use dmy dates|date=August 2014}}
{{Use dmy dates|date=August 2014}}
{{Infobox scientist
{{Infobox scientist
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| caption = Manjul Bhargava in 2014
| caption = Manjul Bhargava in 2014
| image = File:Manjul_Bhargava_FieldsMedal.jpg
| image = File:Manjul_Bhargava_FieldsMedal.jpg
| birth_date = {{birth date and age|1974 or 1975|8|8|df=y}}
| birth_date = {{birth date and age|1974|8|8|df=y}}
| birth_place = [[Hamilton, Ontario]], Canada
| birth_place = [[Hamilton, Ontario]], Canada
| nationality = [[Canada]]<br>[[United States]]
| nationality = [[Canada]]<br />[[United States]]
| workplaces = [[Princeton University]]<br>[[Leiden University]]<br>[[University of Hyderabad]]
| workplaces = [[Princeton University]]<br />[[Leiden University]]<br />[[University of Hyderabad]]
| education = [[Harvard University]] ([[Bachelor of Arts|AB]])<br>[[Princeton University]] ([[Doctor of Philosophy|PhD]])
| education = [[Harvard University]] ([[Bachelor of Arts|AB]])<br />[[Princeton University]] ([[Doctor of Philosophy|PhD]])
| thesis_title = Higher composition laws
| thesis_year = 2001
| thesis_url = https://www.proquest.com/docview/304722465
| doctoral_advisor = [[Andrew Wiles]]<ref name=mathgene>{{MathGenealogy}}</ref>
| doctoral_advisor = [[Andrew Wiles]]<ref name=mathgene>{{MathGenealogy}}</ref>
| doctoral_students = {{plainlist|1=
| doctoral_students = {{plainlist|1=
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*[[Evan O'Dorney]]
*[[Evan O'Dorney]]
*[[Melanie Wood]]
*[[Melanie Wood]]
*[[Arul Shankar]]
*[[Piper Harron]]
}}
}}
| known_for = [[Bhargava factorial]]<br>[[Bhargava cube]]<br>[[15 and 290 theorems]]<br>[[average rank of elliptic curves]]
| known_for = [[Bhargava factorial]]<br />[[Bhargava cube]]<br />[[15 and 290 theorems]]<br />[[average rank of elliptic curves]]
| awards = [[Fellow of the Royal Society]] (2019)<br>[[Padma Bhushan]] (2015)<br> [[Fields Medal]] (2014)<br> [[Infosys Prize]] (2012)<br>[[Fermat Prize]] (2011)<br>[[Cole Prize]] (2008)<br>[[Clay Research Award]] (2005)<br>[[SASTRA Ramanujan Prize]] (2005)<br>[[Blumenthal Award]] (2005)<br> Hasse Prize (2003)<br>[[Morgan Prize]] (1996)<br>[[Hoopes Prize]] (1996)<br>[[Hertz Fellowship]] (1996)
| awards = [[Fellow of the Royal Society]] (2019)<br />[[Padma Bhushan]] (2015)<br /> [[Fields Medal]] (2014)<br /> [[Infosys Prize]] (2012)<br />[[Fermat Prize]] (2011)<br />[[Cole Prize]] (2008)<br />[[Clay Research Award]] (2005)<br />[[SASTRA Ramanujan Prize]] (2005)<br />[[Blumenthal Award]] (2005)<br /> [[Merten M. Hasse Prize]] (2003)<br />[[Morgan Prize]] (1996)<br />[[Hoopes Prize]] (1996)<br />[[Hertz Fellowship]] (1996)
| website = {{URL|https://www.math.princeton.edu/people/manjul-bhargava}}
| website = {{URL|https://www.math.princeton.edu/people/manjul-bhargava}}
}}
}}
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'''Manjul Bhargava''' {{post-nominals|country=GBR|FRS}} (born 8 August 1974)<ref>{{cite book |last=Gallian |first=Joseph A. |year=2009 |title=Contemporary Abstract Algebra |location=Belmont, CA |publisher=Cengage Learning |isbn=978-0-547-16509-7 |page=571 |url=https://books.google.com/books?id=CnH3mlOKpsMC&q=Contemporary%20Abstract%20Algebra&pg=PA571 }}</ref> is a [[Canadian Americans|Canadian-American]] mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at [[Princeton University]], the Stieltjes Professor of Number Theory<ref>{{cite press release|url=http://www.news.leiden.edu/news-2014/fields-medal-for-leiden-professor-of-number-theory-manjul-bhargava.html |title= Fields Medal for Leiden Professor of Number Theory Manjul Bhargava |date= 13 August 2014 |access-date= 13 August 2014}}</ref> at [[Leiden University]], and also holds Adjunct Professorships at the [[Tata Institute of Fundamental Research]], the [[Indian Institute of Technology Bombay]], and the [[University of Hyderabad]]. He is known primarily for his contributions to [[number theory]].
'''Manjul Bhargava''' {{post-nominals|country=GBR|FRS}} (born 8 August 1974)<ref>{{cite book |last=Gallian |first=Joseph A. |year=2009 |title=Contemporary Abstract Algebra |location=Belmont, CA |publisher=Cengage Learning |isbn=978-0-547-16509-7 |page=571 |url=https://books.google.com/books?id=CnH3mlOKpsMC&q=Contemporary%20Abstract%20Algebra&pg=PA571 }}</ref> is a [[Canadian Americans|Canadian-American]] mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at [[Princeton University]], the Stieltjes Professor of Number Theory<ref>{{cite press release|url=http://www.news.leiden.edu/news-2014/fields-medal-for-leiden-professor-of-number-theory-manjul-bhargava.html |title= Fields Medal for Leiden Professor of Number Theory Manjul Bhargava |date= 13 August 2014 |access-date= 13 August 2014}}</ref> at [[Leiden University]], and also holds Adjunct Professorships at the [[Tata Institute of Fundamental Research]], the [[Indian Institute of Technology Bombay]], and the [[University of Hyderabad]]. He is known primarily for his contributions to [[number theory]].


Bhargava was awarded the [[Fields Medal]] in 2014. According to the [[International Mathematical Union]] citation, he was awarded the prize "for developing powerful new methods in the [[geometry of numbers]], which he applied to count rings of small rank and to bound the average rank of elliptic curves".<ref>{{cite press release|url=https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2014|publisher=International Mathematical Union|title=Fields Medal 2014|access-date=10 February 2021}}</ref><ref>{{Cite web|date=10 February 2021|title=Press Release - Manjul Bhargava|url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2014/news_release_bhargava.pdf|website=International Mathematical Unioin}}</ref><ref>{{Cite web|title=Fields Medallists 2014 awardees with brief citations {{!}} International Mathematical Union (IMU)|url=https://www.mathunion.org/imu-awards/fields-medal/fields-medal-2014/fields-medallists-2014-awardees-brief-citations|access-date=2021-02-09|website=www.mathunion.org}}</ref>
Bhargava was awarded the [[Fields Medal]] in 2014. According to the [[International Mathematical Union]] citation, he was awarded the prize "for developing powerful new methods in the [[geometry of numbers]], which he applied to count rings of small rank and to bound the average rank of elliptic curves".<ref>{{cite press release|url=https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2014|publisher=International Mathematical Union|title=Fields Medal 2014|access-date=10 February 2021}}</ref><ref>{{Cite web|date=10 February 2021|title=Press Release - Manjul Bhargava|url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2014/news_release_bhargava.pdf|website=International Mathematical Unioin}}</ref><ref>{{Cite web|title=Fields Medallists 2014 awardees with brief citations {{!}} International Mathematical Union (IMU)|url=https://www.mathunion.org/imu-awards/fields-medal/fields-medal-2014/fields-medallists-2014-awardees-brief-citations|access-date=2021-02-09|website=www.mathunion.org}}</ref> He was also a member of the [[Padma Award]] committee in 2023.<ref>{{Cite web |date=April 2023 |title=Padma Awards Committee |url=https://www.mha.gov.in/sites/default/files/2023-04/PadmaAwardsCommittee_13042023.pdf |access-date=2024-08-21 |website=[[Ministry of Home Affairs (India)|Ministry of Home Affairs]] |format=PDF}}</ref>


==Education and career==
==Education and career==
Bhargava was born to an [[India]]n family in [[Hamilton, Ontario]], Canada, but grew up and attended school primarily in [[Long Island]], [[New York (state)|New York]]. His mother Mira Bhargava, a mathematician at [[Hofstra University]], was his first mathematics teacher.<ref>{{cite web|url=https://paw.princeton.edu/article/play-fields-math |title=At Play in the Fields of Math |access-date=September 29, 2016}}</ref><ref>{{cite web|url=http://news.rediff.com/specials/2009/mar/21/fareed-zakaria-is-india-abroad-person-of-the-year.htm |title=Fareed Zakaria is India Abroad Person of the Year&nbsp;— Rediff.com India News |publisher=News.rediff.com |date=2009-03-21 |access-date=2014-08-14}}</ref> He completed all of his high school math and computer science courses by age 14.<ref>{{cite web|url=http://www.indiaabroad-digital.com/indiaabroad/personoftheyear/?pg=29 |title=India Abroad&nbsp;— Archives 2003-2008 |publisher=Indiaabroad-digital.com |date=2009-12-30 |access-date=2014-08-14}}</ref> He attended [[Plainedge High School]] in [[North Massapequa, New York|North Massapequa]], and graduated in 1992 as the class [[valedictorian]]. He obtained his AB from [[Harvard University]] in 1996. For his research as an undergraduate, he was awarded the 1996 [[Morgan Prize]]. Bhargava went on to pursue graduate studies at Princeton University, where he completed a doctoral dissertation titled "Higher composition laws" under the supervision of Andrew Wiles and received his Ph.D. in 2001, with the support of a [[Hertz Foundation|Hertz Fellowship]].<ref>{{Cite book|last=Bhargava|first=Manjul|url=https://catalog.princeton.edu/catalog/3399787|title=Higher composition laws|date=2001|language=en}}</ref> He was a visiting scholar at the [[Institute for Advanced Study]] in 2001–02,<ref>{{cite web|url=http://www.ias.edu/people/cos/ |title=Institute for Advanced Study: A Community of Scholars |publisher=Ias.edu |access-date=2014-08-14}}</ref> and at Harvard University in 2002–03. Princeton appointed him as a tenured Full Professor in 2003. He was appointed to the Stieltjes Chair in [[Leiden University]] in 2010.
Bhargava was born to an [[India]]n family in [[Hamilton, Ontario]], Canada, but grew up and attended school primarily on [[Long Island]], [[New York (state)|New York]]. His mother Mira Bhargava, a mathematician at [[Hofstra University]], was his first mathematics teacher.<ref>{{cite web|url=https://paw.princeton.edu/article/play-fields-math |title=At Play in the Fields of Math |date=21 January 2016 |access-date=September 29, 2016}}</ref><ref>{{cite web|url=http://news.rediff.com/specials/2009/mar/21/fareed-zakaria-is-india-abroad-person-of-the-year.htm |title=Fareed Zakaria is India Abroad Person of the Year&nbsp;— Rediff.com India News |publisher=News.rediff.com |date=2009-03-21 |access-date=2014-08-14}}</ref> He completed all of his high school math and [[computer science]] courses by age 14.<ref>{{cite web|url=http://www.indiaabroad-digital.com/indiaabroad/personoftheyear/?pg=29 |title=India Abroad&nbsp;— Archives 2003-2008 |publisher=Indiaabroad-digital.com |date=2009-12-30 |access-date=2014-08-14}}</ref> He attended [[Plainedge High School]] in [[North Massapequa, New York|North Massapequa]], and graduated in 1992 as the class [[valedictorian]]. He obtained his AB from [[Harvard University]] in 1996. For his research as an undergraduate, he was awarded the 1996 [[Morgan Prize]]. Bhargava went on to pursue graduate studies at Princeton University, where he completed a doctoral dissertation titled "Higher composition laws" under the supervision of [[Andrew Wiles]] and received his PhD in 2001, with the support of a [[Hertz Foundation|Hertz Fellowship]].<ref>{{Cite book |last=Bhargava |first=Manjul |url=https://catalog.princeton.edu/catalog/3399787 |title=Higher composition laws |date= |publisher=[[Princeton University]] |year=2001 |isbn=978-0-493-19386-1 |editor-last=Wiles |editor-first=Andrew |language=en}}</ref> He was a visiting scholar at the [[Institute for Advanced Study]] in 2001–02,<ref>{{cite web|url=http://www.ias.edu/people/cos/ |title=Institute for Advanced Study: A Community of Scholars |publisher=Ias.edu |access-date=2014-08-14}}</ref> and at Harvard University in 2002–03. Princeton appointed him as a tenured Full Professor in 2003. He was appointed to the Stieltjes Chair in [[Leiden University]] in 2010.


Bhargava is also an accomplished [[tabla]] player, having studied under gurus such as [[Zakir Hussain (musician)|Zakir Hussain]].<ref>{{cite web|url=https://www.princeton.edu/pr/pwb/03/1208/1b.shtml |title=Bhargava strikes balance among many interests |publisher=Princeton.edu |date=2003-12-08 |access-date=2014-08-14}}</ref> He also studied [[Sanskrit]] from his grandfather Purushottam Lal Bhargava, a well-known scholar of Sanskrit and ancient Indian history.<ref>An International Conference in Honor of the 100th Birth Anniversary of Professor P. L. Bhargava [http://www.plbhargava-conference.org/bio.htm]</ref><ref name="Fields Medal Winner Bhargava">{{cite web|url=http://www.businessinsider.com/fields-medal-winner-bhargava-2014-8 |title=Fields Medal Winner Bhargava |publisher=Business Insider |access-date=2014-08-14}}</ref> He is an admirer of Sanskrit poetry.<ref name="TOI-20140818">{{cite news|url=http://timesofindia.indiatimes.com/india/Interest-at-home-among-NRIs-resurrects-Sanskrit/articleshow/40354569.cms|title=Interest at home, among NRIs resurrects Sanskrit|last=Dasgupta|first=Sucheta|date=2014-08-18|work=Times of India|access-date=18 August 2014}}</ref>
Bhargava has also studied the [[tabla]] under gurus such as [[Zakir Hussain (musician)|Zakir Hussain]].<ref>{{cite web|url=https://www.princeton.edu/pr/pwb/03/1208/1b.shtml |title=Bhargava strikes balance among many interests |publisher=Princeton.edu |date=2003-12-08 |access-date=2014-08-14}}</ref> He also studied [[Sanskrit]] from his grandfather Purushottam Lal Bhargava, a scholar of Sanskrit and ancient Indian history.<ref>An International Conference in Honor of the 100th Birth Anniversary of Professor P. L. Bhargava [http://www.plbhargava-conference.org/bio.htm]</ref><ref name="Fields Medal Winner Bhargava">{{cite web|url=http://www.businessinsider.com/fields-medal-winner-bhargava-2014-8 |title=Fields Medal Winner Bhargava |publisher=Business Insider |access-date=2014-08-14}}</ref> He is an admirer of Sanskrit poetry.<ref name="TOI-20140818">{{cite news|url=http://timesofindia.indiatimes.com/india/Interest-at-home-among-NRIs-resurrects-Sanskrit/articleshow/40354569.cms|title=Interest at home, among NRIs resurrects Sanskrit|last=Dasgupta|first=Sucheta|date=2014-08-18|work=Times of India|access-date=18 August 2014}}</ref>


==Career and research==
==Career and research==
His PhD thesis generalized [[Gauss]]'s classical law for composition of [[Binary quadratic form|binary quadratic forms]] to many other situations. One major use of his results is the parametrization of quartic and quintic orders in [[Algebraic number field|number fields]], thus allowing the study of asymptotic behavior of arithmetic properties of these orders and fields.
Bhargava’s PhD thesis generalized [[Gauss]]'s classical law for composition of [[binary quadratic form]]s to many other situations. One major use of his results is the parametrization of quartic and quintic orders in [[Algebraic number field|number fields]], thus allowing the study of the asymptotic behavior of the arithmetic properties of these orders and fields.


His research also includes fundamental contributions to the [[representation theory]] of [[quadratic form]]s, to [[interpolation theory|interpolation problems]] and [[p-adic analysis]], to the study of [[ideal class group]]s of [[algebraic number field]]s, and to the [[arithmetic theory]] of [[elliptic curve]]s.<ref>{{cite web|url=http://www.claymath.org/fas/research_fellows/Bhargava/ |title=Fellows and Scholars &#124; Clay Mathematics Institute |publisher=Claymath.org |access-date=2014-08-14}}</ref> A short list of his specific mathematical contributions are:
His research also includes fundamental contributions to the [[representation theory]] of [[quadratic form]]s, to [[interpolation theory|interpolation problems]] and [[p-adic analysis]], to the study of [[ideal class group]]s of [[algebraic number field]]s, and to the arithmetic theory of [[elliptic curve]]s.<ref>{{cite web|url=http://www.claymath.org/fas/research_fellows/Bhargava/ |title=Fellows and Scholars &#124; Clay Mathematics Institute |publisher=Claymath.org |access-date=2014-08-14}}</ref> A short list of his specific mathematical contributions are:


*Fourteen new Gauss-style composition laws.
*Fourteen new Gauss-style composition laws.
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*Proof of the [[15 and 290 theorems|15 theorem]], including an extension of the theorem to other number sets such as the odd numbers and the [[prime number]]s.
*Proof of the [[15 and 290 theorems|15 theorem]], including an extension of the theorem to other number sets such as the odd numbers and the [[prime number]]s.
*Proof (with Jonathan Hanke) of the [[15 and 290 theorems|290 theorem]].
*Proof (with Jonathan Hanke) of the [[15 and 290 theorems|290 theorem]].
*A novel [[generalization]] of the [[factorial]] function, [[Bhargava factorial]],<ref name="Bhargava Factorial Function Generalization">{{cite journal | last=Bhargava | first=Manjul | title=The Factorial Function and Generalizations | journal=The American Mathematical Monthly | publisher=Informa UK Limited | volume=107 | issue=9 | year=2000 | issn=0002-9890 | doi=10.1080/00029890.2000.12005273 | pages=783–799| s2cid=18356188 }}</ref> providing an answer to a decades-old question of [[George Pólya]].<ref name="Walter de Gruyter GmbH pp. 97–116">{{cite journal | title=Über ganzwertige Polynome in algebraischen Zahlkörpern. | journal=Journal für die reine und angewandte Mathematik (Crelle's Journal) | publisher=Walter de Gruyter GmbH | volume=1919 | issue=149 | date=1919-01-01 | issn=0075-4102 | doi=10.1515/crll.1919.149.97 | pages=97–116| last1=Pólya | first1=Georg | s2cid=120316910 }}</ref>
*A novel [[generalization]] of the [[factorial]] function, [[Bhargava factorial]], resolving a decades-old [[Pólya conjecture|conjecture by George Pólya]].
*Proof (with Arul Shankar) that the average [[Rank of an elliptic curve|rank]] of all [[elliptic curve]]s over '''Q''' (when ordered by height) is bounded.
*Proof (with Arul Shankar) that the average [[Rank of an elliptic curve|rank]] of all [[elliptic curve]]s over '''Q''' (when ordered by height) is bounded.
*Proof that most hyperelliptic curves over '''Q''' have no rational points.
*Proof that most hyperelliptic curves over '''Q''' have no rational points.


In 2015 Manjul Bhargava and Arul Shankar proved the [[Birch and Swinnerton-Dyer conjecture]] for a positive proportion of elliptic curves.<ref>{{Cite journal |last1=Bhargava |first1=Manjul |author-link=Manjul Bhargava |last2=Shankar |first2=Arul |author-link2=Arul Shankar |title=Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 |year=2015 |journal=[[Annals of Mathematics]] |volume=181 |issue=2 |pages=587–621 |doi=10.4007/annals.2015.181.2.4 |arxiv=1007.0052|s2cid=1456959 }}</ref>
In 2015, Manjul Bhargava and Arul Shankar proved the [[Birch and Swinnerton-Dyer conjecture]] for a positive proportion of elliptic curves.<ref>{{Cite journal |last1=Bhargava |first1=Manjul |author-link=Manjul Bhargava |last2=Shankar |first2=Arul |author-link2=Arul Shankar |title=Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 |year=2015 |journal=[[Annals of Mathematics]] |volume=181 |issue=2 |pages=587–621 |doi=10.4007/annals.2015.181.2.4 |arxiv=1007.0052|s2cid=1456959 }}</ref>


==Awards and honours==
==Awards and honours==
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Bhargava has won several awards for his research, the most prestigious being the [[Fields Medal]], the highest award in the field of mathematics, which he won in 2014.
Bhargava has won several awards for his research, the most prestigious being the [[Fields Medal]], the highest award in the field of mathematics, which he won in 2014.


⚫
He received the [[Morgan Prize]] in 1996.<ref>{{cite web|url=https://www.ams.org/notices/199612/comm-morgan.pdf |title=1996 AMS-MAA-SIAM Morgan Prize |access-date=2014-08-14}}</ref> and [[Hertz Fellowship]]<ref>{{cite web|url=http://www.hertzfoundation.org/dx/fellows/fellows.aspx |title=Hertz Foundation Fellows: Rare individuals elevate and inspire us through bold thinking and leadership. |access-date=2015-09-09}}</ref> He was named one of ''[[Popular Science]]'' magazine's "Brilliant 10" in November 2002. He then received a [[Clay Mathematics Institute|Clay]] 5-year Research Fellowship and the Merten M. Hasse Prize from the [[Mathematical Association of America|MAA]] in 2003,<ref>{{cite web|url=http://www.maa.org/awards/hasse.html |title=About the MAA |publisher=Maa.org |access-date=2014-08-14}}</ref> the [[Clay Research Award]], the [[SASTRA Ramanujan Prize]], and the Leonard M. and Eleanor B. Blumenthal Award for the Advancement of Research in Pure Mathematics in 2005.
Bhargava was conferred a Fellowship at the Royal Society in 2019.<ref>{{cite web|url=https://royalsociety.org/news/2019/04/royal-society-announces-2019-fellows|title=Distinguished scientists elected as Fellows and Foreign Members of the Royal Society}}</ref>

Bhargava is the third-youngest<ref>{{cite web| url=http://m.economictimes.com/magazines/panache/meet-manjul-bhargava-the-fields-medal-winner-for-mathematics-who-is-also-a-musician/amp_articleshow/40266561.cms|title=Meet Manjul Bhargava: The Fields Medal winner for mathematics, who is also a musician|publisher=The Economic Times|date=2014-08-14|access-date=2017-04-03}}</ref> full professor in Princeton University's history, after [[Charles Fefferman]] and [[John Pardon]].

⚫
In addition, he won the [[Morgan Prize]]<ref>{{cite web|url=https://www.ams.org/notices/199612/comm-morgan.pdf |title=1996 AMS-MAA-SIAM Morgan Prize |access-date=2014-08-14}}</ref> and [[Hertz Fellowship]]<ref>{{cite web|url=http://www.hertzfoundation.org/dx/fellows/fellows.aspx |title=Hertz Foundation Fellows: Rare individuals elevate and inspire us through bold thinking and leadership. |access-date=2015-09-09}}</ref> in 1996, a [[Clay Mathematics Institute|Clay]] 5-year Research Fellowship, the Merten M. Hasse Prize from the [[Mathematical Association of America|MAA]] in 2003,<ref>{{cite web|url=http://www.maa.org/awards/hasse.html |title=About the MAA |publisher=Maa.org |access-date=2014-08-14}}</ref> the [[Clay Research Award]] in 2005, and the Leonard M. and Eleanor B. Blumenthal Award for the Advancement of Research in Pure Mathematics in 2005.


[[Peter Sarnak]] of [[Princeton University]] has said of Bhargava:<ref>[http://www.dailyprincetonian.com/2005/10/11/13413/ Bhargava GS '98 awarded Clay Research prize] {{webarchive |url=https://web.archive.org/web/20110614221559/http://www.dailyprincetonian.com/2005/10/11/13413/ |date=14 June 2011 }}</ref>
[[Peter Sarnak]] of [[Princeton University]] has said of Bhargava:<ref>[http://www.dailyprincetonian.com/2005/10/11/13413/ Bhargava GS '98 awarded Clay Research prize] {{webarchive |url=https://web.archive.org/web/20110614221559/http://www.dailyprincetonian.com/2005/10/11/13413/ |date=14 June 2011 }}</ref>


{{quote|At mathematics he's at the very top end. For a guy so young I can't remember anybody so decorated at his age. He certainly started out with a bang and has not let it get to his head, which is unusual. Of course he couldn't do what he does if he wasn't brilliant. It's his exceptional talent that's so striking}}
{{blockquote|At mathematics he's at the very top end. For a guy so young I can't remember anybody so decorated at his age. He certainly started out with a bang and has not let it get to his head, which is unusual. Of course he couldn't do what he does if he wasn't brilliant. It's his exceptional talent that's so striking}}

He was named one of ''[[Popular Science]]'' magazine's "Brilliant 10" in November 2002. He won the $10,000 [[SASTRA Ramanujan Prize]], shared with [[Kannan Soundararajan]], awarded by [[Shanmugha Arts, Science, Technology & Research Academy|SASTRA]] in 2005 at [[Thanjavur]], India, for his outstanding contributions to [[number theory]].

⚫
In 2008, Bhargava was awarded the [[American Mathematical Society]]'s [[Cole Prize]].<ref>{{cite web|url=https://www.ams.org/notices/200804/tx080400497p.pdf |title=2008 Cole Prize in Number Theory |access-date=2014-08-14}}</ref> The citation reads:

⚫
{{quote|Bhargava's original and surprising contribution is the discovery of laws of composition on forms of higher degree. His techniques and insights into this question are dazzling; even in the case considered by Gauss, they lead to a new and clearer presentation of that theory}}

⚫
In 2009, he was awarded the Face of the Future award at the India Abroad Person of the Year ceremony in New York City.<ref>{{Citation|last=Rajesh Karkera|title=The India Abroad Face of the Future Award - Manjul Bhargava|date=2009-03-22|url=https://www.youtube.com/watch?v=pimiDwd0E_A|access-date=2018-07-17}}</ref> In 2014, the same publication, the most prestigious and most widely read of the diaspora publications, gave him a second prize, India Abroad Publisher's Prize for Special Excellence.<ref>{{Citation|last=Rajesh Karkera|title=The India Abroad Publisher's Special Award for Excellence 2014: Manjul Bhargava|date=2015-06-13|url=https://www.youtube.com/watch?v=2JJYi0OilWM|access-date=2018-07-17}}</ref>


⚫
In 2008, Bhargava was awarded the [[American Mathematical Society]]'s [[Cole Prize]].<ref>{{Cite journal |date=April 2008 |title=2008 Cole Prize in Number Theory |url=https://www.ams.org/notices/200804/tx080400497p.pdf |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |volume=55 |issue=4 |pages=497-498}}</ref> The citation reads:
In 2011, he was awarded the [[Fermat Prize]] for "various generalizations of the Davenport-Heilbronn estimates and for his startling recent results (with Arul Shankar) on the average rank of elliptic curves".<ref>[http://www.math.univ-toulouse.fr/PrixFermat Fermat Prize 2011] {{webarchive |url=https://web.archive.org/web/20111103125517/http://www.math.univ-toulouse.fr/PrixFermat |date=3 November 2011 }}</ref>


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{{blockquote|Bhargava's original and surprising contribution is the discovery of laws of composition on forms of higher degree. His techniques and insights into this question are dazzling; even in the case considered by Gauss, they lead to a new and clearer presentation of that theory.}}
In 2011, he delivered the Hedrick lectures of the [[Mathematical Association of America|MAA]] in Lexington, Kentucky.<ref>{{cite web|url=http://www.maa.org/awards/hedrick.html |title=Earle Raymond Hedrick Lecturers |publisher=Maa.org |access-date=2014-08-14}}</ref> He was also the 2011 Simons Lecturer at MIT.<ref>{{cite web |url=http://www-math.mit.edu/news/simons/ |title=MIT Mathematics &#124; Simons |publisher=Math.mit.edu |access-date=2014-08-14 |url-status=dead |archive-url=https://web.archive.org/web/20140203022306/http://www-math.mit.edu/news/simons/ |archive-date=3 February 2014 |df=dmy-all }}</ref>


⚫
In 2009, he was awarded the Face of the Future award at the India Abroad Person of the Year ceremony in New York City.<ref>{{Citation|last=Rajesh Karkera|title=The India Abroad Face of the Future Award - Manjul Bhargava|date=2009-03-22|url=https://www.youtube.com/watch?v=pimiDwd0E_A |archive-url=https://ghostarchive.org/varchive/youtube/20211214/pimiDwd0E_A |archive-date=2021-12-14 |url-status=live|access-date=2018-07-17}}{{cbignore}}</ref> In 2014, the same publication gave the India Abroad Publisher's Prize for Special Excellence.<ref>{{Citation|last=Rajesh Karkera|title=The India Abroad Publisher's Special Award for Excellence 2014: Manjul Bhargava|date=2015-06-13|url=https://www.youtube.com/watch?v=2JJYi0OilWM |archive-url=https://ghostarchive.org/varchive/youtube/20211214/2JJYi0OilWM |archive-date=2021-12-14 |url-status=live|access-date=2018-07-17}}{{cbignore}}</ref>
In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award,<ref>{{cite web|url=http://foundationcenter.org/pnd/news/story.jhtml?id=386600006 |title=Simons Investigator Award Recipients in Math, Physics, and Computer Science Announced |publisher=Foundationcenter.org |date=2012-07-24 |access-date=2014-08-14}}</ref> and became a fellow of the [[American Mathematical Society]] in its inaugural class of fellows.<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref>


In 2011, he was awarded the [[Fermat Prize]] for "various generalizations of the Davenport-Heilbronn estimates and for his startling recent results (with Arul Shankar) on the average rank of elliptic curves".<ref>[http://www.math.univ-toulouse.fr/PrixFermat Fermat Prize 2011] {{webarchive |url=https://web.archive.org/web/20111103125517/http://www.math.univ-toulouse.fr/PrixFermat |date=3 November 2011 }}</ref> In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award,<ref>{{cite web|url=http://foundationcenter.org/pnd/news/story.jhtml?id=386600006 |title=Simons Investigator Award Recipients in Math, Physics, and Computer Science Announced |publisher=Foundationcenter.org |date=2012-07-24 |access-date=2014-08-14}}</ref> and became a fellow of the [[American Mathematical Society]] in its inaugural class of fellows.<ref>{{Cite web |title=List of Fellows of the American Mathematical Society |url=https://www.ams.org/cgi-bin/fellows/fellows.cgi |access-date=2012-11-10 |website=[[American Mathematical Society]]}}</ref> He was awarded the 2012 [[Infosys Prize]] in mathematics for his "extraordinarily original work in [[algebraic number theory]], which has revolutionized the way in which [[number fields]] and [[elliptic curves]] are counted".<ref name="hindu">{{cite news
He was awarded the 2012 [[Infosys Prize]] in mathematics for his "extraordinarily original work in [[algebraic number theory]], which has revolutionized the way in which [[number fields]] and [[elliptic curves]] are counted".<ref name="hindu">{{cite news
| url=http://www.thehindu.com/news/subrahmanyam-chaudhuri-get-infosys-prize/article4127589.ece
| url=http://www.thehindu.com/news/subrahmanyam-chaudhuri-get-infosys-prize/article4127589.ece
| title=Subrahmanyam, Chaudhuri get Infosys Prize
| title=Subrahmanyam, Chaudhuri get Infosys Prize
Line 88: Line 81:
In 2014, Bhargava was awarded the [[Fields Medal]] at the [[International Congress of Mathematicians]] in [[Seoul]]<ref name="Fields Medal Winner Bhargava"/> for "developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves".<ref>{{cite web|url=http://www.mathunion.org/general/prizes/2014/prize-citations/ |title=List of all 2014 awardees with brief citations |publisher=mathunion.org |access-date=2014-08-24}}</ref>
In 2014, Bhargava was awarded the [[Fields Medal]] at the [[International Congress of Mathematicians]] in [[Seoul]]<ref name="Fields Medal Winner Bhargava"/> for "developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves".<ref>{{cite web|url=http://www.mathunion.org/general/prizes/2014/prize-citations/ |title=List of all 2014 awardees with brief citations |publisher=mathunion.org |access-date=2014-08-24}}</ref>


In 2015, he was awarded the [[Padma Bhushan]], the third-highest civilian award of India.<ref name="Padma Bhushan">{{cite web |url=http://pib.nic.in/newsite/PrintRelease.aspx?relid=114952 |title=This Year's Padma Awards announced |publisher=[[Ministry of Home Affairs (India)|Ministry of Home Affairs]] |date=25 January 2015 |access-date=2 February 2015 |url-status=dead |archive-url=https://www.webcitation.org/6VrWjEuo3?url=http://pib.nic.in/newsite/PrintRelease.aspx?relid=114952 |archive-date=26 January 2015 }}</ref>
In 2015, he was awarded the [[Padma Bhushan]], the third-highest civilian award of India.<ref name="Padma Bhushan">{{cite web |url=http://pib.nic.in/newsite/PrintRelease.aspx?relid=114952 |title=This Year's Padma Awards announced |publisher=[[Ministry of Home Affairs (India)|Ministry of Home Affairs]] |date=25 January 2015 |access-date=2 February 2015 |url-status=dead |archive-url=https://web.archive.org/web/20150128022143/http://pib.nic.in/newsite/PrintRelease.aspx?relid=114952 |archive-date=28 January 2015 }}</ref>


In 2017, Bhargava was elected as a member of the [[American Academy of Arts and Sciences]].<ref>{{Cite web|title=Manjul Bhargava|url=https://www.amacad.org/person/manjul-bhargava|website=American Academy of Arts & Sciences|language=en|access-date=2020-05-13}}</ref>
In 2017, Bhargava was elected as a member of the [[American Academy of Arts and Sciences]].<ref>{{Cite web|title=Manjul Bhargava|url=https://www.amacad.org/person/manjul-bhargava|website=American Academy of Arts & Sciences|language=en|access-date=2020-05-13}}</ref> In 2018, Bhargava was named as the inaugural occupant of The Distinguished Chair for the Public Dissemination of Mathematics at The [[National Museum of Mathematics]] (MoMath). This is the first visiting professorship in the United States dedicated exclusively to raising public awareness of mathematics.<ref>[https://www.prweb.com/releases/momath_announces_first_distinguished_chair_for_the_public_dissemination_of_mathematics_first_visiting_professorship_in_u_s_dedicated_to_raising_public_awareness_of_math/prweb15669001.htm MoMath Announces First Distinguished Chair for the Public Dissemination of Mathematics] The National Museum of Mathematics, August 2, 2018</ref> Bhargava was conferred a Fellowship at the Royal Society in 2019.<ref>{{cite web|url=https://royalsociety.org/news/2019/04/royal-society-announces-2019-fellows|title=Distinguished scientists elected as Fellows and Foreign Members of the Royal Society}}</ref>

In 2018 Bhargava was named as the inaugural occupant of The Distinguished Chair for the Public Dissemination of Mathematics at The [[National Museum of Mathematics]] (MoMath). This is the first visiting professorship in the United States dedicated exclusively to raising public awareness of mathematics.<ref>[https://www.prweb.com/releases/momath_announces_first_distinguished_chair_for_the_public_dissemination_of_mathematics_first_visiting_professorship_in_u_s_dedicated_to_raising_public_awareness_of_math/prweb15669001.htm MoMath Announces First Distinguished Chair for the Public Dissemination of Mathematics] The National Museum of Mathematics, August 2, 2018</ref>


==Selected publications==
==Selected publications==
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* {{cite journal | last1=Bhargava | first1=Manjul | last2=Shankar | first2=Arul | title=Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves | year=2015 | journal=[[Annals of Mathematics]] | volume=181 | issue=1 | pages=191–242 | mr=3272925 | doi=10.4007/annals.2015.181.1.3| arxiv=1006.1002 | s2cid=111383310 }}
* {{cite journal | last1=Bhargava | first1=Manjul | last2=Shankar | first2=Arul | title=Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves | year=2015 | journal=[[Annals of Mathematics]] | volume=181 | issue=1 | pages=191–242 | mr=3272925 | doi=10.4007/annals.2015.181.1.3| arxiv=1006.1002 | s2cid=111383310 }}
* {{Cite journal |last1=Bhargava |first1=Manjul |last2=Shankar |first2=Arul |title=Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 |year=2015 |journal=[[Annals of Mathematics]] |volume=181 |issue=2 |pages=587–621 |doi=10.4007/annals.2015.181.2.4 |arxiv=1007.0052|s2cid=1456959 }}
* {{Cite journal |last1=Bhargava |first1=Manjul |last2=Shankar |first2=Arul |title=Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 |year=2015 |journal=[[Annals of Mathematics]] |volume=181 |issue=2 |pages=587–621 |doi=10.4007/annals.2015.181.2.4 |arxiv=1007.0052|s2cid=1456959 }}

==See also==
* [[Indians in the New York City metropolitan area]]


==References==
==References==
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[[Category:Foreign Fellows of the Indian National Science Academy]]
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[[Category:American academics of Indian descent]]
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[[Category:Recipients of the Padma Bhushan in science & engineering]]
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[[Category:Canadian fellows of the Royal Society]]

Revision as of 02:58, 23 September 2024

Manjul Bhargava
FRS
Manjul Bhargava in 2014
Born (1974-08-08) 8 August 1974 (age 50)
Hamilton, Ontario, Canada
NationalityCanada
United States
EducationHarvard University (AB)
Princeton University (PhD)
Known forBhargava factorial
Bhargava cube
15 and 290 theorems
average rank of elliptic curves
AwardsFellow of the Royal Society (2019)
Padma Bhushan (2015)
Fields Medal (2014)
Infosys Prize (2012)
Fermat Prize (2011)
Cole Prize (2008)
Clay Research Award (2005)
SASTRA Ramanujan Prize (2005)
Blumenthal Award (2005)
Merten M. Hasse Prize (2003)
Morgan Prize (1996)
Hoopes Prize (1996)
Hertz Fellowship (1996)
Scientific career
InstitutionsPrinceton University
Leiden University
University of Hyderabad
ThesisHigher composition laws (2001)
Doctoral advisorAndrew Wiles[1]
Doctoral students
Websitewww.math.princeton.edu/people/manjul-bhargava

Manjul Bhargava FRS (born 8 August 1974)[2] is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory[3] at Leiden University, and also holds Adjunct Professorships at the Tata Institute of Fundamental Research, the Indian Institute of Technology Bombay, and the University of Hyderabad. He is known primarily for his contributions to number theory.

Bhargava was awarded the Fields Medal in 2014. According to the International Mathematical Union citation, he was awarded the prize "for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves".[4][5][6] He was also a member of the Padma Award committee in 2023.[7]

Education and career

Bhargava was born to an Indian family in Hamilton, Ontario, Canada, but grew up and attended school primarily on Long Island, New York. His mother Mira Bhargava, a mathematician at Hofstra University, was his first mathematics teacher.[8][9] He completed all of his high school math and computer science courses by age 14.[10] He attended Plainedge High School in North Massapequa, and graduated in 1992 as the class valedictorian. He obtained his AB from Harvard University in 1996. For his research as an undergraduate, he was awarded the 1996 Morgan Prize. Bhargava went on to pursue graduate studies at Princeton University, where he completed a doctoral dissertation titled "Higher composition laws" under the supervision of Andrew Wiles and received his PhD in 2001, with the support of a Hertz Fellowship.[11] He was a visiting scholar at the Institute for Advanced Study in 2001–02,[12] and at Harvard University in 2002–03. Princeton appointed him as a tenured Full Professor in 2003. He was appointed to the Stieltjes Chair in Leiden University in 2010.

Bhargava has also studied the tabla under gurus such as Zakir Hussain.[13] He also studied Sanskrit from his grandfather Purushottam Lal Bhargava, a scholar of Sanskrit and ancient Indian history.[14][15] He is an admirer of Sanskrit poetry.[16]

Career and research

Bhargava’s PhD thesis generalized Gauss's classical law for composition of binary quadratic forms to many other situations. One major use of his results is the parametrization of quartic and quintic orders in number fields, thus allowing the study of the asymptotic behavior of the arithmetic properties of these orders and fields.

His research also includes fundamental contributions to the representation theory of quadratic forms, to interpolation problems and p-adic analysis, to the study of ideal class groups of algebraic number fields, and to the arithmetic theory of elliptic curves.[17] A short list of his specific mathematical contributions are:

In 2015, Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves.[20]

Awards and honours

Four Fields medallists left to right (Artur Avila, Martin Hairer (at back), Maryam Mirzakhani, with Maryam's daughter Anahita) and Bhargava at the ICM 2014 in Seoul

Bhargava has won several awards for his research, the most prestigious being the Fields Medal, the highest award in the field of mathematics, which he won in 2014.

He received the Morgan Prize in 1996.[21] and Hertz Fellowship[22] He was named one of Popular Science magazine's "Brilliant 10" in November 2002. He then received a Clay 5-year Research Fellowship and the Merten M. Hasse Prize from the MAA in 2003,[23] the Clay Research Award, the SASTRA Ramanujan Prize, and the Leonard M. and Eleanor B. Blumenthal Award for the Advancement of Research in Pure Mathematics in 2005.

Peter Sarnak of Princeton University has said of Bhargava:[24]

At mathematics he's at the very top end. For a guy so young I can't remember anybody so decorated at his age. He certainly started out with a bang and has not let it get to his head, which is unusual. Of course he couldn't do what he does if he wasn't brilliant. It's his exceptional talent that's so striking

In 2008, Bhargava was awarded the American Mathematical Society's Cole Prize.[25] The citation reads:

Bhargava's original and surprising contribution is the discovery of laws of composition on forms of higher degree. His techniques and insights into this question are dazzling; even in the case considered by Gauss, they lead to a new and clearer presentation of that theory.

In 2009, he was awarded the Face of the Future award at the India Abroad Person of the Year ceremony in New York City.[26] In 2014, the same publication gave the India Abroad Publisher's Prize for Special Excellence.[27]

In 2011, he was awarded the Fermat Prize for "various generalizations of the Davenport-Heilbronn estimates and for his startling recent results (with Arul Shankar) on the average rank of elliptic curves".[28] In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award,[29] and became a fellow of the American Mathematical Society in its inaugural class of fellows.[30] He was awarded the 2012 Infosys Prize in mathematics for his "extraordinarily original work in algebraic number theory, which has revolutionized the way in which number fields and elliptic curves are counted".[31]

In 2013, he was elected to the National Academy of Sciences.[32]

In 2014, Bhargava was awarded the Fields Medal at the International Congress of Mathematicians in Seoul[15] for "developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves".[33]

In 2015, he was awarded the Padma Bhushan, the third-highest civilian award of India.[34]

In 2017, Bhargava was elected as a member of the American Academy of Arts and Sciences.[35] In 2018, Bhargava was named as the inaugural occupant of The Distinguished Chair for the Public Dissemination of Mathematics at The National Museum of Mathematics (MoMath). This is the first visiting professorship in the United States dedicated exclusively to raising public awareness of mathematics.[36] Bhargava was conferred a Fellowship at the Royal Society in 2019.[37]

Selected publications

See also

References

  1. ^ Manjul Bhargava at the Mathematics Genealogy Project Edit this at Wikidata
  2. ^ Gallian, Joseph A. (2009). Contemporary Abstract Algebra. Belmont, CA: Cengage Learning. p. 571. ISBN 978-0-547-16509-7.
  3. ^ "Fields Medal for Leiden Professor of Number Theory Manjul Bhargava" (Press release). 13 August 2014. Retrieved 13 August 2014.
  4. ^ "Fields Medal 2014" (Press release). International Mathematical Union. Retrieved 10 February 2021.
  5. ^ "Press Release - Manjul Bhargava" (PDF). International Mathematical Unioin. 10 February 2021.
  6. ^ "Fields Medallists 2014 awardees with brief citations | International Mathematical Union (IMU)". www.mathunion.org. Retrieved 9 February 2021.
  7. ^ "Padma Awards Committee" (PDF). Ministry of Home Affairs. April 2023. Retrieved 21 August 2024.
  8. ^ "At Play in the Fields of Math". 21 January 2016. Retrieved 29 September 2016.
  9. ^ "Fareed Zakaria is India Abroad Person of the Year — Rediff.com India News". News.rediff.com. 21 March 2009. Retrieved 14 August 2014.
  10. ^ "India Abroad — Archives 2003-2008". Indiaabroad-digital.com. 30 December 2009. Retrieved 14 August 2014.
  11. ^ Bhargava, Manjul (2001). Wiles, Andrew (ed.). Higher composition laws. Princeton University. ISBN 978-0-493-19386-1.
  12. ^ "Institute for Advanced Study: A Community of Scholars". Ias.edu. Retrieved 14 August 2014.
  13. ^ "Bhargava strikes balance among many interests". Princeton.edu. 8 December 2003. Retrieved 14 August 2014.
  14. ^ An International Conference in Honor of the 100th Birth Anniversary of Professor P. L. Bhargava [1]
  15. ^ a b "Fields Medal Winner Bhargava". Business Insider. Retrieved 14 August 2014.
  16. ^ Dasgupta, Sucheta (18 August 2014). "Interest at home, among NRIs resurrects Sanskrit". Times of India. Retrieved 18 August 2014.
  17. ^ "Fellows and Scholars | Clay Mathematics Institute". Claymath.org. Retrieved 14 August 2014.
  18. ^ Bhargava, Manjul (2000). "The Factorial Function and Generalizations". The American Mathematical Monthly. 107 (9). Informa UK Limited: 783–799. doi:10.1080/00029890.2000.12005273. ISSN 0002-9890. S2CID 18356188.
  19. ^ Pólya, Georg (1 January 1919). "Über ganzwertige Polynome in algebraischen Zahlkörpern". Journal für die reine und angewandte Mathematik (Crelle's Journal). 1919 (149). Walter de Gruyter GmbH: 97–116. doi:10.1515/crll.1919.149.97. ISSN 0075-4102. S2CID 120316910.
  20. ^ Bhargava, Manjul; Shankar, Arul (2015). "Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0". Annals of Mathematics. 181 (2): 587–621. arXiv:1007.0052. doi:10.4007/annals.2015.181.2.4. S2CID 1456959.
  21. ^ "1996 AMS-MAA-SIAM Morgan Prize" (PDF). Retrieved 14 August 2014.
  22. ^ "Hertz Foundation Fellows: Rare individuals elevate and inspire us through bold thinking and leadership". Retrieved 9 September 2015.
  23. ^ "About the MAA". Maa.org. Retrieved 14 August 2014.
  24. ^ Bhargava GS '98 awarded Clay Research prize Archived 14 June 2011 at the Wayback Machine
  25. ^ "2008 Cole Prize in Number Theory" (PDF). Notices of the American Mathematical Society. 55 (4). American Mathematical Society: 497–498. April 2008.
  26. ^ Rajesh Karkera (22 March 2009), The India Abroad Face of the Future Award - Manjul Bhargava, archived from the original on 14 December 2021, retrieved 17 July 2018
  27. ^ Rajesh Karkera (13 June 2015), The India Abroad Publisher's Special Award for Excellence 2014: Manjul Bhargava, archived from the original on 14 December 2021, retrieved 17 July 2018
  28. ^ Fermat Prize 2011 Archived 3 November 2011 at the Wayback Machine
  29. ^ "Simons Investigator Award Recipients in Math, Physics, and Computer Science Announced". Foundationcenter.org. 24 July 2012. Retrieved 14 August 2014.
  30. ^ "List of Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 10 November 2012.
  31. ^ "Subrahmanyam, Chaudhuri get Infosys Prize". The Hindu. Bangalore. 24 November 2012. Retrieved 24 November 2012.
  32. ^ "Professor Manjul Bhargava Has Been Elected to National Academy of Sciences". Math.princeton.edu. Archived from the original on 23 October 2014. Retrieved 14 August 2014.
  33. ^ "List of all 2014 awardees with brief citations". mathunion.org. Retrieved 24 August 2014.
  34. ^ "This Year's Padma Awards announced". Ministry of Home Affairs. 25 January 2015. Archived from the original on 28 January 2015. Retrieved 2 February 2015.
  35. ^ "Manjul Bhargava". American Academy of Arts & Sciences. Retrieved 13 May 2020.
  36. ^ MoMath Announces First Distinguished Chair for the Public Dissemination of Mathematics The National Museum of Mathematics, August 2, 2018
  37. ^ "Distinguished scientists elected as Fellows and Foreign Members of the Royal Society".
Retrieved from "https://en.wikipedia.org/w/index.php?title=Manjul_Bhargava&oldid=1247161093"