ISSN 1556-4975

OffCourse Literary Journal

 Published by Ricardo and Isabel Nirenberg since 1998


Chapter 14 of a memoir by Ricardo Nirenberg

Exact, Physical, and Natural Sciences.

Having read this far, the alert and critical reader may ask how come I chose Exactas instead of Filosofía y Letras, I whose favorite subject in high school was Latin, and who was congratulated on my performance in the philosophy exam and in no other.  I am as much in the dark as you are.  The only conclusion I’ve been able to draw after long scrutinizing my memories, is, quite simply, that I am stubborn.  I find support for this conclusion as I recall my very first experiences at school: when I was four and was in kindergarten, the teacher, exasperated, said to me, — No seas cabezón (Don’t be headstrong).  I didn’t precisely know the meaning of that word, yet I felt offended anyway and doggedly refused to go back to that school, which proves beyond reasonable doubt that I’m ab ovo very, very stubborn.  Therefore, once I had decided, early in life, that I would be a chemist, I would contemplate no other possibility.

I am not complaining.  Trying chemistry, then physics, and eventually settling on math, I feel I got a better deal than I'd have had by going directly into philosophy and the humanities.  Partly, because the faculty at Exactas was better, and partly because I’m inclined to agree with Plato, who thought that the basics of math, or geometry as he called it, are a necessary preparation for philosophy, a propaedeutic, a preface to a good education.  We shouldn’t forget that Virgil spent some time as a young man in Rome and in Milan studying math; the catch is, however, that like Virgil, one must leave math behind, since professional mathematicians cannot be said to be well educated, any more than one who reads only prefaces could be called a well-read man.

Exactas was not only a place to develop an intelligence but rather, as the poet John Keats once put it, just the place to school an Intelligence and enchant it so as to make it a Soul.  I was struck by the number of refugees or children of refugees from the wars in Europe who studied there: French Jews like Danielle Gattegno and Mireille Perec, who became inorganic chemists, several Italian Jews who shared the illustrious name Segrè, or a strapping young man, Manolo Calvelo, a refugee from Spain’s Civil War, the son of anarchists, who wore sandals, unusual in Argentina at the time, and was an impassioned political speaker.  Cesare Mazzonis, born in Turin, went back to Italy after getting his chemistry degree, switched to music, and eventually became Artistic Director of La Scala de Milano.  Or Jacques Mehler, born in Barcelona in 1936, whom I met in 1957, when he was about to graduate from Exactas with a chemistry degree, and who later became a psycholinguist in Paris at the École des Hautes Études en Sciences Sociales.

In high school, at the Colegio, just as in grammar school, most opportunities to develop and fertilize the critical intelligence were ignored or, more perversely, avoided.  Take for example the national anthem and the national coat of arms: the French Revolution’s triple motto, « Liberté, Égalité, Fraternité » is translated into graphic symbols in the Argentine coat of arms: two clasped hands (fraternity) holding a measuring rod (equality) with a Phrygian cap on top of it (liberty).  That was fine, but when the motto appears in the national anthem, cloaked in the stale language of monarchic Spain, the result is ridiculous, with phrases like “Ved en trono a la noble igualdad” (See Noble Equality sitting on her throne).  But to point this out to the students would have been sacrilegious: the mission of the teachers was to nurse not intelligent critics but unquestioning patriots.  In 2007 Isabel and I flew to Buenos Aires to attend the 50th anniversary of my class graduation from the Colegio, and there, at the aula magna where Einstein had explained Relativity in 1925, the authorities had all of us men in their late sixties stand up and sing the Marcha Aurora, a hymn to the Argentine flag bursting with absurdities and sunk in the unbuoyant seas of commonplace.  To my amazement, I saw that from not a few of my old, wrinkled fellows’ eyes, tears were flowing from emotion.

The spirit at Exactas was the opposite, fiercely critical, or so it seemed to me that first year, in which I bit on more than I could swallow.  I had not realized that this was not the Colegio, where one always took seven or eight subjects at the same time, that here at Exactas every course meant not only a “theoretical lecture” several times a week, but also the “practical works,” where one tried to do exercises and solve problems, and the hours of lab practice required by the chemistry and the physics courses.  There was no way I could successfully and simultaneously have taken Mathematical Analysis One (Calc 1, as it is usually called in the U.S.), Algebra, Physics One, and Intro to Chemistry, in my first semester, and I didn’t: I failed the final exam of Analysis One.  That I can now recall the details of that flunk attests to its psychological import.

My flunker was Professor Manuel Sadosky, who had published, with his collaborator Rebeca Guber, a best-selling textbook on Calculus 1.  He asked me to show why the derivative of ex is ex, and the derivative of ln(x) is 1/x.  I was going in circles, I could prove one by using the other, but not from scratch.  That was my inauspicious introduction to Manuel Sadosky.  He and his family — Cora Ratto, his wife, and Corita, their daughter — had a strong influence on post-Perón Exactas, and left their mark on me.  One of their valuable efforts was on behalf of Mischa Cotlar, a Ukrainian Jew born in 1913 who had emigrated to the River Plate in 1928, like my grandparents had some twenty years earlier.  He had been a member of the Math Institute at the University of Cuyo until the ouster of Perón, and 1957, my first year as a student at Exactas, was Cotlar’s first year as a professor there; he had got the job partly thanks to the influence of Manuel Sadosky.  The first thing I heard Cotlar say has been, ever since, present in my mind.  The illustrious John von Neumann had died in February of that year, and Cotlar commented: “He was a very great mathematician, but a very bad person.”

I had little idea at the time either of von Neumann’s mathematical achievements or of his doings; nevertheless, the phrase resonated: it seemed, from the beginning, atypical.  But why?  I could not put my finger quite on it.  I thought of William Blake’s view of Isaac Newton as a demonic force oblivious of the earthly. What was normal in a Romantic poet sounds surpassingly strange if it comes from a scientist.  Is it the mix that sounds strange?  The mix of Kant’s pure reason with his practical reason, of logic with ethics: we have been long used, at least since the Enlightenment, to keep them separate.  This may help me understand why the first utterance I heard from Mischa Cotlar impressed me so much; most people, however, on first meeting Mischa were most impressed by his modesty.  — “You know so much more than I,” he would often say to a student: no wonder a number of my colleagues thought such modesty smacked of hypocrisy.  They didn’t suspect that Mischa, a student of Vedanta, had likely undergone an enlightenment different from the Kantian sort.

You’ll probably be reminded of Oppenheimer, the better-known, tormented scientist who couldn’t separate knowledge from ethics either and who learned Sanskrit in order to read the Gita in the original.

Returning to Manuel Sadosky, my flunker in the Calc 1 exam in June of 1957: in November of that same year José Babini, the historian of science, was succeeded as dean of Exactas by Rolando García, a meteorologist, and Sadosky became vice-dean a couple of years later.  As for myself and Calc 1, I took the exam again at the first opportunity, after studying seriously and solving thousands of problems: this time I did well.  I was talking a little while ago of my stubbornness which, I suspect, pushed me into studying chemistry; now that same stubbornness was playing a role in pulling me in the direction of math.  Or perhaps it was a mix of stubbornness, pride, and contrariness, as if I were saying to Urania or to my own star, “Flunking me in math was a low blow; now I’ll show you!”

As it turned out, chemistry was not fulfilling my expectations: chemistry was full of facts but, at this level, poor in explanations.  “You’ll have to wait until you study quantum mechanics,” I was told by the Jefe de Trabajos Prácticos, the guy in charge of our lab sessions, when I asked him, “Why is this or that so?”  I began to mull that over and wonder, “Then why not start instead by studying physics?”  And even though I had an excellent and congenial lab partner, the cellist Edgardo “Buby” Zollhofer, as I have told in the chapter “Early Music,” neither of us was excited about the chemical experiments we were told to perform.  We talked about music mostly.  I remember telling him that I found Carl Maria von Weber’s music much easier to understand than Anton Webern’s, and he replying that it was the opposite with him.  The following year, 1958, Buby quit chemistry and Exactas to devote himself to music, and the results proved the wisdom of his decision — you can easily find in YouTube excellent recordings from the 1980s by the String Quartet Buenos Aires, in which Buby played the cello —, while I switched from chemistry to physics, only to switch again to math in 1959, a slide toward the more basic and abstract, the self-sufficient.

But I keep getting ahead of myself.  In October of 1957, the Soviets launched the first Sputnik, starting the space race, an event that improved the professional prospects of young science students all over the world.  My father had been worried when I entered Exactas to study chemistry. “Why don’t you try the School of Medicine,” he would say, “that way you will assure your financial independence.”  Nothing to do with his pocket: the University was completely free, as was the Colegio and all public education in Argentina.  He just didn’t see much of a future for chemists.  In time, as I switched to physics and finally to math, he became even more worried.  For global economic issues his nose, even though robustly Jewish, was as poor as it was for local business.  On that October night when the Sputnik was supposed to be visible from Buenos Aires some students and I went up to the roof of Exactas (you may remember I had been there two years before, but don’t feel bad if you don’t), to try to sight the satellite.  Don Julio Rey Pastor, a Spaniard who arrived in Argentina in 1917 and is considered the founder of the Argentine school of mathematics, was up there with us.  As none could see a trace of the Sputnik in the sky, don Julio proposed, — “Perhaps we should consult with Sadosky.”

That piece of sarcasm subsisted in my memory together with a perplexity: was don Julio being merely malevolent — perhaps he resented the fact that the calculus book by Sadosky & Guber sold better than his own, written with Pi Calleja and Trejo — or was he right, that Sadosky had a special place in his heart for the Soviet Union?  As I was writing this chapter, I consulted my friend Pablo Jacovkis, who was Dean of Exactas in 1998-2006, and who wrote an excellent biography of Sadosky.

Sadosky, who died in 2005, Pablo replied, was always pro-Soviet; not only that, but he belonged to the Argentine Communist Party until he was expelled in 1946, perhaps because he disagreed with Secretary-General Codovilla’s positions in regard to Peronism.  In 1949 he published in Science and Research (the journal of the Argentine Society for Progress in Science) —while knowing nothing about genetics — an article in defense of the doctrines of Lysenko, convincing proof of his love for the USSR. 

Rey Pastor had a point, therefore.  It had been clear to me from the beginning that the Communist Party was the dominant force among the students, so that it controlled the student centers — the chemistry student center, the physics, math, and meteorology student center, and the geology and biology student center.  The “Centros” were more important than the name suggests, since the students participated significantly in the governance of the University and of each of the schools, in particular of Exactas.  Their adherence to the same opinions to within a narrow margin was as strict, perhaps, as among the Nazis I had met, like Adolfo Urruty and his father the colonel, or among the members of Catholic Action at the Colegio; but here, among the communist students, it was more conspicuous.  In my first year at Exactas, I remember them buzzing from one closed-door meeting to another: after Khrushchev’s secret speech, “On the Cult of Personality,” in February of the previous year, they seemed confused — what should they be saying about Stalin now? — and messengers from higher levels were coming to the old and dear building at Perú 222 to transmit instructions to the troops.  My non-communist comrades called them bolches teledirigidos, remote-controlled bolshevists.  As you can see, I was well aware that the Communists were prevalent among the students, yet I found it hard to believe that a prestigious professor like Manuel Sadosky was a Stalinist.

But then I was quite naïve.  I observed some pages back that I’ve been from the beginning a mix of stubbornness, pride, and contrariness, each of which conspires in its own way against my joining other fellows in any kind of ideological party, sect, cenacle, or clique.  Wander alone, like the rhinoceros.  Is my opinion the same as yours?  I don’t believe it: dig a little deeper, and you will find some difference.  Be aware that not only two different leaves in a tree cannot be the same, as Leibniz taught, but not even one leaf can remain the same, identical to itself.  Still and all, were a foundation be founded to defend humanity against the ravages of Sameness, I would not join it.  I have mentioned that at the start of my second year at Exactas I switched to physics; I had already taken Physics I, so now I was taking Physics II, which involved optics.  Our professor, Enrique Gaviola, a man in his late fifties, was a celebrity, considered the first Argentine astrophysicist, director of the Astronomical Observatory in Córdoba, and it was rumored that he had studied with Max Planck, Max Born and Albert Einstein at the University of Berlin. 

In one of his lectures, he used the words “coherent light,” and since he didn’t explain further, somebody asked what coherent light was.  His answer was surprising: — “It is light from the same photon.”  Here we go, I thought, the Empire of the Same strikes again!  Why couldn’t light beams from different photons be coherent?  As far as I could see, it is only necessary that they have the same wavelength (color) and be in phase.  That was the first bad omen about the possible benefit of studying physics in Exactas to my disoriented soul.  Another physics professor I met at that time, Mario Bunge, was my advisor, assigned by the Physics Dept.  He came from a distinguished and wealthy family originally from the Low Countries, part of which, in partnership with the Born family, founded in the 1880s what soon became the largest Argentine corporation, Bunge y Born.  I never took the trouble to find out what the relation was between the physicist and the wealthier part of the family; there was a Bunge in my class in my first year at the Colegio, and he sat beside a Born in the last row of desks; when I saw this Bunge again at the 50th anniversary of our graduation he told me he was in charge of his uncle Mario’s affairs in Buenos Aires.  So, Bunge my once classmate turned out to be the nephew of my old advisor.

On the other hand, I knew that Mario (1919-2020) was the nephew of the author and sociologist Carlos Octavio Bunge (1875-1918), a champion of Compte’s positivism in Argentina.  At the time of our first, and as far as I remember, only meeting as advisor and advisee, I didn’t know that Mario Bunge was already becoming an international figure in philosophy of science: his work updated for the 20th century the positivism of his uncle Carlos Octavio.  Professor Bunge was sitting in the first row of the large Physics classroom, near the door, and I was standing facing him; he asked me about the physics books I had been reading of late, and I mentioned one by Sir Arthur Eddington on the philosophy of physics.  I was particularly struck by Eddington’s parable of the ichthyologist who studies sea life by catching creatures with a fishing net, and concludes that creatures the size of ants, so abundant on earth, are not to be found in the sea — never noticing that the net he’s using has a 2in.x2in. diameter netting.  Professor Bunge seemed well pleased with my readings and tastes, so much so that he grew communicative, almost confidential, and with flair and a sharp and vivacious style of arguing and gesturing, he mocked the mentality of Argentine military officers; I particularly remember his imitation of their standing to attention, perhaps because my experience at the Río Tercero Army Works four years before was still vivid in my memory.  Mario Bunge left Argentina in 1963; I heard him say, much later, that he was certain that had he stayed, he would have been killed.  By 1963, however, I was trying hard to become a professional mathematician, and in that process, willy-nilly, one automatically acquires a good dose of contempt for neighboring fields or professions which are not considered as rigorous or are viewed as less difficult than hard-core math: fields such as history of math, or philosophy of math or physics, or even logic, which is at the basis of math.  In my own mind, accordingly, Mario Bunge was deposed from his exalted throne, and so was Gregorio Klimovsky, the logician and epistemologist at Exactas, although I had thoroughly enjoyed his Logic course.  It sounds crazy, but so it was.

Since professional mathematicians are likely to deny that they feel contempt for fields such as history or philosophy of science, or even logic, and the non-mathematical readers will not just take my word for such a crazy feeling, I must quote some less impeachable authorities.  Walter Rudin, a mathematician of note in the area of analysis, gave once a talk at the University of Wisconsin – Milwaukee in which he said that history of math is a very difficult subject for it requires a previous knowledge of math and who, being in possession of such knowledge, would not do math rather than the history of it?  Granted, this might have been said tongue in cheek, but the conceit would have lost its barb if there hadn’t been in it a point of truth.  Of vastly wider reach and appeal than Rudin’s talk was the book by E.T. Bell, Men of Mathematics, first published in 1937.  Intended for the young, it inspired many who later became top mathematicians; I read it in a Spanish translation before I got into Exactas.  Bell’s book is purportedly a collection of biographies of the most eminent mathematicians, but it is also a catechism to instill the superiority of math over all other kinds of human endeavor.  Blaise Pascal, a founder of probability theory, was the first to state explicitly the Principle of Induction, a fundamental axiom of math: Bell takes him to task for wasting much of his life on fruitless religious disputes and the idle (sic) thoughts of his Pensées

Ignorant arrogance or arrogant ignorance?  Apparently, both.  Pascal saw clearly, as Bell did not, that just as math must be based on axioms or first principles that cannot be demonstrated but must be taken on faith, so must the existence of God be.  That numbers are infinitely many, and that God exists are both unprovable postulates.  Thus the rational theology dear to Aquinas, to Suárez, to the Jesuits, for Pascal can only take us up to this: whether we want to do math or put our faith in God, in both cases we must begin by silencing reason and listening to the heart.

Another sad example.  In Bell’s chapter on the prodigious Leonhard Euler there is an apocryphal story intended rather asininely to increase Euler’s glory.  Both the Swiss mathematician and the French polymath Denis Diderot were at the court of Catherine II of Russia, and the story goes that the Czarina asked Euler to rid her of Diderot, whose atheism threatened to corrupt her court: that’s Bell’s first bêtise.  His second, third, and fourth come next, when he says that Euler challenges Diderot to a debate in the presence of the Czarina’s court; Euler begins by declaring, — Monsieur, e to the power 2πi is equal to 1, therefore God exists.  Répondez ! — Diderot, poor guy, defenseless, didn’t know how to respond, and thoroughly embarrassed, left St. Petersburg in a hurry, crushed by his ignorance of fairly recent research in math (for e2πi = 1 is a formula due to Euler himself, published in 1748, while the date of Diderot’s false discomfiture would have been late March or early April 1774, when Diderot left the court of St. Petersburg).  Bell’s bêtises are depressingly familiar: Diderot belonged to the first rank of European philosophers; his influence went far beyond his time and the frontiers of France; but what was that to Bell?  Diderot was a philosopher, hence, deserving the contempt of the true mathematician, be he run of the mill like Bell or great like Euler.  Bell’s arrogance reaches its maximum when he forgets that it might have occurred to Diderot to reply that the existence of God cannot logically follow from any mathematical formula or fact, whether Diderot knew about Euler’s formula or not.  Until 1757 Jean le Rond d’Alembert, the French mathematician, was a close friend of Diderot and his partner in the creation of the Encyclopedia, so Diderot might have known Euler’s formula; it is possible, but of no great relevance: the sad part is that crucial and infamous “therefore” Bell attributes to Euler.  But enough said about E.T. Bell and his inspiring but dispiriting book.

Regarding macho mathematicians’ contempt for logic, I remember Paul Cohen at the Stanford Math Dept. lounge in 1968 deprecating logic problems for being too easy compared to those of hard-core math.  This judgment is the more remarkable coming from Cohen, one of the two top logicians of the 20th century — the other being Gödel —, and the only logician who ever won the Fields Medal, in 1966.  Only one Fields Medal ever awarded for a work on mathematical logic!  Which suggests to the innocent eye that, in fact, contempt for logicians is rather extended among mathematicians, although not as sharp and not as extended as their contempt for philosophy.

Regarding this latter, my beloved professor and namesake Louis Nirenberg liked to tell the following joke: two university presidents are talking about their strategies for saving money.  One says that he tries to hire mathematicians because they use only paper, pencil, and eraser.  The other replies that he prefers to hire philosophers, who use only paper and pencil.

The above is my justification for not having respected those two professors, Mario Bunge and Gregorio Klimovsky, as I should have as a young man: I was trying to imitate the attitude I saw among the hard-core mathematicians around me, and, in the process, trying to armor my choice of Exactas against all scruples about not having chosen Filosofía y Letras instead.  You may criticize the excessive length of my justification, but it is adequate to the depth of my guilt.  Once, after I had graduated and was now being paid as Jefe de Trabajos Prácticos, a math buddy and I came up with an idea for a practical joke: we posted announcements for a conference to be given by Professor Gregario (from Gregorio and Mario) Bungovsky (from Bunge and Klimovsky), a conference with a freakish, mocking title I have mercifully forgotten.

Yet my choice of Exactas instead of Filosofía y Letras did not need a justification based on contempt for the disciplines taught at the latter, like philosophy or history.  A better justification — unavailable to me at the time, though — would have been to point out that a majority of the graduates in humanistic disciplines have no idea of the most basic notions of math, without which they cannot have any real understanding of the changes in Western civilization from Plato to NATO, so to speak.  I first got a peek at the awful ditch between the humanities and basic math when once having lunch with an old friend, a professor in the Humanities division. I mentioned the importance of the discovery, attributed to the ancient Pythagoreans, of the non-existence of a fraction whose square is two.  — “But that’s obvious, isn’t it?” was his reply.  I was perplexed, until I grasped his thread of thought: one times one is one, and two times two is already four, so, I bet he concluded, there’s no number whose square is exactly two.  It didn’t occur to him that the problem was to find a fraction between 1 and 2 whose square was exactly 2, and I didn’t find it in myself to let him know what Plato says in his Laws, where he dwells at length on education: those who don’t understand the “not-being” of the square root of two are not human but suckling pigs.

So, we are agreed that some scientific knowledge is an important element of the soul — some math, as the ancient Platonists required.  But let me add again that it is not nearly enough.  At the Aula Magna, where calculus was taught by day, by night we watched, many of us for the first time, Eisenstein’s “October” and “Alexander Nevsky” and those strange McLaren shorts.  One night I came out transformed and shaken by Bergman’s “Sawdust and Tinsel.”  The film shows a series of humiliations: the clown is humiliated by his wife, the circus owner, Albert, and his lover Anne are humiliated by the theater director from whom they are soliciting help; one after the other, everyone working in the circus is humiliated, but most of all and most consistently the owner, Albert.  I was shaken, and it didn’t take me long to realize why.  Albert was tall, fat and mustachioed, something of a hypocrite and ready to betray, much like Father, whose humiliations, each worse than the one before, deeply marked my puberty and adolescence.  Years later I found that the actor who played Albert was Åke Grönberg, who died in 1969, aged 55.  Father had also died in 1969, aged 56.  It was the earliest uncanny coincidence I remember having perceived.

Now here I am, twenty-eight years older than they, nailed to a mattress by assorted pinched nerves, trying not to take a finger to my nose, because with each such scrutiny blood spills out on my sheets.  And where are they, my friends from Exactas?  Where are they, exactly?  Ubi sunt?  Half of them non sunt any longer; the other half are half sunt.  Horacio Porta rarely responds to my mails inquiring about his health.  Back then, one night he and I went to Retiro, not to the park — we had put paid to that stage of life — but for no particular purpose to the Retiro train station; we were walking up a platform when a train arrived and a crowd came out of it, among them a man screaming “¡Viva Perón!”  At the time, such expressions were still forbidden, and the man’s daring naturally attracted us.  He looked fortyish, disheveled, and responded to our words with drunken cordiality, inviting us for a drink at his brother’s law chambers.  The man happened to be the good-for-nothing younger brother of Dr. Schóo Lastra, whose office, high up in the Trust Joyero Relojero building, looked majestically upon the obelisk.  Once there, the three of us proceeded, at our host’s invitation, to drink a whole bottle of Scotch and to smoke three of the lawyer’s Partagás cigars.  The lawyer was of course not there.  After Horacio and I managed to get up and take our leave with our host’s drunken blessing, once in the elevator we hugged each other for balance, and as soon as the elevator started down, prompted by the downward acceleration and Newton’s Third Law, we both vomited across the other’s shoulder.  It was a clean, perfectly synchronized performance.  Out in the street, we said to each other, “One of these nights will be the last one.”  We were both sure we were right, that we were destined to die young.

But as it turned out, we were wrong.  Look at us now, more than sixty years later, greatly diminished, disgruntled, and despondent.  As for Néstor “el Vasco” Rivière, another close friend from Exactas, he is no more.  He has been no more for a long time, since 1978.  At our first mathematics conference, we saw some elderly mathematicians, old masters like the illustrious Beppo Levi, a refugee from Mussolini’s fascism, and Néstor, remarking on their involuntary up-and-down motion of the jaw, impishly described them, — “There they go, chewing on their peanut.”  His wit in oral expression was matched by the orthographic disaster of his written one: his spelling reminded us of César Bruto, one of the most popular Argentine humorists of that time.  Avalanches of misspellings are to be expected from illiterate hands, but Néstor read far and wide.  It was he who introduced us to Alfred Jarry, to Père Ubu and Mère Ubu, to the “rod of physics” and the “rod of finance,” and to Jarry’s “pataphysics,” by which Jarry meant a kind of philosophy whose realm extends beyond metaphysics.  I found later that the poet Guillaume Apollinaire (1880-1918), in Le Flâneur des deux rives, remarked that among the admirers of Jarry one found mathematicians mostly. 

But to continue with Néstor.  He would break out into a joyous clamor, — “¡Al parque!  ¡Al parque!” (To the park!) for no apparent reason.  He was imitating Gombrowicz.  This time something from Ferdydurke, the 1937 novel translated to Spanish in 1947: Néstor had discovered it and promptly introduced it to his friends.  He was imitating Mientus, one of Ferdydurke’s characters, who called out to an unidentified Polish park.  He often introduced significant variations.  — “To the park!  Let’s go out to the park to peer at the couples while you chew on your little peanut!”  The bit about the couples may have been the influence of Brassens’ “Les amoureux des bancs publics”, which back then was heard frequently on the radio.  Anyway, Néstor, as you can see, was impious and did not commiserate with old folk.  Perhaps the Moirai, who had in mind the original Néstor, he of sandy Pylos and prototype of the old fart, disapproved our Néstor’s impiety and so curtailed his lifespan.  Like his beloved Alfred Jarry, who died in 1907 at thirty-four, Néstor died at age thirty-seven, at the peak of his mathematical career, a professor at the University of Minnesota.

Let’s stop here, for we have two characters, Horacio and Néstor, which suffices to give a fleshed example of what I meant by calling Exactas a vale of soul making.  While we were students there, and then paid teaching assistants, roughly between 1957 and 1963, those two friends of mine had many adventures together, some with me, others by themselves, and I never heard either talk disparagingly of the other’s math skills.  But some five years later, after all of us had gone through graduate school — Horacio and I at NYU’s Courant Institute, and Néstor at the University of Chicago — and gotten our PhDs, mingling with students and faculty from all over the world, and all of us had started on our academic careers at USA universities, I began to hear both sprinkling mathematical discredit on each other, saying that the other had not lived up to his promise.  Competitiveness, the engine of professionalism, had taken over, and had ruined the old harmony we had enjoyed at Exactas, a harmony that needs a far better poet to describe.  In the Second Book of “The Prelude,” titled “School Time,” Wordsworth recalls the races he rowed with his friends, and their arrival at the isle that was the end point: 

“In such a race
So ended, disappointment could be none,
Uneasiness, or pain, or jealousy:
We rested in the shade, all pleased alike,
Conquered and conqueror. Thus the pride of strength,
And the vainglory of superior skill,
Were tempered; thus was gradually produced
A quiet independence of the heart.”

A quiet independence of the heart, gradually produced: that expresses well my school time, my experience at Exactas.  By the time I was writing my doctoral dissertation in New York I missed that experience so keenly that I peppered the thirty-page thesis with quotes from Don Quixote.  Lipman Bers, my advisor, commented, — “I don’t know if this is the best thesis I’ve seen, but certainly it is the most literary.”  The fact is all my friends at Exactas had read the soul-making novel and we used to toss at each other sundry quotations from it, whereas here, in the U.S., none but some faculty at the Spanish departments, or perchance someone in an English department specializing in Wordsworth know it.  For in the Fifth Book of “The Prelude” the poet records an enigmatic dream of his involving Don Quixote:

“While I was seated in a rocky cave
By the seaside, perusing, so it chanced,
The famous history of the errant knight
Recorded by Cervantes...”

About that dream of Wordsworth, in conjunction with Descartes’ dreams, which I also mentioned in the previous chapter, I learned from Elizabeth Sewell, who gave a series of lectures at the University at Albany in the early 1980s: her passion – Quixotic, we may say, but more accurately Frühromantiker — for reconciling poetry and science kindled mine, and she was, after Madame de La Barre, my most memorable and deepest touching teacher. 

But let’s not jump so far ahead; let’s take a shorter jump.  After I got my PhD in 1966, my ulterior professional life, first as a lecturer at Brandeis University near Boston, then as assistant and associate professor at the University of Wisconsin in Madison, was marked by unhappiness.  I was aware that (a) mathematical research did not really interest me, (b) I just wasn’t good at it, (c) I had no connecting interest, no sense of communion with the mathematicians around me, but (d) I had two small sons to provide for, so I’d better get tenure, then we’ll see.  Perhaps it wasn’t the right life path: we’ll never know.

Getting back to Exactas, many of its graduates ended up getting doctorates in the U.S. or in Europe like Néstor, Horacio, “Coco” Recht, or myself.  Some, like “Pucho” Larotonda, got a doctorate at Exactas and stayed there for the rest of their lives; others, the majority, never got a doctorate and took jobs as math teachers, or statisticians, or authors of elementary books.  Of the many I knew in that majority I must mention Clarita Rubinstein because I had fallen in love with her.  In the first semester of 1958, when we were both taking Analysis II (Calc 2), she would climb up and down the steps of Aula 2, her sunlit face, her tender smile, her high heels chipping at and peeling away the plaster from my heart.  We became friends.  Her father had a toy store near Plaza Italia, and on January 5th, eve of Three Kings Day, I was there to help with the sale of toys.  Later in January I went to Mar del Plata for a week or so with Clarita, her fiancé, her younger sister with her fiancé, and a cousin of hers whom they intended to inflict on me.  All my attention, my adoration, was focused on Clarita: I had placed her on die ferne Geliebte pedestal; she was my amor de lonh, my Dulcinea.

Soon, however, the tension became too painful; to see her, the precious, yoked to a vulgar bore was insufferable, so I decided to break off our friendship. Naturally, Clarita noticed that something was amiss, and demanded an explanation.  We went out to the Café El Progreso, where I told her of my love for her, of my sufferings, and of my final decision to put some soothing distance between us.  After she told me how sorry she was, we left, I at the border of tears, and she deep in thought.  Here is the place to mention the only corner I didn’t explore in the old building of Perú 222: the ladies’ room, first door on the left as you entered.  A week or so after my conversation with Clarita at El Progreso, a female friend, Pilar Castro, told me that my distant beloved had been venting her hesitation in the ladies’ room about a difficult decision: whether to stick to her fiancé or to drop him for me.  As time passed, I was relieved that Clarita had stuck to her schmuck.

Are those loves-at-a-distance soul shaping in any way?  I can only say that one of the first things I did upon arriving in New York in 1963 was to go down to the basements of Dauber & Pine on 4th Avenue, where I found disintegrating copies of Cervantes' novel and of Amadís de Gaula.  I used to read it in between writing paragraphs of the Notes of Jacob Schwartz’ course on Non-Linear Functional Analysis.  It might have been my way of coping with absence — the absence of the familiar, of Buenos Aires, of Exactas, to be sure, but also the total absence of Quixotism in a space solidly filled by the ethics of Professionalism.

My friends Horacio and Néstor, and Héctor “El Tano” Fattorini, had distinguished careers at U.S. universities: University of Illinois, University of Minnesota, and UCLA respectively: they seemed happy there and proud of their achievements.   Néstor died young as I said before, and I haven’t had any communication with Fattorini since he got his PhD in 1965; but three years ago I visited Horacio Porta at his assisted living facility north of Chicago: when we parted, both conscious that it was probably the last time we’d be together, we hugged, and he said, — “You’re the only one who hasn’t been competing with me.”  Goodness gracious.  Was then Wordsworth’s quiet independence of the heart something unknown to him?  Did he view all his confrères and all his co-authors (I personally knew a few of them), both from Exactas and from elsewhere, as his actual or potential rivals? What a self-tormented life.

Back to Exactas, April of 1959.  Horacio, Néstor, and especially El Tano Fattorini were enthusiastic about a course they had arranged with a young professor, Enzo Gentile, and they invited me to participate.  The subject of the course was a recent book, Fundamental Concepts of Algebra, written by Claude Chevalley, a founding member of Bourbaki.  For the benefit of the uninitiated, Nicolas Bourbaki is not an individual but rather a select group of young French mathematicians who collaborated in the multivolume Structures fondamentales de l’analyse.  Among many — and those included my friends — Bourbaki was le dernier cri in human thought.  Remember the heyday of structuralism?  That inhuman doctrine seduced the academics in the humanities and the social sciences, who believe it had originated in linguistics and that its paradigmatic text was “« Les Chats » de Charles Baudelaire” by Roman Jakobson and Claude Lévi-Strauss, published in 1962.  In that essay, cats, poor beasts, are untailed, unwhiskered, and unfleshed: only their skeleton subsists.  Well, Bourbaki had been doing the same with math long before, since the 1930s: of math they presented only the clean, logical skeleton — definition, lemma, theorem, corollary, etc. — and never mentioned examples or explained motivations.  That was the style of Chevalley’s book as well, and Professor Gentile did nothing to humanize or mitigate it.

So, I don’t think he was a good teacher, even though I’ve heard younger people who years later took his first-year algebra course say they liked him, he was cool.  Why am I now writing about Gentile then?  For two reasons.  One is that he was cool.  Locally, his jokes and his songs became much more widely known than the mathematical results of his colleagues.  One morning, we were waiting for him for the Chevalley course, and when he arrived he excused himself, — “Sorry I’m a little late, guys; I tripped on a meridian.”  Or his presentation of Nestlé as a manufacturer of mathematical operators: you take Nescafé, add water, and you get coffee; you take Nestea, add water, and you get tea; you take Neswater, add water, and you get... water.  Or his opening joke at our course on Chevalley: the first subject to be discussed was monoids, i.e., sets with a binary associative operation and an identity element (for example, the natural numbers 0, 1, 2, ... and multiplication; the identity element is 1); Gentile started by writing on the board, “Johannes Monoid, 1773-1834,” and claimed he was the “inventor” of monoids.

I agree with you: this last one is rather silly.  But Gentile’s songs were at the top of the charts: all math students and faculty in Exactas knew them and sang them:

Algebrista, oligarca de la ciencia,              
matemático bacán...    
(Algebraist, scientific oligarch / posh mathematician... To a tango tune!)

This one, alla marcia, about the Math Institute at the University of Cuyo, where Gentile got his doctorate in 1957:

"Con Mischa y Ricabarra..." (With Mischa and Ricabarra...)

Here he claims to be among the founders, along with Mischa Cotlar, Rodolfo Ricabarra, Jorge Bosch, and Gregorio Klimovsky, of the Instituto de Cuyo.  The “with,” however, stretches a point: “behind” would have been more accurate, since Gentile was still a student, and all the others had doctorates.

And finally, the statement of the theorem of Heine-Borel, to the tune of Rossini’s aria “La Calunnia”:

"Dado un conjunto cerrado que es acotado..."     (Given a closed and bounded set...)

That was cool.  But the other, the more important reason for writing about Gentile here, in this chapter about Exactas, is his determination to stay there until death, in the vale of soul making and of quiet independence of the heart, and his distrust of professionalism as a way of life incompatible with that determination.

After the lackluster course on Chevalley’s book, Gentile left for the U.S. to spend two years at the Princeton IAS (6/1960 – 6/1962).  A year later I left for New York myself, and I did not see Gentile until the end of June 1966, when I travelled to Buenos Aires right after I had been PhD’d, with Isabel and our two mischief-loving toddlers.  We arrived just in time for the coup of June 29th by Onganía, an army general in whom Jesuitism cohabited in rare harmony with a total absence of education.  And just in time, too, for the revolting novelty of a TV set in the dining room and father, mother, and sister glued to it during meals.  Father watched the announcement of the abolition of the constitution, of congress, of the supreme court, and celebrated the news: the constitutional government of Arturo Illia, he said, was inefficient.

Joe Kohn, whom I had met in NYC, came to Buenos Aires a little later, after a brief visit to Ecuador.  I owe Joe so much, it would be sinful to let him go without a full paragraph in his memory, the more so since he died last week in Princeton as I am writing this.

Joseph J. Kohn was born in Prague in 1932; in 1938, as the Nazis occupied the Czech lands, his Jewish family escaped to Ecuador.  Weird?  Not at all.  At the time, no country in the Americas admitted Jewish refugees except Bolivia, Cuba, and Ecuador: a shameful fact little known in the U.S.A.  To think that my aunts had silver-framed photos of President Roosevelt on their mantlepieces.  Anyway, at the end of WWII Joe’s family moved to the U.S., but those six or seven years spent in Ecuador left a strong imprint in his mind: he spoke Spanish perfectly and was determined to seek a life partner from Spanish-America.  Between 1958 and 1966, Joe was a professor at Brandeis University and so was Denah Levi, Isabel’s aunt; Joe visited Raimundo and Denah occasionally, and that’s how we met him.  By 1966 Joe had found the right woman, Anna Rosa, a native of Quito, and had flown to Ecuador to see her, after which he flew on to Buenos Aires, invited by the math department at Exactas to give a course.

I took the course and learned about Kohn’s deep and important work on partial differential equations in relation to several complex variables.  Then, to the austere marvels of abstract thought followed the frightful wonders of human passions: Joe saw Gentile and, joyously surprised, went towards him ready for a hug or at least a hearty handshake, but Gentile gave him the cold shoulder.  Stunned, crestfallen, Joe said to me that he and Gentile had been friendly four or five years before, in Princeton, and that now he couldn’t understand what got into him.  I could tell him what got into him, but I did not.  At Princeton, Gentile had been where some of the best mathematicians in the world talk and interact: he had tasted the fruit from the Tree of Knowledge.  Then he decided to retreat, to hide himself where he could avoid what professional mathematicians do: search for new results.  But having eaten from the forbidden tree meant that Gentile had also absorbed the mathematicians’ presumption of godlike superiority, so in the presence of a consummate professional like Joe Kohn he felt shame.  That’s what had got into him, red-masqued shame, as happened to my father when at age twelve I asked him about the human orgasm.

Therefore Exactas was not really the isle where a quiet independence of the heart was gradually produced, as I had fancied, but perhaps a peninsula where all sorts of hearts claimed their spot.  Trying to unearth my feelings on the occasion, I find it was there and then that my self-confidence, or rather my confidence that the life path of the professional mathematician was the right one for me, was at its zenith, hence I did not feel pity nor sympathy for Gentile, but simply scorn.



The catastrophe took place a few days later, on July 29th, 1966, at night.  General Onganía, who had usurped the presidency exactly a month before, ordered the police to wreak havoc on Exactas and on the School of Philosophy and Letters.  Some aides had likely advised the general that those were the most dangerous spots, since they focused on critical thinking, but Onganía was already convinced that vector calculus was subversive.  Why?  Don’t ask: who can fathom the unbuoyant dead sea that’s the brain of an Argentine ultra-catholic general?  Roughly at the same time he ordered the closing of the most popular humor magazine, “Tía Vicenta,” because it had depicted his Excellency, with his big moustache, as a walrus.

That night, known since as “the Night of the Long Sticks,” the police ordered everyone in the new Exactas building to get out, and as students, faculty, and the dean himself were coming out, hands up, they were all beaten by the goons with their sticks.  I saw photos of my friends bloody faces.  400 were taken to jail that night, and soon 1,400 professors resigned, 300 scientists among them, who emigrated to the U.S, to Europe, or to other Latin-American countries.  La Noche de los Bastones Largos is a long, long night: to this day Argentina is exporting most of her talent for free and at her own expense, providing the world with artists, scientists, and entrepreneurs.  Incidentally, Gentile did not resign, and Exactas was his redoubt until the end of his life.

After this disaster, any possibility of returning to my vale of soul-making as an assistant professor had vanished.  Joe Kohn, who had been chair of the math department at Brandeis University, and was now moving to Princeton where he stayed for the rest of his life, was kind enough to get me a position at Brandeis for two years as a lecturer.  The pain of seeing Exactas dispersed, and six years later the pain of seeing the old, dear building of Perú 222 demolished and a parking lot laid on its dust: those were the pains of a brutal extraction of my homeland from my heart.

In the 1980s, after I had abandoned the professional math path, leafing through Keats’ Letters I discovered, in the poets’ 1819 letter to his brother George, the full sense of “vale of soul-making,” and that all was as it should be, that all those pains were a necessary part of the process:

“Do you not see how necessary a World of Pains and troubles is to school an Intelligence and make it a soul?  A Place where the heart must feel and suffer in a thousand diverse ways!”


Ricardo Lida Nirenberg is an editor of Offcourse

Return to Offcourse Index.