By the Numbers

Indian mathematicians from an elite club remember the man who got them there

Paul Erdős, who died in 1996, authored 1,525 papers and was the most prolific mathematical collaborator of all time. COURTESY COLM MULCAHY / WWW.CARDCOLM.ORG
01 February, 2014

IN EARLY 1975, the Hungarian mathematician Paul Erdős delivered a lecture at Colorado State University in Fort Collins, USA, during which he described a conjecture in graph theory that he had been unable to prove using methods from the field of combinatorics. Navin Madhavprasad Singhi, then a 25-year-old visiting scholar at the university, was in the audience. Singhi realised that he could solve the problem using vector spaces, a method he was familiar with. Excitedly, he approached Erdős after the talk and told him so. When Erdős saw the value of Singhi’s approach, he remarked, “Vector spaces are my weakness.”

“That was his humility,” Singhi said over the phone last month from Mumbai, where he works at the city’s Tata Institute of Fundamental Research. Erdos and Singhi went on to collaborate with the Soviet mathematician Michael Deza on a paper that used Singhi’s ideas to prove the conjecture Erdos had described. This makes Singhi one of an elite group of around 500 mathematicians with an Erdos number of 1—an instantly recognisable marker in scientific circles, which means a scientist has jointly written at least one paper with Erdos. (Singhi went on to co-write three.) A researcher who has authored a paper with someone with an Erdos number of 1 receives an Erdos number of 2, and so on. It’s the science and math world’s little degrees-of-separation game.

Paul Erdos, who died in 1996, authored a record 1,525 papers—the most ever by a mathematician—and was also the most prolific mathematical collaborator of all time, working in subjects such as combinatorics, graph theory, probability theory and number theory. Erdos lived as a vagabond, travelling the world with no job and few possessions, meeting mathematicians and scientists and writing papers whose impacts now stretch beyond mathematics into the social sciences, cryptography, and even the study of biological networks.

Renu Chakravarti Laskar, an Indian professor of mathematics at Clemson University, USA, who also has an Erdos number of 1, told me of Erdos’s affable and unassuming tone in his letters to her. She first met Erdos at a conference in Colorado in the late 1970s. Soon afterwards, he wrote to her enquiring about the problems she was working on. In her response, Laskar addressed him as “Professor Paul”. Erdos prefaced his reply by saying, “Don’t call me professor. Call me Paul; if you cannot call me Paul, call me Uncle Paul.”

Among the 20 or so Indian mathematicians Erdos worked with is Krishnaswami Alladi, today a professor of mathematics at the University of Florida, USA. In 1974, when Krishnaswami was studying for his undergraduate degree at Vivekananda College in Madras, he grew interested in number theory. He came upon a particular conjecture in prime numbers that he was unable to prove.

As he struggled with it, Alladi’s father, a renowned mathematician himself, suggested he write to Erdos. He did so, and received a response within two weeks. Erdos re-routed a journey from Calcutta to Australia through Madras so that he could meet Alladi. “I was very nervous,” Alladi said of their first meeting at the airport in Madras. Erdos seemed to sense Alladi’s diffidence, and broke the ice by reciting a poem about the pecking order in Madras’s caste system, adapted from a similar verse on the pecking order among upper-class families in Boston, USA. “I was immediately at ease,” Alladi said.

Among the mathematicians I spoke to, some believed Erdos chose his vagrant lifestyle because of his love for people, but others felt it stemmed from his single-minded pursuit of his subject. Prasad Tetali, a mathematician at the Georgia Institute of Technology in Atlanta, USA, with an Erdos number of 1, told me of the time in 1996 when Erdos found out that Tetali and his wife were considering buying a house. “Don’t you think that is a big nuisance?” Tetali recounted Erdos asking him. “The choices he made—to live singly, to not have a permanent home—were the key to his freedom,” Tetali said. “He really had no impediment in pursuing what he enjoyed the most.”