A great friend of mine during many years in India has died recently and I want to pay my tribute to him. He was Professor P. C. Vaidya, head of the mathematics department in the Gujarat University. Scholar, intellectual, teacher, communicator, writer, founder of the first mathematics magazine in an Indian vernacular, heart and soul of the introduction of the ‘new math’ at the middle of the last century in Gujarat. On a certain occasion I invited him to give a talk to staff and students in our St Xavier’s College, and in my introduction of him I said before the public: ‘If I had done for the cause of the Gospel what this man has done for the cause of mathematics, I would be a saint.’ What prompted me to say that?

I was lucky to study the then new mathematics subject, ‘Modern Algebra’, at Loyola College, Chennai, a subject which had been up to that moment unknown in India. It was always introduced with the attempt at humour that Modern Algebra was not modern and was not algebra, but it was all the rage in mathematical circles at the time. The French Jesuit Fr Charles Racine had just brought from Europe the new subject and I took it for my optional subject in the last year of the degree course. Set theory, group theory, ring theory, field theory, vector spaces, matrix algebra, vector spaces were topics that were written about in research magazines but had not yet entered the classroom. Racine placed in my hand’s Nicholas Bourbaki’s Théorie des Ensembles which I eagerly enjoyed, and mathematicians know what I’m talking about, as Bourbaki never existed but his name brought a revolution to the field.

When I arrived in Ahmedabad to teach mathematics at St Xavier’s College, the subject was yet unheard of there since, as Racine himself had textually said, ‘the word “set” has not yet been pronounced in the classroom’, a thing which now seems impossible but such was the situation then. To introduce the new subject in Gujarat, Vaidya, who knew I had arrived fresh from Chennai with the new knowledge, asked me to conduct a summer course on Modern Algebra for postgraduate teachers so that, working our way from the top down, the new topic would filter down from postgraduate teachers to college teachers, high school teachers, primary school teachers through all the levels through the whole state. That was how I found myself conducting classes for postgraduate teachers before I had even given a single class to B.Sc. students. Thus I landed on my feet in Gujarat University. In my first class I somehow mischievously quoted to them Nicholas Bourbaki’s book as the first reference for the course’s bibliography, being fully aware that none of them knew French. I smiled wickedly as I watched the good professors writing carefully in their notebooks Théorie des Ensembles, knowing perfectly well that none of them would be able to read the book. That’s always one up for the teacher, and a little trick can go a long way to establish authority from the start. I remained all my life grateful to Vaidya for having introduced me so generously into the Gujarat University.

May is the month when the thermometers shoot up in Ahmedabad, and I would sweat copiously as I rode on my bicycle in a 42º sun in my new white cassock wrapped awkwardly around me and my bike as I pedalled along to Gujarat College where the course was being held, but it was worthwhile. If I was sweating bodily I made them sweat mentally. All learned eagerly the new concepts and theorems and problems so that they could soon go on to explain them in their classes to their students. One day I asked my teacher-students to propose a mathematical example of a binary relation that would be symmetrical, transitive, but not reflexive, and I promised as a prize a sweet I had in my pocket and which I placed on the table. Professor Rao, head of geometry, put up his hand, I invited him to come to the blackboard, he explained his example and I asked the remaining professors whether they agreed with him. They all said yes. But then something very upsetting happened to me. I had withdrawn to the far bottom of the classroom, and even if the professor’s demonstration and the agreement of all the others were overwhelming, I knew inside myself that the example was wrong. Something was essentially wrong with it. I was absolutely sure of it. But I didn’t know what was wrong! That is, all my body, my head and my soul and my whole being claimed that the example was wrong, I was feeling it in my veins and in my neurons and in all my bones, but I had not the slightest idea what exactly was the concrete failure in a seemingly perfect argument. And in a moment I would have to say something. An onslaught of scientific existential anguish swept through my whole being and froze me for an instant. I lived in that instant the situation where it becomes clear that it is not the brain by itself that understands and assimilates and reasons out and ‘knows’ but the whole body. Here was my body existentially bursting with the negative, while my reason found no cause for the earthquake. Overwhelming perplexity.

Just as well the hall was large, and I advanced slowly, very slowly to the front, measuring every step and teasingly delaying the moment of truth as far as possible. What was I going to say? How could I give the sweet to professor Rao when I inwardly knew that his example was wrong? But then how could I say it was wrong when I could not prove its falsehood? I reached the dais. I went up. I turned towards the class, and in that very moment the spark flashed in my brains and I knew the answer. I knew why the example was wrong. I smiled to myself and to my listeners who didn’t know what was waiting for them. I asked the class: ‘Shall we give Professor Rao the sweet?’ They all answered, ‘Yes!’ I took the sweet, played for a cruelly delectable moment with it in my hands, and then I slowly announced: ‘I am very sorry for two reasons. For one, I have to disagree with all of you, and for another, I appreciate professor Rao as a teacher and I hold him as a friend. But the example is wrong.’ There was a sudden and expectant silence. I turned to the blackboard. I wrote down the equations that showed up the flaw in the professor’s proof. The relation was certainly symmetrical and non reflexive as it had to be, and it also appeared to be transitive, and it was so in some cases, but not in all as it had to be, and I had just thought of a concrete case in which it was not. That was the crunch. Professor Rao got up a little excited and wanted to defend his case, but Vaidya told him gently, ‘Sit down, sit down, the father is right.’ All saw it, and in the end professor Rao too. I ate the sweet. It tasted great.

Vaidya and I took upon ourselves the mission to spread the message of modern mathematics from village to village, from school to school, from classroom to classroom, with true apostolic zeal and with a complete lack of financial interest. The great English mathematician G. H. Hardy (whose book ‘Pure Mathematics’ I translated into Gujarati at the request of the State University) who introduced mathematical rigor through the length and breath of the Commonwealth at the middle of last century, used to say about himself that he taught modern mathematics to students with the zeal of a missionary preaching the Bible to cannibals. That was what we did. A true mission for us both. We founded the first mathematical magazine in an Indian language of which he wanted to make me the editor, but I refused and told him I knew how to write but not how to make other people write. Every month we published in the magazine articles on the last tendencies, discoveries, and challenges of modern mathematics.  

I used to read three mathematical magazines without missing an issue. The American Mathematical Monthly, The Mathematical Gazette, The Mathematics Teacher. I waited for them with concupiscent delight, and I read them with greed in the University library out of which they could not be taken. One day I was interested in taking home an issue to take down a series of results from it, and I went to the librarian to ask for his permission. He answered me: ‘You can take it whenever you want, as you are the only one who reads these magazines.’ I’ve enjoyed reading those magazines and those books as much as reading other books and magazines that have interested and fascinated me along my whole life. Books on literature, on classical music, on languages and cultures, on history, on Latin America, on Christology, on Bible studies, on St Paul, on St Ignatius, on Eastern topics, on Zen, on cybernetics, on autobiographies. And I always derived as much satisfaction from my efforts to cheer up my mathematics students in their theorems and in their exams as I now derive from my efforts to cheer you up, my readers and listeners in my books and in my Web, in the midst of your problems and of life’s crises for you. All from the heart and full of joy and hope. It was a wonderful period in my life, and I remember my classes and readings and mathematical congresses and mathematical meetings with the same joy and enthusiasm with which I remember the Spiritual Exercises and confessions and Eucharists and the whole of my priestly ministry. I don’t admit one activity to be inferior to the other. I am as much of a person when I’m giving a mathematics class as when I’m saying Mass. Everything is service. Everything is joy. Vaidya, good Brahmin that he was and able to quote Sanskrit by the mile, was an atheist, and his life was far fuller and deeper than that of many faithful believers. Just as well by then I had already come across the Christian theologian Paul Tillich’s famous definition, ‘Whoever takes something fundamentally seriously in their life – be it their faith, their profession, or their wife – is not an atheist.’ It is our commitment that defines us.  

Vaidya had written a textbook on Mathematical Dynamics that was very popular with students and teachers and which had already sold out several printings. When the course of that subject was going to be changed in the new math, the publisher of the book came to know about it and, as he knew Vaidya had influence in the University, he told him to prevent the change from taking place, since otherwise the book would stop being published. Vaidya answered him it was he himself who had changed the course. He was not interested in money but in good education.

The University written exams are corrected by professors who change every year, and who do not know whose are the papers they are correcting, just as the students do not know who is the teacher correcting their papers. But some do get to know. One such student approached an examiner, told him he knew his paper was in his hands, gave him his number on the paper, confessed that he had not written very well, but he was offering a good sum of money for being passed. The professor answered him with indignation, ‘Don’t you know that I am Dr Vaidya’s student?’ Such was my good friend’s reputation.

When asked a few years ago what was his age he answered with a steady voice, ‘Minus twelve.’ That is, a hundred minus twelve. Counting from 100 down. 88. He has died at 93. He was in good health in body and in mind till his wife died twenty months before. Solitude after so many years of life together took him to his end in twenty months. Theirs was an exemplary marriage. His daughter, Smita, has informed me of his death. I’ve watched in Internet a video in which he recently talked on his favourite topics. I was touched by seeing his face and hearing his voice. Living with great men has enriched my life. He was one of them.