Mathukumalli (Matukumalli) Venkata Subbarao (May 4, 1921 – February 15, 2006) was an

Indo-Canadian Indian Canadians are Canadians who have ancestry from India. The terms ''Indo-Canadian'' or ''East Indian'' are sometimes used to avoid confusion with the Indigenous Peoples of Canada. Categorically, Indian Canadians comprise a subgroup of S ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, specialising in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

. He was a long-time resident of

Edmonton, Alberta Edmonton ( ) is the capital city of the Canadian province of Alberta. Edmonton is situated on the North Saskatchewan River and is the centre of the Edmonton Metropolitan Region, which is surrounded by Alberta's central region. The city anch ...

, Canada. Subbarao was born in the small village of

Yazali, Guntur, Andhra Pradesh Yazali is a village in Guntur district of the Indian state of Andhra Pradesh. It is located in Karlapalem mandal of Tenali revenue division. Geography Yazali is situated to the south of the mandal headquarters, Karlapalem, at . It is spread ...

, India. He received his

master's degree A master's degree (from Latin ) is an academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice.

from

Presidency College, Madras Presidency College is an art, commerce, and science college in the city of Chennai in Tamil Nadu, India. On 16 October 1840, this school was established as the Madras Preparatory School before being repurposed as a high school, and then a gra ...

in 1941. He went on to complete a

doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' ...

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined ...

, advised by Ramaswamy S. Vaidyanathaswamy. He worked at Presidency College, Madras,

Sri Venkateswara University Sri Venkateswara University (commonly referred as S. V. University or SVU) is a public state university located in Tirupati, Andhra Pradesh, India. The university is named after Lord Venkateswara, whose shrine is located in the city. The ...

, and the

University of Missouri The University of Missouri (Mizzou, MU, or Missouri) is a public land-grant research university in Columbia, Missouri. It is Missouri's largest university and the flagship of the four-campus University of Missouri System. MU was founded ...

, before moving in 1963 to the

University of Alberta The University of Alberta, also known as U of A or UAlberta, is a public research university located in Edmonton, Alberta, Canada. It was founded in 1908 by Alexander Cameron Rutherford,"A Gentleman of Strathcona – Alexander Cameron Ruth ...

, where he spent the rest of his professional career. In the 1960s Subbarao began to study the

congruence Congruence may refer to: Mathematics * Congruence (geometry), being the same size and shape * Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure * In mod ...

properties of the partition function, p(n), which became one of his favourite problems. For example, he conjectured that if A and B are integers with 0 ≤ B < A, there are infinitely many n for which p(An+B) is even and infinitely many n for which p(An+B) is odd.

Ken Ono Ken Ono (born March 20, 1968) is a Japanese-American mathematician who specializes in number theory, especially in integer partitions, modular forms, umbral moonshine, the Riemann Hypothesis and the fields of interest to Srinivasa Ramanujan. ...

showed that the even case is always true and that if there is one number n such that p(An+B) is odd, then there are infinitely many such numbers n. The odd case was finally settled by Silviu Radu. A more general variant of the conjecture was formulated by

Morris Newman Morris may refer to: Places Australia *St Morris, South Australia, place in South Australia Canada * Morris Township, Ontario, now part of the municipality of Morris-Turnberry * Rural Municipality of Morris, Manitoba ** Morris, Manit ...

predicting that for any given r and m, there are infinitely many n such that p(n)= r(mod m). At the end of his life, Subbarao co-authored a book on partition theory with A.K. Agarwal and Padmavathamma.

Partition theory In number theory and combinatorics, a partition of a positive integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same part ...

is ubiquitous in mathematics with connections to the representation theory of the

symmetric group In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group ...

and the

general linear group In mathematics, the general linear group of degree ''n'' is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible ...

modular forms In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory of ...

, and

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...

. Thus, Subbarao's conjectures, though seemingly simple, will generate fundamental research activity for years to come. He also researched special classes of

divisor In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...

s and the corresponding analogues of

divisor function In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (includi ...

s and

perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. T ...

s, such as those arising from the exponential divisors ("e-divisors") which he defined. Many other mathematicians have published papers building on his work in these subjects. A prolific collaborator, Subbarao had more than 40 joint authors (including Paul Erdős, giving him

Erdős number The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individua ...

1). He continued producing mathematics papers into the final years of his life. He died in

Edmonton Edmonton ( ) is the capital city of the Canadian province of Alberta. Edmonton is situated on the North Saskatchewan River and is the centre of the Edmonton Metropolitan Region, which is surrounded by Alberta's central region. The city anc ...

at the age of 84. Subbarao was the father of Prof.

Mathukumalli Vidyasagar Mathukumalli Vidyasagar (born 29 September 1947) is a leading control theorist and a Fellow of Royal Society. He is currently a Distinguished Professor in Electrical Engineering at IIT Hyderabad. Previously he was the Cecil & Ida Green (II) C ...

Selected publications

References

External links

* {{DEFAULTSORT:Subbarao, Mathukumalli V. 1921 births 2006 deaths Telugu people 20th-century Indian mathematicians 21st-century Indian mathematicians Indian emigrants to Canada Indian number theorists Academic staff of the University of Alberta University of Missouri mathematicians Scientists from Andhra Pradesh Scientists from Edmonton People from Guntur district Presidency College, Chennai alumni Canadian mathematicians