"Louis Nirenberg in a Dream", by Ricardo Nirenberg

Last night I dreamt with Louis.  He was wearing his thick glasses and his dark and bushy goatee-mustache, much like when I met him, fifty-seven years ago, at my first Christmas party in the USA.

Back then I lived at the Judson Hall dormitory, adjacent to the Judson church, on the south side of Washington Square.  To anybody who asked what was I doing there, I replied that I was working toward a PhD in mathematics, which was true; if, noticing my Hispanic open vowels and my hesitations and errors, they asked where I was from, I mentioned the Argentine pampas.  My state of mind, the nostalgia that played old tangos in my head like a scratched record, the bitter homesickness, and the frequent spells of feeling that this strange, monstrous city must be the land of the Laestrygonians – those things I kept to myself.

In those four months between mid-August, when I arrived, and mid-December, I had experienced quite a few shocks.  Once, walking on the Bowery, while my eyes slid from a wretched drunk lying on the gutter to another wretched drunk, I noticed that one of my shoelaces was undone.  As I used to do in Buenos Aires, I placed my foot on a car bumper to facilitate the tying, and immediately heard a booming, threatening voice: “Get your fucking foot off my car!”  The hatred in those fearful fricatives were my first alert to the “Don’t tread on me” frame of mind and the frenzied sanctity of private property in the land of the free and home of the brave.  Not that I had the slightest inclination to steal or damage anything, public or private, but that didn’t save me from an unpleasant interaction with the police, as you will see.

I used to find irresistible a pair of shapely, generously sized female buttocks gracefully balanced on a pair of high heels, and that is precisely what appeared before my eyes as I was walking on 14th Street toward the setting sun.  I quickened my pace, and when close to the lady I said in the best English I could muster, “Can you tell me the way to heaven whence you have descended?”  She didn’t catch my meaning, so I repeated the question more slowly.  Without a word or glance in my direction, she went straight to a cop and said something to him pointing at me.  Partly out of curiosity, partly because it would have been stupid to attempt to flee, I stood where I was, putting on an air of bewildered innocence about to be sorely tested.  “I hear you’ve been harassing this woman,” the cop said, ominously.  That word was unknown to me.  “Hearsing? what’s that?” I mumbled.  “She says you’ve been molesting her.”  With the strongest Spanish accent I could muster, I said, “Officer, I was asking for directions.”  “Directions?,” said the woman querulously; “he said I was an angel who had descended from heaven, or something like that.”  “No!  I asked how to go to Seven Avenue,” said I, softening the s of Seventh and avoiding the final th, which anyway I found hard to pronounce.  Disgruntled and perhaps confused, the cop waved me away.  So away I went, sad and head bent, thinking, They dress to kill, and when they see you agonizing and wriggling at their feet, they kick you you know where.  “È sempre misero chi a lei s’affida”.  “Eras mujer: Woman you were” – right after Rigoletto, my mind flipped to Discepolo’s tango – “Pensé en mi madre y me clavé: I thought of Momma and I was trapped.”  Not a single glance at me.  Why is it that all these people keep their eyes averted from yours and from one another?  Because of fear?  No, no doubt it is from shame; they are ashamed of dwelling in this New Nineveh, whose wickedness reaches higher than the Empire State building.        

However, the truth was more complicated.  The eyes-averted rule they kept while on the streets; at the dorm it was quite different.  Sure, the people who lived there were graduate students, all adults, roughly of sound mind, and capable of informed consent on matters sexual.  All the same, during those four months I had to swallow episodes I still find difficult to digest.  At the Judson Hall there was a common room with a TV set, a record player, and some records.  One evening I was looking through those records and found Renata Tebaldi’s famous and moving “Un bel dì vedremo”.  I would have liked to play it, but right then the noisy crowd of fans of Lucille Ball came in, anxious to watch her TV show.  A dark-haired, thin young woman detached herself from the throng and approached me, who was still holding the record.  “Found anything interesting?” she asked.  When I explained, she was very enthusiastic; she loved Italian opera, she said, and especially Madame Butterfly.  In point of fact, she thought that Puccini was being staged at the Met that very night.

Her name was Marta Di Marco, she was a grad student in the English Department at NYU; while walking uptown we chatted a little about opera, and she initiated me in the lore of Italian-Americans; I was surprised to learn that Columbus is their hero and Columbus Day, October the twelfth, the occasion for their communal celebration.  In Argentina and in Mexico (I told her) that day is called “Día de la Raza”, understood, if at all, as the “Hispanic race,” the result of the fusion of aboriginal women and Spanish men.  “But Columbus was Italian, wasn’t he?”  “If you had asked him, he would have called himself Genoese.”  “Genoa is a part of Italy,” she insisted, “therefore...” To avoid the intricacy of historical detail, I interrupted and changed the subject a bit: “My own favorite Italian-American happens to be Lorenzo Da Ponte.  He founded the first opera house in New York, you know...”  Marta had never heard of Da Ponte, and when we arrived at the Old Met we found that it was locked and dark, so we started on our way back.

My mind was working hard and fast to figure how to end the evening so that it wouldn’t be total disappointment, and I could not find anything better than do as I used to in Buenos Aires, that is, suggest a cup of coffee.  After all, there was no lack of open-till-late coffee shops in Greenwich Village.  I was gobsmacked when she accepted eagerly and added, “Come to my room, I’ll make some coffee.”  Never in my socially sexual life had I been invited to bed that fast.  It reminded me of a joke which was current in Argentina, one of those beastly-cousin jokes.  Whenever BC, the beastly cousin, is introduced to a girl, he’s in the habit of asking her right away to bed; RC, the refined cousin, tells him, “That’s not the way to succeed with girls; you should first initiate a less intimate conversation.”  “What do you mean, a less intimate conversation?” asks BC.  “Oh, I don’t know; about music, for example.  You might ask if she likes Beethoven...”  Thus instructed, the next time he’s introduced to a girl, BC asks, “Do you like Beethoven, Señorita?”  “Oh yes, he’s one of my favorites.”  “Okay then,” he rubs his hands in eager anticipation, “how about the two of us getting in the sack right now?”

But this was no joke.  In a little while I was to find myself facing a female I had just met, one who was not ugly by any means but who left me indifferent.  Not at all like the Venus of 14th Street.  To refuse Marta’s invitation would have been rude, out of the question.  And once in her room, to act coy and decline coitum ran contrary to my education and training as an Argentine male: my dad and my uncles would not have approved of it.  It would have seriously worried them.  However, unlike the beastly cousin, ever ready to perform, I had some discrimination.  Perhaps I was old fashioned, or Buenos Aires may have been far behind New York regarding the change in sexual mores which was to culminate only five years later in widespread, casual copulation under the banner, “Make love, not war.”  Sounds great, don’t misunderstand me, I’m all for peace, but what on earth has love to do with sex?  You aren’t making love when you have sex.  Yet there you have it: hacer el amor, faire l’amour, Liebe machen, everywhere the same deception, the same willful confusion between the brief spasms after enough rubbing of two epidermides, and the more lasting, mutual penetration of two souls.  Some medievalists have suggested the confusion started with the Provençal troubadours and their view of sex as a surplus of love, a kind of extra bonus.  I am not qualified to judge, but I think it is something similar to saying, “So-and-so passed away” instead of “So-and-so died.”  As everybody knows, the history of civilization is the story of a few euphemisms.  Don’t get me wrong, though: if a person loves another and also finds her or him sexually attractive, lucky he or she, beatus ille aut illa, and mazel tov to both from the depth of my heart.

Marta’s room, a single, was up in the tower of Judson Hall; while we were sitting on her bed, sipping instant coffee, she told me about the course in Old English she was taking, how very difficult it was; hard to imagine why one has to learn that stuff when all one’s interested in is modern literature; but, she sighed, it’s a requirement for the PhD.  We finished our coffee and she sighed again; then we kissed.  To cut a short story shorter, in the end I was rather satisfied with my performance.  I thought I had discovered pure sex, unmixed with any other emotions or feelings, or anything that isn’t sex itself.  It must have been the influence of my juvenile and sporadic attempts at German philosophy, I imagine.   Kant and his pure reason, the neo-Kantian Hermann Cohen and his pure thought,  whose paradigm he took to be the differential calculus, Husserl’s pure phenomenology, and so forth: purity after purity, a nefarious Teutonic obsession with purity.  Or it might have been the Catholic culture where I grew up and its obsession with purity, which means free from sin, which means free from sex.  Whatever might have inspired me, my notion of pure sex had to involve no love or friendship nor even mere sympathy, no admiration or respect, nor, on the opposite side, anything like the sadistic or domineering feelings that often accompany coupling with a person one despises.  I can hear a smartass object that surely I had masturbated enough before my little adventure at the tower of Judson Hall to be well acquainted with pure sex; to which I reply that indeed I had masturbated enough as an adolescent, and also presently, in the bathroom of Judson Hall, with the glossy assistance of just-discovered Playboy magazine.  But this type of sexual transaction was invariably accompanied, in my case, by shame and sadness, so for me it was very impure sex.

Again, I was rather satisfied with my discovery and with my performance.  What comfort to be assured that your genitals act gentlemanly; that unhesitantly, without any mental effort or engagement on your part, they will not disappoint a lady.  Why did Augustine of Hippo feel horror and shame when he was sixteen and he had an erection at the baths?  He should have been proud and relieved, as indeed his father was, as he writes in his Confessions.  Augustine’s horror at a visible part of his body which seemed to act on its own and did not obey his mind’s commands is the mark of a control freak; the fact that his heart, which also beat without conscious consent, did not cause him shame and horror, goes to show he was a hypocrite.  And this Augustinian combination of control freakiness and hypocrisy became the hallmark of Western Christianity: it is heartbreaking.  For my own part, I felt so good that I pressed another grateful kiss on Marta’s lips, whereupon I noticed that she was weeping.  “Oh my God, have I done anything wrong?,” I asked.

“No, it’s not you,” she sobbed, “nothing to do with you.”  She would not tell me anything further, and I was about to conjecture aloud, “Sad is the flesh, alas, and Beowulf’s a bore?,” but I stopped myself, and the reason for Marta’s weeping became almost clear in my mind: pure sex, which I had just found soothing and congenial, was for her, perhaps, a source of woe and despondency.

Soon after, the assassination of JFK occurred.  I happened to be attending a lecture given by Louis Nirenberg when the news broke: for a while, Fourier integrals ceased being chalked on the boards, and our brains found themselves before the brink.  Was this the end times? a communist conspiracy? a mafia plot? the start of another world war?  All of us students sat numb and aghast; as for myself, I cursed the academic stars that had led me to this diabolical place.  Why, oh why hadn’t I stayed in purgatorial Argentina?  But this bewildered interval didn’t last.  “Nothing at all will be gained by us trying to figure this out,” said Louis, with an ataraxy and composure that would have gained him the envy of the assembled Stoa; “let’s go on with Sobolev spaces.”  And so he did.  I don’t know about the others, but I wouldn’t or couldn’t follow him there.  I knew that he was right, that leading the audience away from the bloody deeds of Dallas and back into the security of Fourier integrals and Sobolev spaces was the only responsible thing to do.

I knew it, but I couldn’t follow him; my thoughts were elsewhere, wondering how Louis could keep his cool in the face of the shock.  I remembered that Kim, in Kipling’s novel, withstands all the efforts of Lurgan Sahib to hypnotize him, something no one else has been able to do.  Kim keeps the secret of how he did it to himself, but Kipling tells us: he was going silently in his mind through multiplication tables.  Concentrating on numbers keeps other types of thought and all emotions away.  Naturally, if you are counting money, or the victims of an earthquake, or, as Leporello, females by his master bedded, other thoughts, feelings and emotions may easily slip in, but Kim was dealing with abstract numbers; he was thinking about pure mathematics, which will resist admixture.  Pure math, Kipling knew, is the impregnable fortress of the mind.

Then I remembered that Pascal, one of the ablest mathematicians of the 17th century, when science and math began their vertiginous expansion, had, one night in late November 1654, a mystical experience, whereupon he abandoned the truths of mathematics for the truths of the Lord: “Thy righteousness is an everlasting righteousness, and thy law is the truth” (Psalm 119: 142).  Nevertheless, even after Pascal’s conversion, once when he was afflicted by a terrible toothache, after having prayed to Saint Apollonia with no ensuing relief, he returned to his beloved math for a few days, and the pain dissolved.  Pain, unlike the Lord, cannot penetrate the fortress.

During the first few days after the assassination, one could often see students, not math students of course, weeping at Judson Hall.  Marta was disconsolate, and more to my surprise, Jay, a student of business who was the first Republican I ever met, was weeping too.  Certainly, this was very different from my experience in Argentina, where coup after military coup and wholesale, barefaced corruption, had made most people inured to outrage and hopeless about mostly everything except for their favorite soccer team.  People in the USA, I concluded, seemed to care more about their system of governance. 

Three weeks later, however, the emotional weather had completely changed; another news cycle, Christmas season, was upon us with its muzaky carols, bearded Santas, and frenzied shopping.  The Math Department had its Christmas party.  I learned this was a tradition, that all offices and workplaces in America have their annual Christmas parties; this is even so, some student told me, at J. Edgar Hoover’s FBI.  Back in Argentina I had known nothing of the sort: Christmas parties were family affairs which my family, being secular Jews, ignored as best they could.  But I was away from home, lonely, and curious about what a combination of math and Bethlehem might look like.

Well, it was a rather drab affair, students and faculty standing in small groups, each person nursing a drink, talking quietly and rarely laughing.  A record was playing unfamiliar and insipid pop music. I walked around, pausing here and there to listen into some of the conversations; as far as I could gather, they all qualified as vaguely shop talk.  Suddenly, and when I was already preparing to slip out without being noticed, Louis appeared out of nowhere, with his thick eyeglasses and his dark and bushy goatee-mustache.  “Are you having fun yet?,” he asked.  I replied, “So, so; more or less.”  “Well, drink some more,” he said, pointing to the table and the bowl of punch.

I’ve often thought about those words, apparently so trivial, and the effect they had on me.  The tone, the smile, were such as to convey genuine sympathy on Louis’ part and a care for my having a good time, but the notion of drinking some more liquor as a means to achieve that purpose seemed strange to me.  Being drunk, I had already had the opportunity to experience, is no fun; perhaps it all comes down to finding the ethylic level in your brain that maximizes fun and to stop drinking right there; I wouldn’t know.  Anyhow, the good will evidenced by the great mathematician’s face and words seemed beyond mere yuletide cheer, and it also seemed, in recollection, stronger than the previous time I had talked with him.  That first time, he wanted to know if we were relatives, given the coincidence of our family names.  I could only contribute the little I knew – that my paternal grandfather was named Marcos or Mordechai, that he emigrated from the Ukraine to Argentina about 1905, and that his father’s given name was Wolf.  Louis’ parents came from the Ukraine too, but they had migrated toward the opposite pole, to Canada.  Our information proved inconclusive: there were simply too many Nirenbergs come from the shtetls and ghettos of Eastern Europe.  Between that first genealogical encounter with Louis and this drab Christmas party, I had aced the preliminary written exam given to all graduate students: that performance, I suspected, must have been a reason for the increase of his interest in me and his joviality.

Something I discovered only much later: the importance Louis placed on the idea of “fun.”  Through the years, in all the interviews where he was asked when and why and how he had become a mathematician, or even without being asked, he would invariably answer, “Math is fun.”  This apparently simple explanation, I realized in time, modestly hid, beneath it, a long, bizarre history of fantastic notions about the divinity of mathematics.  Pythagoras, so they say, taught that everything that is, is number, nothing but number; Plato thought there is something else indeed, a god, but that all this god does by day or night is math; Aristotle, many believe, was less extreme, but in fact he was as mathematically besotted as his master, and taught that the only part of the soul that survives death is the part which is able to do math; Augustine, the father of the Church who was horrified and ashamed of his erections, was exceedingly proud of having proved to his own satisfaction the existence of God from the irrefragable truth that seven plus five equals twelve, and already in modern times Spinoza affirmed the old Aristotelian faith that our mind is eternal insofar as it thinks from the viewpoint of eternity. 

I don’t know how familiar Louis was with those old fantasies of immortality.  But he was certainly aware of the views of some of his most prestigious colleagues, and you can bet that he was in the audience when Hermann Weyl lectured at Columbia University in 1952 about the unity of the mathematical sciences.  Before the Nazi takeover Weyl was a professor at Göttingen and a colleague of Richard Courant, the founder of the NYU graduate mathematics department, later named after him, where Louis got his PhD in 1949 and where he stayed as a professor all his life.  In addition, Louis’ doctoral thesis provided a solution to a problem in differential geometry first considered by Weyl thirty-three years before, so you can see why it is safe to bet that Louis was in attendance at that Columbia lecture.  There, Weyl diagnosed the everyday world, the world of subjectivity, of feelings, desire, opinions, politics, as broken beyond repair.  That was not, he hastened to add, worth a tear, since the world of mathematized science is one, whole and unfractured.  Math, he added, is the only secure shield we have against the human fatal tendency to wishful thinking and self-deception. 

To judge from my interchanges with Louis seven or eight years after my first Christmas party, that is, in 1970 or 71, he must have agreed with Weyl in some basic way.  By that time, I was employed by the University of Wisconsin in Madison, a job I had gotten, I’m pretty sure, thanks to Louis’ vastly exaggerated recommendation, and I ended up joining the radicalized students in their protests against the war in Vietnam and, more specifically, against the presence on campus of the Army Math Research Center.  When this center, entirely supported by the US Army, extended an invitation to a score of mathematicians for a conference, I sent a letter to each of those people, urging them to refuse the invitation.  Only Louis bothered to respond, telling me that as long as the Army Center contributed to the defense of the US, he supported it.  A year or two after that, when I invited Louis to a conference at the University at Albany, he asked my wife Isabel, who was driving him from the train station, if Ricardo was done with politics, quite as if he had been asking if I had recovered from some dangerous disease.

Yes, Louis basically agreed with Weyl: political and everyday life are wide open and susceptible to wishful thinking and self-deception.  But Louis would never say anything like what Weyl said about the secure shield of math, behind which, or under which, mankind can safely advance toward the ramparts of Truth like Roman legionnaires in testudo formation; it would not have been like Louis: too metamathematical, too metaphysical.  His only justifications, at least the only ones he voiced, the only ones I ever heard from him, were that math is fun, and that mathematicians all over the world form a wonderful family.  Nor would it have been like Louis to glorify the call of the pure mathematician the way others have done, presumptuously and pompously, like André Weil.

I must inform the uninitiated, who may confuse Weyl and Weil, of some of the differences between them:  Weyl rhymes with “vile,” while Weil rhymes with “veil.”  For the rest, the reader may consult the abundant references on the Internet.  Regarding Louis, I have already pointed out that his doctoral thesis was about a problem first considered by Weyl, and now I add that an early famous result, the Newlander-Nirenberg theorem of 1957, was motivated by Weil, who at a lecture at the Courant Institute proposed the problem to “you people in partial differential equations,” so Louis picked it up and solved it with his doctoral student August Newlander.  Besides this connection, Louis professed to admire Weil’s ability to view mathematics as a whole and to preach urbi et orbi about its future and its worth: that is something Louis never did and modestly insisted he was unable to do.  As an échantillon of Weil’s prophetic plectrum, I offer the final paragraph of an essay he wrote first in French in 1946, soon after the war, and then published under the title “The Future of Mathematics,” in The American Mathematical Monthly of May 1950.  

After excoriating “mass education” in the USA and wondering if there is a danger that this disease will infect Europe’s older and more refined cultures, an attitude thoroughly unoriginal in a French intello, Weil ends as follows:

“But if, as Panurge, we ask the oracle questions which are too indiscreet, the oracle will answer us as it did Panurge: Trink! This advice the mathematician follows gladly, pleased as he is to believe that he will be able to slake his thirst at the very sources of knowledge, convinced as he is that they will always continue to pour forth, pure and abundant, while others have to have recourse to the muddy streams of a sordid reality.  If he be reproached with the haughtiness of his attitude, if he be summoned to do his part, if he be asked why he persists on the high glaciers whither no one but his own kind can follow him, he will answer, with [Carl Gustav Jacob] Jacobi: For the honor of the human spirit.”

The reference to Panurge is from Book V, chapter 44 of Rabelais’ history of Pantagruel, whose farcical character makes it dubious that Weil meant to be taken seriously; the remainder of the quote, so prissy and priestly, makes one wonder what the relation might be between the two parts, especially since the oracular response from the divine bottle, Trink, means drink wine, not water, however “pure and abundant” the water might be.  Chez Rabelais, in wine there is truth, in vino veritas, not in water, were it from “the very sources of knowledge.”  As for Weil’s “sordid reality” and “muddy streams,” they are at first blush nothing but the Platonist platitude, grown stale through millennia of overuse – dust, mud, death and rot all around on this earth of ours, while up above, in heaven, we may contemplate the eternal archetypes and listen to the harmony of the spheres.  Yet it may also allude to Weil’s imprisonment in 1940 for failure to report to duty when war was declared between France and Germany: that is, when he was “summoned to do his part” for France.  In 1939 Weil was travelling in Finland and Scandinavia, literally “on the high glaciers.”  Whether he refused to return “for the honor of the human spirit” or for his own safety, I’m unwilling to judge.  In any case, there you have a small sample of the many self-serving fabulations woven around the art and science of the mathematician.  Now, Weil may rant all he want about the purity of “the very sources of knowledge”: Louis’, I think, is the genuine vision of pure math, because it is unmixed with ethical, theological, mythological, self-justifying, or any other sort of extra-mathematical consideration.  For him, math is fun, and “fun” is a vague enough word to mean, I do math because I enjoy it, period.  Just as you may enjoy playing pinochle.  That may be the reason why, in my mind, Louis has remained the very model of the pure mathematician.

About his wisdom regarding how to have fun at math department Christmas parties I had serious doubts, but I was willing to give it a try; so I helped myself to two servings of punch, one right after the other.  True to the promise of its name, they made me groggy, after which my memories of the evening become disconnected and blurred.  I may have had a few extra drinks.  I do remember that at one point the music changed from blah or outright ugly into something familiar from south of the border, Cha-cha-cha de las secretarias, cha-cha-cha de las taquimecanógrafas, which moved me to start dancing as I used to dance back in Buenos Aires, with little leaps, turns, and shakes.  As in a Fred Astaire movie, people stopped dancing to look at me.  The next thing I remember is Abigail Baum taking me away to her small apartment nearby.  She was a young woman, pretty and perky, who worked as a secretary and typed math papers. 

I know it is highly unlikely and that it would have been highly unethical, but I’m fond of the fantasy that Louis, so as to complete my fun, suggested she take me home with her.  At Abby’s place we kissed and necked on her couch, but she wisely refused to go further, for I was quite drunk, and as Rabelais or perhaps some other Frenchman of yore wrote somewhere, « de trop boire, d’amour déboire ».  She promised to satisfy all my wishes another day, once I had sobered up, and sent me back to Judson Hall.  I never asked her to keep her promise, because a week later Isabel Lida, a student of mine the previous semester in Análisis Uno (Calc 1), with whom I was exchanging letters, flew from Buenos Aires to spend some time in the USA; two months later we were married, and I have remained her lover and her student for a lifelong intensive course.

And now, nine months after Louis’ death, he appears in my dream.  

Guillaume de Lorris, the first author of the medieval blockbuster Le Roman de la rose, begins his story by saying that it was a dream he had when he was twenty, the age when Love, or rather Eros, exacts its toll from youth:

« Où vintiesme an de mon aage,
Où point qu’Amors prend le paage
Des jones gens ».

I am at the age when the toll is payed back with interest, like a 401K, in the form of enigmatic dreams.  I was at a party, of that I am sure, and not a party full of stiff, strait-laced, stuffed-shirted nerds, like my first Christmas party at the Courant Institute, but one full of joking, singing, and laughter.  Louis was there, eating and drinking and laughing with the best of them.  Then my eyes were caught by a woman who was sashaying seductively and snapping her fingers at a rhythm I couldn’t hear; she reminded me of the callipygian Venus of 14th Street.  From then on, with growing admiration, I followed her wherever she went, without however getting too close, lest some cop pop up from nowhere.  Yet somehow, at some point, the way those things happen in dreams in violation of Leibniz’ Principle of Continuity, she and I did communicate.  It was a peculiar form of communication, through a bookcase.  At our house in Albany, where Isabel and I have lived for almost fifty years, there is a large bookcase open on both sides; in it I keep those books which can be classified as philosophy.  There was a similar bookcase in my dream, with an empty space between Derrida and Descartes, large enough for the divine female and me to look at each other eye-to-eye, almost lips to lips, although we were on opposite sides.  I asked her, “Will you be my guide to heaven?”  And she replied, “Sure thing.  In forty minutes, let’s meet at the door.”  Having said, she left and I lost track of her.  During those forty minutes I felt tempted more than once to reach for a stiff drink, but I resisted, mindful of the old quarrel between Eros and alcohol.  When the hour approached, I moved toward the door, looking around, trying to locate my angel.  At the appointed hour I was at the door, but did not see her.  Other people were milling around, but not her.  In a loud voice I asked them, “Have you seen my angel?”  I repeated the question, loudly, until I caught the ear of a man who replied, “Oh yes, she left with Louis, in his car.”

Forty, fifty years ago, on awakening, I would have felt the taste of defeat, the sting of jealousy, and the cold Oedipal wind on my back; now, instead, I felt the satisfaction after an intellectual discovery, a kind of long look upon the calm of the gods.  I had found that it was possible, or at least conceivable, if only in dreams, to harbor two purities at once, since the purest mathematician could also become a master of pure sex.  A passage of Rousseau’s Confessions is one of those youthful readings that I will not forget until I forget my own name.  It happens during Jean-Jacques’ tenure as secretary to the French ambassador to Venice, in 1743 or 1744, so he must have beenthirty-one or thirty-two, an age when Eros is strict in exacting his toll.  He goes to visit a whore, Giulietta – in the Venetian dialect, Zulietta –, who is, Rousseau insists and presses the point, the most beautiful and one of the most experienced whores in la Serenissima.  Her breasts are magnificent and well proportioned, but there is a glitch: one of her nipples is buried and refuses to come out.  This perturbs Jean-Jacques enough that he goes limp and, in spite of Zulietta’s minutious ministrations and wise caresses, to his bitter chagrin and embarrassment he stays limp.  Historians should have paid at least some attention to the contrast between those two formidable writers of confessions.  Augustine, who deduced the existence of God from 7 + 5 = 12, and whose influence on Western Christianity is immense, was ashamed of having an erection; Rousseau, whose influence on the Enlightenment, on Romanticism, and on modernity is as immense, was ashamed of not having an erection.  But I’ll leave the elaboration of this insight to more enterprising spirits, and return to Zulietta and her john, Jean-Jacques.  Finally she gives up on him and stands up, red with anger.  We must imagine her now pacing the room, either naked or in a pellucid bedgown, fanning herself with a swan feather fan, while Jean-Jacques sits on the edge of the bed, abashed.  With a cold and contemptuous voice, Rousseau tells us, the whore offers him this advice, “Zanetto, lascia le donne, e studia la matematica”.  Johnny, leave women alone and study mathematics.

Either / or.  So goes the opinion of the experts – Hermann Weyl and André Weil, joined by the numerous Pythagorean retinue, as well as Rousseau’s Venetian courtesan – and also the vulgar opinion: pure sex and pure math are opposites, and in a single brain never the twain shall meet.  Yet in my dream they did.  In wakeful reality no one, to my knowledge, and myself least of all, has imagined Louis as a ladies man.  But that is not the point.  The contentment I derived from my dream had not to do with any discovery about Louis but rather with the confirmation of something I have long suspected about myself: I have a phobia.  I detest the notion of strict opposites in nature with no possibility of shading in between; I agree that a number must be either even or odd and not both, but that’s because we have constructed numbers so.  And I can’t stand the idea of taking a stand for one of two supposedly mutually exclusive options when there are no pre-agreed-upon legal, ethical, or logical rules for deciding for one rather than the other.  I’m happy to affirm that the sum of two odd numbers is even and the sum of two even numbers is also even, if we have previously agreed to play by the axioms of arithmetic, just as I’ll readily concede a chess game if my king is in check and cannot move anywhere.  But I reject any Platonic conceit that math is the escalator up to heaven, and any Neo-Platonic meshugas that the senses are the slippery slope to hell.  Am I for that reason anti-Platonic?  By no means.  Plato’s Symposium is a masterpiece of irony, and Diotima’s discourse reported by Socrates is the best linguistic account of eros and love that I know of.  The wise woman, professor of the shading and of the in-between!  And the ending is both a lesson in ethylic control and a last salvo for the Heraclitean coincidence of the opposites.  When everybody else is asleep or gone, only Agathon (the tragic poet), Aristophanes (the comic poet), and Socrates are awake, still drinking and conversing.  Socrates is leading them to admit that a very accomplished tragic poet can be a comic poet too.  When, at dawn, Agathon and Aristophanes begin to nod, Socrates leaves, fresh as a lettuce.