MS Sparsha
There are only about 514 people in the world who can claim to have co-authored a research paper directly with Paul Erdős, one of the most prolific and eccentric mathematicians of the 20th century. Among them were a remarkable group of Indian and Indian-origin mathematicians whose encounters with Erdős created an unusual bridge between his itinerant mathematical world and India’s own rich tradition of mathematical scholarship.
Erdős wrote an astonishing 1,525 mathematical papers—more than any other mathematician in history. He had no permanent home, no conventional academic career and, for much of his life, no fixed address. He travelled from one university or mathematician’s home to another, carrying little more than his belongings and an inexhaustible appetite for problems.
His legendary arrival at a colleague’s doorstep was often accompanied by the simple declaration: “My brain is open.”
For those fortunate enough to collaborate with him, the reward was not merely a joint paper. It was an entry into one of mathematics’ most famous informal networks. A direct collaborator with Erdős acquired an Erdős number of 1. Someone who collaborated with an Erdős-1 mathematician became Erdős-2, and so the chain continued.
Among those with the coveted Erdős-1 distinction were several mathematicians of Indian birth or origin.
- Ramakrishna Reddy, associated with the University of Hyderabad and the Indian Institute of Science, specialised in mathematical analysis and co-authored an impressive 11 papers with Erdős.
- V. Subbarao, who travelled from Andhra Pradesh to Alberta, became an Erdős-1 in 1972. T. N. Shorey of the Tata Institute of Fundamental Research also entered this select circle in 1976, through work involving the prime factors of numbers of the form 2^p − 1.
Then there was Navin M. Singhi of TIFR, whose story captures the sheer spontaneity of Erdős’ mathematical encounters. During a 1975 lecture, Singhi reportedly solved an Erdős conjecture from the audience. Erdős’ memorable response was: “Vector spaces are my weakness.” The exchange eventually led to two joint papers in 1977.
- Ramachandra, another TIFR mathematician, co-authored two papers with Erdős in 1975. His contribution to mathematical scholarship extended beyond research: in 1978, along with R. Balasubramanian, he founded the Hardy-Ramanujan Journal.
Erdős’ travels even produced extraordinary personal stories. Krishnaswami Alladi, who moved from Madras to Florida, recalled an encounter in which Erdős rerouted a flight through Madras simply to meet him. Their collaboration produced five papers beginning in 1977.
Other Indian-origin mathematicians in this remarkable network included Gutti Jogesh Babu, with three joint papers from 1975; Prasad Tetali, known for his work in combinatorics and probability; K. Vijayan, who co-authored a 1985 paper on random graphs with Erdős and Louis Caccetta; and Renu C. Laskar, a distinguished graph theorist whose correspondence with Erdős reportedly carried the affectionate salutation “Uncle Paul.”
Brothers M. Ram Murty and V. Kumar Murty, who traced their roots to Guntur before building distinguished academic careers in Canada, both became Erdős-1 through the same 1987 paper.
And then there was Hansraj Gupta, born in Rawalpindi in undivided Punjab. He became an Erdős-1 in 1976 and later served as president of the Indian Mathematical Society.
What makes these stories remarkable is not merely the mathematics. They reveal a largely invisible network of intellectual friendships, curiosity and collaboration that crossed continents, institutions and generations.
There is an even more poetic connection. Srinivasa Ramanujan, India’s legendary mathematical genius, is generally assigned an Erdős number of 3—through G. H. Hardy, who is Erdős-2. Erdős and Ramanujan never met; Erdős was still a child when Ramanujan died in 1920.
Yet mathematics, like history, has a way of connecting people who never crossed paths.
From Chennai and Hyderabad to Mumbai, Andhra Pradesh and undivided Punjab, these Indian mathematicians became part of Paul Erdős’ extraordinary intellectual journey. They may not always occupy the popular spotlight, but their names form an important—and fascinating—chapter in the story of modern mathematics.
That, perhaps, is what makes them true unsung heroes: their greatest achievements were often written not in headlines, but in equations, conjectures and papers that continue to influence the world long after their authors have left the room.
