My Encounter with Grothendieck

Gordon Edwards

In the summer of 1970, I was at Queen's University in Kingston, Ontario. I was in the process of getting my Ph.D. in math under Paulo Ribenboim when I met Grothendieck and joined the "Survival" movement.

I had never really joined anything before. It was not with any idea of changing my life plan that I went to a conference at l'Université de Montréal -- just the prospect of hearing about some new mathematics and seeing the famous Alexander Grothendieck in action.

It was quite a shock to find myself coming home from this conference in the almost absurd role of (1) co-founder of the movement "Survivre -- et Vivre" (or in English "Survival") along with Grothendieck and two other people whom I have never seen since, and (2) the editor of the English-language edition of the movement's newsletter, which instantly had subscribers in thirteen countries -- those folks attending the conference who had signed up on the spot.

Grothendieck is a very strong-willed individual. I was much moved by his passionate manifesto (written in French) entitled Scientists and the Military Apparatus, which led me to join the Survival movement. The movement was based on a perception that four billion years of evolution are in jeopardy due to the scientific and technological forces unleashed by one species -- humans -- most obviously through all-out nuclear war, whether accidental or malicious. The movement called on scientists to put the survival of the planet first, ahead of the short-term agendas of corporate or political sponsors or employers.

Scientists were urged to become activists, working together urgently on an equal basis with non-scientists, helping to demystify the science needed for understanding this crisis and developing sound strategies for a sustainable future. One important goal was to eliminate the suicidal institution of war -- the greatest single threat to our survival -- and so the movement required that its members adopt a policy of total non-cooperation with the military.

All of this earned my heartfelt support. Still Grothendieck had not secured any commitment from me to act as the newsletter editor. When he publicly announced my "appointment", it was a complete surprise. I protested my unsuitability and suggested his good friend Linus Pauling play that role (he was to visit Pauling within a few days). He shot back, "Excellent suggestion. Until he agrees, you do it." I never heard how Pauling reacted to the proposition; the job was left up to me.

Returning to Kingston, I felt as if I had been picked up by the scruff of the neck, spun around vigorously, then hurled back down with considerable momentum in a brand new direction that I had to scramble to adjust to. My whole life's course had been changed, as it were, by a chance encounter.

I duly started laying out successive issues of Survival on my kitchen table, inspired by the French edition edited by Grothendieck in Paris, but with a uniquely North American slant based on my own research. I would dutifully get the issues printed up in tabloid format, bus them to my home, and mail them out to the 1500 to 2000 subscribers. All without a budget or an office or a staff. And without making much progress on my Ph.D.

I translated Grothendieck's original manifesto into English as well as I could, and it was published a year later in the series Queen's Papers in Pure and Applied Mathematics, under the title The Responsibility of the Scientist Today. The translation was amateurish: my French was not great, and still isn't. Nevertheless the text seems oddly contemporary still, and for me, it encapsulates the most significant transformation of my professional life.

At a certain point, Schurik (as his friends called him) started to wonder why his North American chapter of Survival was not flourishing. He decided he would have to come to see me, to light a fire under me or some such thing. The University was thrilled beyond measure to learn that the world's greatest mathematician wanted to come to Queen's for three months -- what a coup! I don't know how many people, apart from my supervisor Paulo, knew that he was coming to see me.

That's how I came to write a thesis based on a conjecture of Grothendieck's about the Lie algebras of infinitesimal group-schemes. I managed to disprove the conjecture. Everyone agreed this was an achievement, but those on my examining committee for the degree were unfamiliar with the concept of infinitesimal group-schemes; they asked if I could give them a few tutorials so they would be ready to question me at the oral! My old friend from Chicago, fellow Canadian Irving Kaplansky, kindly agreed to be my outside examiner. I got my Ph.D. with jubilation all around, in a subject area that I have never pursued since. My Survival "mission" was taking more and more priority.

The next step in my career started somewhat unusually: I went to a post-doctoral appointment at the University of British Columbia to study the Economics of Ocean Fisheries with a fellow Survival member, Colin Clark. Colin had taken the message of Survival to heart, using his sabbatical year to retrain himself from his previous abstract research in Sobolev Spaces to the practical study of renewable resources -- in particular, the threat of the extinction of ocean fisheries. He rapidly became a real expert on the subject, publishing some striking results. I ended up co-authoring a paper published in the Journal of the Fisheries Research Board of Canada!

In my spare time, I was learning about nuclear power, nuclear wastes, and the health effects of low-level radiation, from such amazing sources as John Gofman at UC Berkeley and Carl Morgan at Oak Ridge, and I began writing on these subjects. It caught my eye when a professor in the UBC Physics Department was quoted in the local newspaper saying that the probability of an accident at a nuclear power plant was about the same as the probability of two fully loaded jumbo jets colliding in mid-air over a crowded baseball stadium during the seventh game of the World Series.

I wrote a letter to the editor saying that as a mathematician, I objected to the language of probability theory being misused by a professional scientist as a mere rhetorical flourish in expressing a personal opinion. I provided some quotes from respectable government and industry studies to the effect that the true probabilities aren't really known.

In response, the head of the Physics Department wrote a letter to the President of the University complaining about my "activities", because in my letter to the editor I had identified myself as a post-doc at the University. The head of the Math Department received complaints from physicists that I was guilty of "unprofessional behaviour". One nuclear physics professor actually offered to throw me bodily down the front steps of the Physics Building if I didn't leave during a university open house. I didn't leave, and he didn't make good on his promise. But I remember saying to him, "What about freedom of speech?" and his reply, "You are unfit to be granted freedom of speech."

I gathered some arguments into a memo that speaks to issues still current today. I distributed this "open letter" to all faculty and grad students in UBC Physics, along with a challenge to hold a public debate on nuclear power. The culmination was a two-hour debate -- actually two one-hour lectures, one pro- and one anti-nuclear-power -- televised on the Vancouver community affairs channel.

This experience extinguished my ambition for a university career: I realized that I would probably face this kind of reaction wherever I went. I have been teaching at a CEGEP (Quebec pre-university college) ever since, until my retirement in 2010, meeting absolutely no restrictions on my freedom of speech, and it has suited me very well. Indeed my research branched out in an interdisciplinary way, so that instead of becoming increasingly inward-looking -- as the pursuit of mathematics can often become -- my mathematical horizon widened to intersect more and more other disciplines.

I also landed a mammoth assignment from the Science Council of Canada: conducting a study of the role of the Mathematical Sciences in Canadian education, industry, government, and science, published in eight volumes. Aside from that -- and of course the Survival newsletter for the five years it lasted -- my focus has been on nuclear technology: nuclear armaments, reactor disaster potential, radioactive waste management, and medical effects of atomic radiation....

In 1974, India's first A-bomb test used plutonium from a Canadian-donated reactor, grimly refuting the protestations that nuclear power is benignly peaceful and irrelevant to the threat of nuclear war. In 1975, homes and schools in Port Hope, Ontario, had to be evacuated due to radioactive contamination from a government-owned refinery of nuclear fuel, contradicting safety assurances given by the industry. Plainly there was need for an organization such as the Canadian Coalition for Nuclear Responsibility (CCNR). Thirty of us got together in a basement at Concordia University and founded it. It thrives, and I have been happy to serve as its President and its most frequent spokesperson.

At the start, CCNR was without a nuclear specialist. Of course, I had irreproachable credentials (gold medal in Math and Physics as an undergraduate at Toronto, solving a Grothendieck problem for my Ph.D., with Kaplansky as my external examiner) -- but only as a mathematician, which would no longer be my specialty except as a teacher. So I set about making myself a nuclear expert.

In 1974, I was declared the winner of a one-hour TV debate with Edward Teller as my distinguished opponent. Over the years, I have been hired as a consultant to government bodies, such as the Ontario Royal Commission on Electric Power Planning and the Auditor General of Canada; to the United Steelworkers of America; and to many native organizations, such as the Assembly of First Nations. And my advice has stood up well. My competence is still sometimes challenged by industry representatives; perhaps they haven't looked up my track record, or (I suspect) they just can't believe that anyone can know the field except those who followed the prescribed courses in engineering leading to work in the industry, and who subscribe to the attitudes that prevail in such circles.

My perspective on the social responsibility of scientists is rather special, clearly. I was dragged into this posture kicking and screaming at first, you may say, but this was followed by a kind of resignation and ultimately by a real sense of satisfaction. For the first year, though, there was a lot of inner conflict. Why am I doing this? Who am I to be telling anyone anything? What if the movement attracts lunatics or dangerous radicals? Won't I be blacklisted and filled with regret?

Working through this, I realized that I felt a whole lot more human being active than inactive. More optimistic. Less scared, even. My philosophy became one of "functional optimism": you ought to be optimistic not because it is particularly rational, but because it works better. Without optimism, you cannot really do anything, or at least you can't do it well. In this way, optimism becomes its own rationale.

Grothendieck helped me profoundly. He made me see that the arguments people give for the futility of the struggle are really rationalizations for doing nothing at all. Yet doing nothing at all is clearly the only course that is guaranteed to be futile! He made me realize that action invigorates thought: as you act, your thoughts evolve. Those who think but do not act are locking themselves into a prison of their own making, where truly strong and independent thoughts are not possible for lack of reinforcement from action.

Grothendieck also observed that science is based on the experimental method -- therefore: How do you know your actions will be ineffective if you never try them out? So act! Wrestle with the problem. See what the results are. That's the experimental method applied to life.

I have been amazed at how many actions that seemed hopeless at the outset turned out to be remarkably effective. Without such successes, I would probably have given up at some point; but I have kept plugging, and sometimes succeeding. Here is a partial list of accomplishments that I have played some role in:

I have never regretted that Schurik put me on course to become a scientific activist and to achieve some notable results. Still the list is painfully short, relative to the work remaining to be done: to weed out technologies that are inconsistent with sustainability, and above all, to eliminate the danger of nuclear war altogether.

Given an indefinite time span, any event with non-zero probability is certain to occur. We are confronted with an unacceptable risk to our survival, so prudence demands that we reduce its probability to zero. This requires a determined effort of education, reflection, and action.

It is my belief that scientists have a uniquely valuable role to play in this endeavour, partly because they have the ability to decipher the jargon of science and mathematics for others -- to make the relevant details comprehensible -- and partly because they can often envisage sensible alternatives. The first step in solving a problem is to understand it correctly. The second step is to discover a context in which it can be resolved.

In Grothendieck's words, we scientists have a responsibility as members of civilized society to "bridge the gap between science and life".


Canadian Coalition for Nuclear Responsibility