Erdos visits Madras
On a winter’s day in January 1975, two men walked down the sandy stretch of the Marina Beach in Chennai. It was still afternoon, but there was a breeze blowing, and they had the place pretty much to themselves. One was a teenager, a final year BSc student from the city’s Vivekananda College; the other an older, frail-looking foreigner. Initially, the older man asked about some landmarks on that stretch, including the impressive Indo-Saracenic building which houses the University of Madras, but after that the conversation centered on a topic in advanced mathematics – additive arithmetic functions. Clearly, this man was no ordinary tourist.
Paul Erdős, the legendary Hungarian mathematician, was on his first trip to Chennai, or Madras, as it was called then. At the age of 21, he had earned his PhD from the University of Budapest. This was in 1934. In the next six decades, he would go on to publish over 1500 papers, an unsurpassed record. He made fundamental contributions to certain branches of mathematics – number theory, in particular – and pioneered discrete mathematics, the foundation of computer science. A bachelor, he had no permanent job or home address. In the pre-Internet era, he connected researchers across the globe who might otherwise have toiled away on problems on their own, making little headway. His life’s mission to discover, and nurture, young mathematicians.
The young man who discussed additive functions with him on the beach was Alladi Krishnaswami was the son of Alladi Ramakrishnan, founder-director of the Institute of Mathematical Sciences (Matscience) in Taramani. Ramakrishnan had invited many Nobel laureates to the southern capital to talk about their work but Erdős had come mainly to speak to Krishnaswami.
Krishnaswami, who is now a professor of mathematics at the University of Florida, Gainesville, recalls how he had contacted the nomadic genius in the first place. As a BSc student, working on an independent project on number theory, he had made some discoveries and had come up with questions, which no one around him knew the answers to. He spoke to many people in the field in India and abroad. One name came up a lot – Erdős, but no one knew his exact whereabouts. So, they advised him to write to this expert in number theory c/o The Hungarian Academy of Sciences. Within a month, Erdős wrote back saying that he was going speak at a symposium at the Indian Statistical Institute in Calcutta that year — could they meet there?
Krishnaswami’s paper had also been accepted for the symposium, but he had his college half-yearly examinations and couldn’t possibly travel to Calcutta that week. So, his father, an invited speaker at the symposium, offered to present the paper. Krishnaswami recounts that at the end of the presentation, Erdős, came up to his father and said, “I am very pleased to meet you, but I’d be much happier to meet your son.” Erdős was leaving for Australia the next week but was happy to re-route that trip via Madras. He agreed to give a few lectures at Matscience as well.
This speaks volumes of his generosity, and his passion to encourage young mathematicians, says Krishnaswami. When he went to the airport to receive the visitor, he recalls being nervous but Erdős broke the ice by reciting a poem about Madras.
This is the city of Madras
The home of the curry and the dhal
Where Iyers speak only to Iyengars
And Iyengars speak only to God.
Erdős explained that he’d modelled it after the ditty, based on the old families in the New England area.
This is good old Boston
The home of the bean and the cod
Where the Lowells speak to the Cabots
And the Cabots speak only to God.
Old New England families are collectively known as the “Boston Brahmins.” The stereotype goes that these aristocrats value education from elite universities, appreciate the classical arts, and shun any ostentatious display of wealth. In Madras, Tamil Brahmins (Tam-Brahms) are either Iyers or Iyengars. Worshippers of Shiva, Iyers are known to pray at the temples of Iyengars. Iyengars, however, tend to worship only Vishnu. It is remarkable that Erdős understood this nuance.
On the drive to the Matscience campus in Taramani, the conversation flowed. Erdős, who stayed at the campus guest house, was a light eater. He enjoyed the local dishes with a side of yogurt to cut any hint of spiciness, says Krishnaswami, who was with Erdős’s throughout the trip.
Erdős also met the Governor of Tamil Nadu, K. K. Shah who was amazed that such a frail-looking man could withstand the rigors of international travel. Erdős explained that he wanted to collaborate with local talent everywhere. The minute he heard of the governor’s fund for scholarships to high school students who excelled in mathematics, he reached into his pocket and pulled out a sheaf of rupee notes – the amount he was given for lectures in Madras – and donated it to the fund.
Before he left, Erdős asked Krishnaswami about his plans for graduate school. Then and there, he wrote him a letter of recommendation to University of California, Los Angeles (UCLA). Ernst Straus, who had worked with Albert Einstein on relativity, would be his thesis advisor. It was a perfect fit, says Krishnaswami. In the fall of ‘75, he started graduate studies with a full fellowship in the US.
Erdős liked to fund worthy causes, not just math-related ones. On another trip to Chennai, when he heard of mathematician Srinivasa Ramanujan’s destitute widow, he wrote her a check. This quirky genius gave away most of his earnings. He never had a chance to meet Ramanujan whose work was an inspiration but read a great deal about India to make up for that.
Another thing Erdős liked to do was put up prize money for problems in mathematics – the amount varied according to the level of difficulty. He had few possessions and traveled the world, solving and posing research problems with collaborators.
Mathematicians of the 20th century like to brag about their Erdős number. Every coauthor of Erdős has the coveted Erdős number of 1. Krishnaswami has written five papers with Erdős, the first of which was based on the topic they discussed that afternoon on the Marina Beach. (That resulted in the Alladi- Erdős theorem, which Krishnaswami says remains a highly cited paper.) Publishing with Erdӧs’s coauthor would give a person an Erdős number of 2. Ramanujan had an Erdős number of 2. Though they never met, both had co-authored papers with the Cambridge mathematician G. H. Hardy. Einstein has an Erdős number of 2 via Straus. Erdos, who was at the center of it all, has an Erdős number of 0.
Today, no one can earn an Erdős number of 1. In 1996, Erdős died of a heart attack at the age of 83, when he was attending a conference in Poland. An obituary said that Erdős had often mused about the perfect death. It would occur just after a lecture, when he had just finished presenting a proof, and a cantankerous member of the audience would have raised a hand to ask, ”What about the general case?” He would have liked to respond: ”I think I’ll leave that to the next generation,” and keel over dead.
The ending was not so dramatic and Erdős’s legacy was far more substantial. Through his life and work, he continues to inspire mathematicians to find elegant solutions to long-standing puzzles and problems.
Krishnaswami Alladi, who edited his father’s memoir, The Alladi Diary, is currently writing his own memoir entitled “Mathematics: People, Personalities and the Profession” to be published by World Scientific.