### Tribute to Shreeram S. Abhyankar

**11-06-2012**

*Shreeram S. Abhyankar, Marshall Distinguished Professor of Mathematics, passed away on November 2, 2012. Below is a tribute from two of his former students, David Shannon and Avinash Sathaye.*

On the morning of Friday, November 2, 2012, at the age of 82, Professor Shreeram Shankar Abhyankar, Professor of Mathematics at Purdue University since 1963 and Marshall Distinguished Professor since 1967, unexpectedly passed away. At the time he was in his study at home, at his desk, doing what he loved—mathematics. Just a few days before, Ram, as he was known to his friends and colleagues, had completed a paper that was a joint work with Professor Enrique Artal on dicritical divisors, and he had now turned his attention to some work on quadratic transformations that he had begun in the summer. As he put the finishing touches on a proof of a key theorem in the paper with Artal, he had called friends, proudly sharing the significant role his grandchildren had played in the proof. The distraction of playing with grandchildren, he said, allowed his mind to see the final essential step in his intricate proof. To outsiders, his passion with mathematics seemed all encompassing. But his friends also saw the devotion and pride that he had in his wife of 54 years Yvonne, his children Hari and Kashi, and his four grandchildren Maya, Kira, Kaia, and Ela. To be doing mathematics and playing with his grandchildren was true joy for Ram.

Professor Abhyankar had being doing mathematics essentially all his life. He was fond of telling stories about when he was very young and would want to study only mathematics. His father tried to make him stop this extreme obsession, even to the point of locking up the mathematics books. Yet, he would find mathematics books and read them late at night! In 1952 he was accepted to do graduate work in mathematics at Harvard University, but because of illness on the boat coming to the U.S. from India, he arrived on a Saturday several days after the semester had started. By chance, and to the good fortune of those of us who work in the fields of algebraic geometry and commutative algebra, he accidentally met Professor Oscar Zariski, one of the giants in twentieth century algebra and geometry. Ram was convinced by Zariski to take a course in projective geometry that Zariski was teaching and soon Ram became a student of Zariski, writing his dissertation in the important algebraic geometry field of resolution of singularities, especially the finite characteristic case. Ram was proud to note that many of the ideas that were emerging to be important in his current research were initially developed and discovered in the work he did in this thesis. Upon completing his graduate work at Harvard, Professor Abhyankar held positions at several top universities including Harvard, Columbia, Cornell, and Johns Hopkins before coming finally to Purdue. During his long tenure at Purdue, he would often visit India, partly to visit parents, but also to search for and nurture students of mathematics. He often visited numerous universities around the world, always interacting with his mathematical family. During the over sixty years of doing mathematics, he made major contributions to algebraic geometry (e.g., resolution of singularities), commutative algebra (e.g., epimorphism theorem and the Jacobian problem), group theory (e.g. representing groups as Galois groups), combinatorics (e.g. Young Tableux). In all he wrote over 200 papers and several books and gave invited lectures at countless conferences and universities worldwide. To adequately describe all of his mathematical contributions would require a very long paper written by experts in several fields. Many of his books and papers were written for experts, well versed in the fields of algebraic geometry and algebra. But he also wrote for the non-expert as well. For example his paper "Historical Ramblings in Algebraic Geometry" received a Chauvenet Prize from the Mathematical Association of America, and his book *Algebraic Geometry for Scientists and Engineers* has been very popular to a variety of audiences. His latest *Lectures on Algebra *is likely to be another widely read reference book.

His influence stretched beyond "pure" mathematics to fields like engineering and computer science. In fact at Purdue, in addition to mathematics he held professorships in computer science and industrial engineering. In his course this semester (he was still teaching a course each semester), there were students from mechanical engineering and electrical engineering as well as mathematics. Ram was proud of these connections and would simply say he taught the same mathematics, but people from all these other disciplines had just discovered the relevance and value in this mathematics. Thus in courses and seminars there would often be found students and professors from disciplines other than mathematics. And he would often be invited to give lectures at a variety of conferences and workshops.

Finally one must note Ram's passion for teaching, for collaboration and for sharing the stories of the history of mathematics and the culture and history of India. He had nearly 30 "official" students, but many more would declare that they were really students of Ram as well. His students will all describe his patience with them as they struggled with complex mathematical ideas and his ability to guide them to important problems and encourage them to the successful solution of these problems. Truly he was a teacher that was able to nurture students, to give them the self-confidence to do mathematics even when they were discouraged, and to help them discover the beauty in mathematics and the doing of mathematics. Many of his papers were collaborations, which would often be derived from his keen insight to get at the heart of the problem. But he also found opportunities to do joint work with his graduate students, as illustrated with two papers he jointly published this past spring. He was an avid reader of the history of mathematics. Having read some classic texts in analysis and special functions when he was young, he had continued interest in these topics (especially when power series were involved), not just algebra and geometry. And of course he never tired of lauding the contributions of Newton and some of the other pre-20^{th} century mathematicians like Galois, Riemann, Sylvester, Salmon, et.al. And to those of us who were unfamiliar with the history and culture of India, he enthusiastically shared with us the many stories of Indian epics like Mahabharata. Reading and discussing history, mythology, and philosophy commanded an equal amount of his passion.

Statements of G.H. Hardy are often quoted. "No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." And "Young men should prove theorems, old men should write books." Well, this may be the case for many of us, but it certainly was not case for Ram. He was as mathematically alive and vibrant at age 82 as he was at 22. As with other great mathematicians, his legacy will certainly include the many mathematical theorems that he proved or to which he made a contribution. But his legacy will also include the inspiration and encouragement that he gave to so many others.