**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.

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