#4,262

Most Influential Person

Indo-Canadian mathematician

Bhargava is the R. Brandon Fradd Professor of Mathematics at Princeton University. He also holds a professorship at Leiden University in the Netherlands and multiple faculty positions at universities in his home country of India. Bhargava’s specialty in mathematics is number theory, the core and historically “famous” study of the integers. Bhargava was born in Canada and raised in Long Island. His mother Mira Bhargava is a mathematician at Hofstra University, who he calls his first math teacher. He received his bachelor’s degree in Mathematics from Harvard in 1996, and his Ph.D. from Princeton in 2001.

Bhargava’s Ph.D. was itself an important result in the world of mathematics, a generalization of the 19th century mathematician Gauss’s law of composition for binary quadratic forms. Among many other accomplishments in number theory as well as fields in arithmetic, algebra, and representation theory, Bhargava has discovered 14 new Gauss-style composition laws in number theory.

Bhargava won the Fields Medal in 2014. He became a Fellow of the Royal Society in 2019. Popular Science named him one of the “Brilliant 10” in 2002.

**Featured in Top Influential Mathematicians Today**

According to Wikipedia, Manjul Bhargava 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 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.

- The density of discriminants of quartic rings and fields (2005) (216)
- Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves (2010) (152)
- Higher composition laws I: A new view on Gauss composition, and quadratic generalizations (2004) (145)
- Higher composition laws III: The parametrization of quartic rings (2004) (127)
- On the Davenport–Heilbronn theorems and second order terms (2010) (105)
- Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 (2010) (103)
- P-orderings and polynomial functions on arbitrary subsets of Dedekind rings. (1997) (102)
- Higher composition laws II: On cubic analogues of Gauss composition (2004) (97)
- The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point (2012) (80)
- Higher composition laws (2001) (71)
- Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants (2007) (71)
- Higher composition laws IV: The parametrization of quintic rings (2008) (63)
- The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1 (2013) (60)
- The Factorial Function and Generalizations (2000) (59)
- Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves (2013) (55)
- Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves (2017) (46)
- The geometric sieve and the density of squarefree values of invariant polynomials (2014) (45)
- Squarefree values of polynomial discriminants I (2022) (44)
- Most hyperelliptic curves over Q have no rational points (2013) (41)
- Universal quadratic forms and the 290-Theorem (2011) (40)
- Coregular spaces and genus one curves (2013) (40)
- Arithmetic invariant theory (2014) (39)
- The average number of elements in the 4-Selmer groups of elliptic curves is 7 (2013) (35)
- Generalized Factorials and Fixed Divisors over Subsets of a Dedekind Domain (1998) (34)
- Error estimates for the Davenport-Heilbronn theorems (2010) (33)
- Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces (2015) (33)
- Factoring Dickson Polynomials over Finite Fields (1999) (29)
- A positive proportion of plane cubics fail the Hasse principle (2014) (29)
- A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture (2014) (29)
- THE DENSITY OF DISCRIMINANTS OF S3-SEXTIC NUMBER FIELDS (2007) (27)
- The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields (2016) (26)
- On the mean number of $2$-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields (2015) (24)
- On the number of cubic orders of bounded discriminant having automorphism group $C_3$, and related problems (2014) (23)
- The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders (2014) (20)
- On P-orderings, rings of integer-valued polynomials, and ultrametric analysis (2009) (20)
- Pencils of quadrics and the arithmetic of hyperelliptic curves (2013) (20)
- A positive proportion of elliptic curves over Q have rank one (2014) (19)
- Higher composition laws and applications (2006) (19)
- Gauss Composition and Generalizations (2002) (18)
- What is the probability that a random integral quadratic form in n variables has an integral zero (2015) (16)
- Continuous functions on compact subsets of local fields (1999) (16)
- On a notion of "Galois closure" for extensions of rings (2010) (14)
- On the average number of octahedral newforms of prime level (2009) (13)
- Congruence preservation and polynomial functions from Zn to Zm (1997) (13)
- The proportion of plane cubic curves over ${\mathbb Q}$ that everywhere locally have a point (2013) (12)
- The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k (2019) (10)
- ORBIT PARAMETRIZATIONS FOR K3 SURFACES (2016) (9)
- Finite generation properties for various rings of integer-valued polynomials (2009) (9)
- 3-Isogeny Selmer groups and ranks of Abelian varieties in quadratic twist families over a number field (2019) (8)
- Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits (2015) (8)
- HEURISTICS FOR THE ARITHMETIC OF ELLIPTIC CURVES (2017) (7)
- The mean number of 2-torsion elements in the class groups of $n$-monogenized cubic fields (2020) (6)
- Elements of given order in Tate–Shafarevich groups of abelian varieties in quadratic twist families (2019) (5)
- Finite Simple Groups: Thirty Years of the Atlas and Beyond (2017) (5)
- A positive proportion of elliptic curves over $\mathbb{Q}$ have rank one (2014) (5)
- A positive proportion of locally soluble hyperelliptic curves over $\mathbb Q$ have no point over any odd degree extension (2013) (4)
- On the number of integral binary $n$-ic forms having bounded Julia invariant (2013) (4)
- A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so (2020) (4)
- The local-global principle for integral points on stacky curves (2020) (3)
- Improved error estimates for the Davenport-Heilbronn theorems (2021) (3)
- The proportion of genus one curves over ℚ defined by a binary quartic that everywhere locally have a point (2020) (3)
- Arithmetic invariant theory II (2013) (2)
- The proportion of genus one curves over $\mathbb{Q}$ defined by a binary quartic that everywhere locally have a point (2020) (2)
- The second moment of the size of the $2$-Selmer group of elliptic curves (2021) (1)
- AVERAGE RANK OF ELLIPTIC CURVES [ after (2012) (1)
- Galois groups of random integer polynomials and van der Waerden's Conjecture (2021) (1)
- On the classification of rings of “ small ” rank (2009) (1)
- A positive proportion of locally soluble Thue equations are globally insoluble (2016) (1)
- What is the probability that a random integral quadratic form in $n$ variables is isotropic? (2013) (1)
- On the number of monogenizations of a quartic order (2021) (1)
- Solutions to the 62 nd William Lowell Putnam Mathematical Competition Saturday , December 1 , 2001 (2013) (0)
- CUBIC RINGS AND FORMS (2010) (0)
- Solutions to the 64th William Lowell Putnam Mathematical Competition Saturday, December 6, 2003 (2003) (0)
- Solutions to the 76 th William Lowell Putnam Mathematical Competition Saturday , December 5 , 2015 (2016) (0)
- A POSITIVE PROPORTION OF LOCALLY SOLUBLE HYPERELLIPTIC CURVES OVER Q HAVE NO POINT OVER ANY ODD DEGREE EXTENSION MANJUL BHARGAVA, BENEDICT H. GROSS, AND XIAOHENG WANG, WITH AN APPENDIX BY TIM DOKCHITSER AND VLADIMIR DOKCHITSER (2017) (0)
- The average elliptic curve has few integral points (2014) (0)
- Factoring Dickson Polynomials over Nite Elds (1997) (0)
- Analysis, Spectra, and Number Theory: A Conference in Honor of Peter Sarnak’s 60th Birthday December 15-19, 2014 (2015) (0)
- Clay Research Conference (2007) (0)
- October 2014 Cover English (2014) (0)
- PARAMETRIZATION OF RINGS OF SMALL RANK : COURSE DESCRIPTION (2008) (0)
- Solutions to the 66 th William Lowell Putnam Mathematical Competition Saturday , December 3 , 2005 (2005) (0)
- Solutions to the 60th William Lowell Putnam Mathematical Competition Saturday, December 4, 1999 (2015) (0)
- Solutions to the 82nd William Lowell Putnam Mathematical Competition Saturday, December 4, 2021 (2021) (0)
- Mass Formulas for Z p and F p Algebras (2012) (0)
- Foreword (2019) (0)
- The average elliptic curve has few integral (2014) (0)
- Foreword (2019) (0)
- Rational points on elliptic and hyperelliptic curves (2014) (0)
- Varieties over finite and local fields 11 S 15 Ramification and extension theory 11 S 80 Other (2022) (0)
- The Work of Manjul Bhargava (2014) (0)
- The density of polynomials of degree $n$ over $\mathbb{Z}_p$ having exactly $r$ roots in $\mathbb{Q}_p$ (2021) (0)
- The Factorial Function and Generalizations (2009) (0)
- Solutions to the 81 st William Lowell Putnam Mathematical Competition Saturday (2018) (0)
- Hermite equivalence of polynomials (2021) (0)
- Solutions to the 68 th William Lowell Putnam Mathematical Competition Saturday , December 1 , 2007 (2007) (0)
- Solutions to the 57 th William Lowell Putnam Mathematical Competition Saturday , December 7 , 1996 (2013) (0)
- John Horton Conway (1937–2020) (2020) (0)
- INTRODUCTION: PRE-HOMOGENEOUS SPACES (2011) (0)

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