by Gian-Carlo Rota

ne morning in 1946 in Los careless in the details of his attire, even how at Harvard they would sit for hours Angeles, Stan Ulam, a newly though his clothing was still expensively on end, day after day, in front of the appointed professor at the chosen. blackboard. Since I met him, Stan never University of Southern Cali- When I met him, many years after did anything of the sort. He would per- fornia,oawoke to find himself unable to the event, I could not help noticing that form a calculation, even the simplest, speak. A few hours later he underwent his trains of thought were unusual, even only when he had absolutely no other an emergency operation. His skull was for a mathematician. In conversation he way out. I remember once watching sawed open and his brain tissue sprayed was livelier and wittier than anyone I him at the blackboard trying to solve with newly discovered antibiotics. The had ever met, and his ideas, which he a quadratic equation. He furrowed his diagnosis----encephalitis, an inflammation spouted out at odd intervals, were fasci- brow in rapt absorption, while scribbling of the brain. After a short convales- nating beyond anything I have witnessed formulas in his tiny handwriting. When cence he managed to recover, apparently before or since. However, he seemed to he finally got the answer, he turned unscathed. studiously avoid going into any details. around and said with relief, “I feel I He would dwell on a given subject no have done my work for the day.” In time, however, some changes in longer than a few minutes, then impa- his personality became obvious to those tiently move on to something entirely The Germans have aptly called Sz7z- who knew him. Paul Stein, one of his unrelated. jleisch the ability to spend endless hours collaborators at Los Alamos, remarked Out of curiosity I asked Oxtoby, at a desk doing gruesome work. Sitz- that, while before his operation Stan Stan’s collaborator in the thirties, about jlezkch is considered by mathematicians had been a meticulous dresser, a dandy their working habits before his oper- to be a better gauge of success than of sorts, afterwards he became visibly ation. Surprisingly, Oxtoby described any of the attractive definitions of tal-

Los Alumos Science Special Issue 1987 23 ent with which psychologists regale us off on the marble of coffee tables in the from time to time. Stan Ulam was able late evenings, in loud and uninhibited to get by without any Sitzjeisch what- brawls. soever. After his bout with encephali- The Lw6w school was made up of tis, he came to lean instead on his own offbeat, undisciplined types. Stan’s unimpaired imagination for new ideas teacher Banach was an alcoholic, and and on the Sitzjeisch of others for tech- his best friend Mazur was a Communist. nical support. The beauty of his insights They cultivated the new fields of mea- and the promise of his proposals kept sure theory, set theory, and functional him amply supplied with young col- analysis, which at the time required laborators always willing to lend (and ence on his personality, and through- very little background. The rival War- sometimes risking to waste) their time. out his life he kept going back to them saw mathematicians, more conservative, A crippling technical weakness cou- for comfort. From Karl May’s numer- looked down on the Lw6w mathemati- pled with an extraordinarily creative ous adventure novels (popular enough cians as amateurish upstarts, but the imagination is the drama of Stan Ulam. in the German-speaking world to be results of the Lwow school soon came Soon after I met him, I was made to un- among the favorite books of both Ein- to be better known and appreciated the derstand that, as far as our conversations stein and Hitler) he derived the childlike world over, largely after the publication went, his drama would be a Forbidden and ever fresh feeling of wonder that is of Banach’s book on linear operators, Topic. Perhaps he discussed it with his often found in great men. From Anatole in which Ulam’s name is the most fre- daughter, Claire, the only person with France he took his man-of-the-world quently mentioned. whom he would occasionally have bru- mannerisms, which in later life would One day the amateur Ulam went one tally frank discussions, but certainly not endear him to young ladies. up on the Warsaw mathematicians, who with anyone else. But he knew I knew, He kept a complete set of Karl May’s cultivated the equally new field of al- and I knew he knew I knew. novels (in German, the other language gebraic topology. While chatting at of his childhood) behind his desk un- the Scottish Caf6 with Borsuk, an out- til he died. He regretted that a Pfiiade standing Warsaw topologist, he saw in a tan Ulam was born into a family edition of Anatole France had not been flash the truth of what is now called the that stood as high on the social published, which he could keep by his Borsuk-Ulam theorem. Borsuk had to sladder as a Jewish family could at bedside. He often gave me paperbacks commandeer all his technical resources the time. He was the golden boy from of Anatole France, bought on his fre- to prove it. News of the result quickly one of the richest families of Lwow. quent trips to Paris and dedicated with swept across the ocean, and Ulam be- In central Europe the Ulam name was inscriptions urging me to read them. I came an instant topologist. then a synonym of banking wealth, not regret to admit I haven’t. unlike the Rothschilds’ in westem Eu- Stan took to cafd-mathematics like a rope. He was educated by private tutors There was never any doubt that he fish to water. He quickly became the and in the best schools. As a child he would study mathematics when, at age most daring of the Lwow mathemati- already showed an unusual interest in seventeen, he enrolled at Lwow Poly- cians in formulating bold new math- astronomy (’’I am star-struck,” he would technic Institute. Shortly after classes ematical conjectures. Almost all his often tell me) and in physics. At the started he discovered with relief that guesses of that time have been proved age of twelve he was reasonably fa- the mathematics that really mattered true and are now to be found as theo- miliar with the outlines of the special was not taught in the classroom, but rems scattered in graduate textbooks. theory of relativity, a great novelty at was instead to be found alive in one In the casual ambiance of the Scot- the time. In high school he was a top of the large caf& in town, the Scot- tish Caf6, Stan blossomed into one of student, far too bright for his age. His tish Caft5. There the Lwow mathemati- the most promising mathematicians of quick wit got him good grades with lit- cians would congregate daily. Between his generation. He also began to dis- tle effort but lent free rein to his lazi- a shot of brandy and a cup of coffee, play the contradictory traits in behavior ness. they would pose (and often solve) what that after his operation were to become The two authors he read thoroughly turned out to be some of the outstand- dominant: deep intuition and impatience in his teens were Karl May and Anatole ing mathematical conjectures of their with detail, playful inventiveness and France. They had a formative influ- time, conjectures that would be dashed dislike of prolonged work. He began to

24 Los Alumor .Rieni (> Speed Issue [987 view mathematics as a game, one that mained emotionally crippled for the rest a well-bred gentleman should not take of their lives. too seriously. His insights have opened Stan Ulam was one of them. Had he whole new areas of mathematics, all of been able to remain in Poland and sur- them still actively cultivated today, but vive the war, as Steinhaus, Kuratowski, he himself could not bear to give his and a few others did, he would have discoveries more than a passing interest, gone on to become one of the leading and at times he would make merciless international figures of pure mathemat- fun of those who did take them too seri- ics, at least on a par with Banach. But ously. after he bade farewell to his friends at The papers in mathematics that he mer of 1939, shortly after he returned to the Scottish Caf6, something died for- wrote by himself date back to this pe- the United States with his brother from ever within him, and his career as a riod. Most were written in one sitting, what would be the last visit to his fam- pure mathematician went permanently often in a night’s work, probably in re- ily, World War II broke out. By acci- adrift. sponse to some colleague’s challenge at dent he had been saved from almost cer- the Scottish Caf&. Much of his present tain extinction. He would never leave Like other immigrants from the Eu- reputation as a mathematician rests on the United States again, except on short ropean leisure class, Stan arrived in the these short, brilliant notes. His measur- trips. United States ill-equipped for the rigors able cardinals, the best idea he had in of puritan society. this period, are still the mainspring of The big open spaces of America, the much present work in set theory. More he belle kpoque, the period that demands for aloneness and self-reliance often, however, his flashes of original- runs between 1870 and the 1930s made him feel estranged. He wished ity, scattered as they are in unexpected T(though some claim that it ended to belong, and he loved this country, contexts, have been appropriated by oth- with World War I), was one of the hap- but he never came to feel fully at home ers with little acknowledgement, and piest times of our civilization. Vienna, in the United States, whether in Cam- have proved decisive in making more Prague, Lw6w, and Budapest were capi- bridge, Madison, or Los Alamos. He than one career in mathematics. For ex- tals of turn-of-the-century sophistication, missed the lively street life of European ample, his paper with Lomnicki on the though they lacked the staid traditions cities, the culture, the rambling conver- foundations of probability, which also of Paris. Florence, or Aranjuez. Robert sations (what the Spanish call tertulias) dates back to his Polish period, con- Musil, Gustav Mahler, Franz Kafka, and viewed with alarm the decay of that tains a casual remark on the existence of Ludwig Wittgenstein, and the philoso- art, which in our day has become all but prime ideals in Boolean algebras, later phers of the Vienna Circle have become extinct. developed by Tarski and others in sev- for us symbols of mitteleuropaische Kul- By now the effective American way 1 eral formidable papers. tur. Most of those now legendary fig- of scientific exchange has imposed it- ures betrayed personality traits similar self on the rest of the world. But fifty The Borsuk-Ulam theorem was strik- to Stan’s: restlessness, intolerance, a years ago life in American universi- ing enough to catch the attention of dialectic of arrogance and contrition, ties was incomparably duller than the Solomon Lefschetz, the leading topol- and an unsatisfied need for affection, caf6-science of Lwow. The atmosphere ogist of the time and the chairman of compounded by their society’s failure to of Cambridge in the thirties was too the Princeton mathematics department. settle on a firm code for the expression cold, and, what was worse, there were Through Lefschetz and von Neumann, of emotion. Perhaps the roots of the no caf&. And then, in Europe, the war with whom he had started to corre- tragedy that befell central Europe should started. spond, Ulam was invited in 1936 to be looked for in those men’s tragic lives visit the Institute for Advanced Study and flawed personalities. rather than In the fall of 1939, Stan would spend in Princeton. in the scurrilous outbursts of some de- endless hours watching the Charles For four years he commuted between mented housepainter. River from his room at Harvard, stu- Poland and America where, first in When the catastrophe came, those pefied by the sudden turn of events Princeton and later at the Harvard Soci- among them who were still alive to that had changed his life and that of so ety of Fellows, he lived in luxury on his watch their world go up in flames never many others. He learned of the fall of parents’ monthly checks. In the sum- recovered from the shock. They re- Poland, of the deportation of his family

Los Alumo.~ .Y

26 L[H A[um[]3 S(ienc < Speed Issue 1987 and recuming self-doubts. Following his uncanny instinct for doing the right out to be better at that game than just thing at the right time, Stan soon found about anyone around him. the way to cheer up his brooding friend. It is hard to overstate how rare such He began to make fun of von Neu- an ability is in a mathematician. The mann’s accomplishments. He would literalness of mathematics is as far re- mercilessly ridicule continuous geome- moved from the practical needs of the tries, Hilbert space, and rings of opera- Neumann to drag him out of his Wis- physicist as might be the story of the tors, cleverly picking on weaknesses in consin rut and to get him a job related Wizard of Oz. As Stan began to dis- von Neumann’s work that were obvious to the war effort. The request fit per- play his newly found talent, he came and expected. Stan’s jibes were an indi- fectly with von Neumann’s plans. He to rely less and less on standard math- rect but firm expression of admiration. had already made up his mind to bring ematical techniques and to view ordi- Rather than feel offended, von Neumann Stan with him to the newly founded Los nary mathematics with some contempt. would burst out in a laughter of relief. Alamos laboratory, where the atomic He admired Fermi’s genius for solving Much later, when Stan related to me bomb project was being launched. physical problems with no more than these events, he affected to regret never The choice of a set theorist for work the minimum amount of math. Since having said a kind word to von Neu- in applied physics might seem eccen- that time Fermi remained for him the mann about his work in pure mathemat- tric, but in retrospect von Neumann ideal of a scientist. In his old age he ics. But I could feel he was not serious. made the right choice. Besides, as the liked to repeat (perhaps with a touch of Deep inside he knew he had been good token mathematician in a sea of physi- exaggeration) that Fermi had been the to his friend. cists (though he was probably one of the last physicist. Stan didn’t fully realize how much finest minds among them, together with von Neumann meant to him until his Fermi and Feynman), von Neumann was But the Magic Mountain lasted only friend began to die of cancer, in 1955. relieved to have his cohort join him. as long as the war. In 1945 it seemed Stan would make frequent trips to Wal- The assembly of geniuses who roamed that the Los Alamos laboratory might ter Reed Hospital in Washington, where the corridors of the Los Alamos labora- close down, like many other wartime for months on end his honored friend tory during World War II has not been projects, and Stan began to look for a was confined to a bed in the Presidential matched in recorded history, with the job elsewhere. Unfofiunately, his list of Suite. Stan came prepared with a bag- possible exception of ancient Greece. In publications was hardly longer now than ful of the latest jokes and prurient Los the hothouse of the Manhattan Project, it had been in 1939, and unpublished Alamos gossip. The little hospital bed Stan’s mind opened up as it hadn’t since work gets no credit. To his chagrin he would shake with the vibrations of von the days of the Scottish Caft5. The joint was ignored by the major universities. Neumann’s big belly as he laughed him- efforts of the best scientists of the time, He finally had to accept the offer of a self to tears, the very tears that Stan was their talents stimulated and strained by professorship at the University of South- fighting to control. Then weeks passed the challenge of a difficult project, made ern California, at the time a second-rate when von Neumann could no longer what could have been a drab weapons institution but one with great plans for recognize anyone. When he finally died, laboratory into a cradle of new ideas. the future. Stan broke into tears. It was probahly In welcome breaks between long stints Suddenly he found himself in the the only time in his life when he openly at the bench, in a comer at some loud middle of an asphalt jungle, teaching lost control of his emotions. drinking party, the postwar revolutions calculus to morons. The memories of in science were being hatched. his friends in Los Alamos, of the end- Los Alamos was a turning point in less discussions, of the all-night poker ack in 1941 shortly after the Stan Ulam’s career. From that time on games, haunted him as he commuted United States entered the war, physics, not mathematics, became the daily among the tawdry streets of Los BStan (then still at Wisconsin) center of his interest. After watching Angeles. The golden boy had lost the began to notice that von Neumann’s let- Fermi and Feynman at the blackboard, company of great minds, his audience ters were becoming infrequent. Curious he discovered that he too had a knack of admirers. Like anguish that could no about his friend’s mysterious unavaila- for accurately estimating physical quan- longer be contained, encephalitis struck. bility, Stan managed one day to cor- tities by doing simple calculations with We still tend to regard disease as a ner him in Chicago. He implored von orders of magnitude. In fact. he turned mere physical occurrence, as an unfore-

LIM Alum(]s .hare Special 15sue 1!287 27 seen impairment of the body that also, havior put him outside the main-line mysteriously, affects the mind. But this Bethe-Fermi-Oppenheimer group, and is an oversimplification. After a man’s not even his fellow Hungarian von Neu- death, at the time of the final reckoning, mann felt at ease with him. This despite an event that might once have appeared the fact that he distinguished himself accidental is viewed as inevitable. Stan from the first days of Los Alamos as Ulam’s attack of encephalitis was the one of the most brilliant applied physi- culmination of his despair. cists there. After recovering from his operation, Teller related with difficulty anddif- Stan resigned his position in a hurry and was a perfect complement to Stan. Af- fidence to other scientists of his age. went back to Los Alamos. ter he had accepted Stan’s invitation to He felt more at ease either with young come to Los Alamos, they joined forces people or with celebrities, highly placed on a long and successful collaboration. politicians, generals and admirals. His he year was 1946, and the Los As their first project they chose the group (what eventually became the Alamos laboratory was now a dif- tbeory of branching processes. They Lawrence Livermore Laboratory af- Tferent place. Gone were most of believed they were the first to discover ter he left Los Alamos in a huffl was the luminaries (though many of them the probabilistic interpretation of func- highly disciplined, rank-conscious, and would make cameo appearances as con- tional composition. (They had ignored loyal. He would sagely guide his stu- sultants), and the federal government all previous work, all the way back to dents and assistants to doing the best was lavishing limitless funds on the lab- Galton and Watson in the nineteenth research work they were capable of, oratory. For a few years Los Alamos century! Stan never had the patience to and he would reward his followers with scientists found themselves coddled, se- leaf through published research papers. top-rank positions in academic adminis- cure and able to do or not do whatever He hated to learn from others what he tration or in government. they pleased, free to roam around the thought he could invent by himself and Since the success of the first bomb, world in red-carpeted MATS flights (that often did). They rediscovered all that Teller had been obsessed by the idea is, until Americans decided to give up had been already done, and added at of the “Super.” Because of disagree- the Empire they had won). least as much of their own. Tbeir re- ments between bim and Oppenheimer, Ulam came back to Los Alamos sults were drafted by Everett in three his project had more than once been on haunted by the fear that his illness might lengthy lab reports, which found sub- the verge of being cancelled. Now, Stan have irreparably damaged his brain. He stantial applications in the theory of Ulam was out to get him by proving knew his way of thinking had never neutron diffusion, an essential step in that his plans for the new bomb would been that of an ordinary mathemati- the understanding of nuclear reactions. not work. cian, and now less than ever. He also These reports were never published, feared that whatever was left of his tal- but they nevertheless had a decisive in- For about two years Everett and Ulam ents might quickly fade. He decided the fluence on the development of what is worked frantically in competition with time had come to engage in some sub- still a thriving branch of probability the- Teller’s group. They met every roo- stantial project that would be a fair test ory. The authors have received little ming for several hours in a little office of his abilities, and one with which his acknowledgement for their work, per- out of the way. Ulam would generate name might perhaps remain associated. haps as a spiteful punishment for their an endless stream of ideas and guesses, While at Wisconsin, Stan had met Ev- own neglect of the work of others. and Everett would check eacb one of erett. They had jointly written the first them with feverish computations. In paper on the subject tbat is now called Their second project was the bydro- a few months’ time Everett wore out algebraic logic (a beautiful paper that gen bomb. several slide rules. At last they proved has been plundered without acknowl- Teller wrong. And then, adding insult edgement). Everett, a seclusive and tac- to injury, Stan, in a sudden flash of in- iturn man, was richly endowed with the tan Ulam and Edward Teller had spiration, came upon a trick to make the ability to compute. He was a good lis- disliked each other from the mo- first hydrogen weapon work. tener, and he suffered from a paranoid sment they had met. Since the The full extent of Stan’s contribution fear of being fired for wasting Lab time days of the Manhattan Project, Teller to the design of the first hydrogen bomb on research in pure mathematics. He had been somewhat of a loner. His be- will never be precisely established. It is

28 L[M Alum<).> S[leme Speed Issue 1987 certain, however, that he was instrumen- passenger on an imaginmy ship, who tal in demolishing misguided proposals survived on momentary thrills designed that would have resulted in consider- to get him through the day. He sur- able waste of time and funds. It is ali rounded himself with traveling com- but certain that the seed idea that finally panions who were fun to be with and worked was his own. At any rate, the to talk to. He went to great lengths to ensuing loud dispute with Teller over avoid being alone. When he was, only the priority of the invention brought him the lure of mathematics could draw his wide publicity. (The patent application mind away from the clamor of his mem- for the device was jointly submitted by ing not to be a “professional” mathe- ories. Teller and Ulam.) The Democrats soon matician and by going into rambling 1 will always treasure the image of saw their advantage in adopting Ulam as tirades against the myopia of much con- Stan Ulam sitting in his study in Santa a bulwark against the Republicans, who temporary mathematics. Fe early in the morning, rapt in thought, had Teller on their side. He was invited scribbling formulas in drafts that would to sit in on important Washington com- The free rein Ulam gave to his fan- probably fill a couple of postage stamps. mittees and later became a darling of tasy fed on one of his latent weaknesses— the Kennedy era. his wishful thinking. He became an At last some of the glitter of his Pol- artist at self-deception. He would go he traits of Stan Ulam’s person- ish youth had come back, if not in the to great lengths to avoid facing the un- ality that became dominant in his form of tangible wealth, at least in the pleasant realities of daily life. When Tlater years were laziness, gen- guise of public recognition. anyone close to him became ill, he erosity, considerateness, and most of all, would seize on every straw to pretend depth of thought. that nothing was really wrong. When Those who knew Stan and did not he late forties and fifties w’ere the absolutely forced to face an unpleasant know what to make of him covered up high point of Stan Ulam’s life. fact, he would drop into a chair and fall the mixture of envy and resentment they THis personality thrived. His con- into a silent and wide-eyed panic. felt toward him by pronouncing him versation, always lively, became all the His severest critics were those close lazy. He was in fact lazy, in the dictio- more witty and engaging. The better to him who felt excluded from his pri- nary sense of the word. In the thirties part of his day was spent telling jokes vate world, who stood outside the mighty he would take a taxi to Harvard from and funny stories and inventing one fortress of mathematics. His daugh- his apartment in Boston to avoid tack- interesting mathematical idea after an- ter would browbeat him and cut him ling the petty decisions that a ride on other, like a wheel of fortune that never to pieces at regular intervals, incredu- the subway required. In Los Alamos stopped. The joke was the literary form lous of her father’s achievements. He there is a spot on a pathway up the he most appreciated. He would come took her criticisms in silence, and was Jemez Mountains that is called Ulam’s up with anecdotes, ideas, and stories on fond of quoting one of James Thurber’s Landing. It is as far as Stan ever went any subject of his acquaintance, how- lovely generalizations: “Generals are on a hike before turning back. More ever little his competence. He so liked afraid of their daughters.” often, he would watch the hikers with to dominate a conversation that some Despite the comfort of the Los Alamos binoculars from the porch of his house, of his colleagues began to take pains to Laboratory (in the fifties and sixties while sipping gin and tonics and talking avoid him. Now he had to win every Ulam was one of two research advisors to his friends. argument. When he felt he was on the to the Director of the laboratory), Stan Like all words denoting human condi- losing side, he would abruptly change could find no peace there. Since his re- tions, laziness, taken by itself, is neutral. the subject, but not before seeing the turn in 1946, he had, unbelievable as it It is a catchall that conceals a tension bottom of the other person’s position may sound, lived out of a suitcase. He of opposites. Fata ducunt, non trahunt. and summarizing it with irritating accu- owned beautiful homes in Los Alamos Ulam turned his laziness into elegance racy. Considering how fast it all hap- and Boulder, but he thought of himself in mathematics and into grand seigneur pened, it is remarkable how seldom he as permanently on the road. (Signifi- behavior in his life. He had to give all misunderstood. Mathematicians felt put cantly, his ashes are now in Montpar- of his thinking an epigrammatic twist down, and Ulam’s ways alienated him nasse Cemetery in Paris.) The Scottish of elegant definitiveness. His failing from the guild. He retaliated by claim- Caf6 was gone forever, and he was a became an imperious demand to get to

[.1)s A/am[)s S( it’n( e Special f\\ue /987 29 the heart of things with a minimum of continued fractions and thereby saved jargon. me much work. Once I bragged to him He had a number of abrupt conversa- about some computations I had done on tion stoppers that he used to get rid of the speed of convergence in the central bores. One of them was a question de- limit theorem, and he showed me how signed to stop some long tirade: “What to derive the same result by an elegant is this compared to E = mc2 ?” When I argument with ordinary square roots. first heard it (undoubtedly it was being used to stop me), I thought it a sign of to impress whomever he met during his Stan did his best work in fields where conceit. But I was wrong. He would travels. no one dared to tread, where he would wake up in the middle of the night and He was also too much of a grand be sure of having the first shot, free compare his own work, too, to E = mc2 , seigrzew to insist on his priority for the from all fear of having been anticipated. and he developed ulcers from these many new ideas he contributed to sci- He used to brag about being lucky. But worries. In truth, his apparent conceit ence. His nonchalance as to the fate and the source of his luck was his boundless was a way of concealing from others, success of his work has unjustly low- intellectual courage, which let him see and most of all from himself, the ag- ered his standing as a scientist. When an interesting possibility where everyone ing of his brain. On rare occasions he he saw one of his ideas circulating with- else could see only a blur. felt overwhelmed by guilt at his inabil- out credit, he remarked, “Why should ity to concentrate, which he viewed as they remember me? No one quotes He refused to write down some of avoidance of “serious” work. He looked Newton or Einstein in the bibliographies his best ideas. He thought he would at me, his intense blue-green eyes pop- of their papers.” find some day the time and the help he ping and slightly twitching (they were His way of expressing himself lent needed to work them out. But he was the eyes of a prophet, like Madame itself to his being exploited. He would misjudging the time he had left. His Blavatsky ’s), his mask about to come speak in sibylline pronouncements that best problems will survive only if his down, and asked, “Isn’t it true that I seemed to make little sense. Those of students ever write them down. am a charlatan?” I proceeded to set his his listeners who decided to pursue his Two of them have struck me. In mind to rest by giving him, as a seda- proposals (and often ended up writing the nineteenth century mathematicians tive, vaned examples of flaming charla- dozens of research papers on them) felt could not conceive of a surface unless tans taken from scientists we both knew they had spent enough of an effort in it was defined by specific equations. (both with and without Nobel Prizes). figuring out what Stan really meant After a tortuous period of abstraction, But soon his gnawing doubts would to reward themselves by claiming full the point-set topologists in this cen- start all over again. He knew he would credit. tury arrived at the abstract notion of a remain to the end a Yehudi Menuhin topological space, which renders in pre- who never practiced. A seed idea is the last thing we want cise terms our intuitive grasp of the no- His generosity was curiously linked to acknowledge, all the more so when tion of extension. Ulam proposed going to his laziness. A generous action is it originates from a native intelligence through a similar process of refinement often impulsive and calls for little fore- seemingly blessed with inexhaustible on Maxwell’s equations to arrive at an sight. Its opposite requires the careful luck. After we silently appropriate it, abstract structure for electromagnetic advance planning that Stan loathed. we will soon enough figure out a way to theory free of algebraic irrelevancies. He fancied himself a grand .yeigneur obliterate all memory of its source. In a The second problem bore on ergodic of bottomless means, and in matters last-ditch effort to salvage our pride, we dynamical systems. Poincare, and sev- of money he was apt to practice the will also manage to find fault with the eral others after him, taught us that in art of self-deception. In his penurious person to whom we are indebted. Stan such a system every state is visited in- years he went to great lengths to con- Ulam’s weaknesses were all too appar- finitely often, given a sufficiently long ceal his shaky financial condition. He ent and made him more vulnerable than time. In practice, however, the recur- always lived as the spirit moved him, most. But the strength of his thinking rence times are so large that one cannot sometimes beyond his means. He car- more than made up for what he lost to observe successive visits, and the prac- ried on his person bundles of fifty and the pettiness of others. tical import of ergodicity is nil. This one-hundred dollar bills, partly from a Stan once showed me in five min- paradox became strikingly evident after remnant of the refugee mentality, partly utes the central idea of the theory of the Fermi-Pasta-Ulam computer sim-

30 L[)s Alum[>.~ S[ [en[e Special Issue 1987 ulations of coupled nonlinear oscilla- drawn to him by a fascination that went tors. (These were written up in one beyond the glitter of new ideas of ar- of Fermi’s last papers. It is rumored resting beauty, beyond the trenchant that Fermi considered this to have been remarks that laid bare the hidden weak- his most important discovery.) In these ness of some well-known theory, be- nonlinear systems the initial state is vis- yond the endless repertoire of amus- ited several times before another set of ing anecdotes. The fascination of Stan available states is even approached. Af- Ulam’s personality rested in his supreme ter observing this phenomenon, Ulam which he will be remembered alongside self-confidence. His self-confidence guessed that in some ergodic systems Teller. was not the complacency of success. the phase space ought to be measure- It rested on the realization that the out- theoretically represented by two or more Only in the last years of his life did come of all undertakings, no matter how big blobs connected by thin tubes. He his thinking take a decisively specula- exalted, will be ultimate failure. From wanted to express his guess in terms of tive turn. He always professed to dis- this unshakeable conviction he drew his ergodic theory. I wish we knew how. like philosophical discussions, and he strength. Stan’s fascination with physics led excoriated ponderous treatises in phi- This conviction of his, of course, was him to formulate mathematical thoughts losophy. He thought them in bad taste, kept silent. What we heard from him that had a background of physics, but “Germanic” (one of his words of repro- instead were rambling tirades against they invariably bore the unmistakable bation). Nonetheless, he had an instinc- mathematicians and scientists who took ring of mathematics. (He once started to tive grasp of philosophical issues, which themselves too seriously. He would tear draft a long paper that was to be titled he refused to express in words. When to shreds some of the physics that goes “Physics for Mathematicians.’’) One of forced to take a philosophical stand, he on today, which is nothing but poor the most striking is his proposal for the would claim to agree with the naive sci- man’s mathematics, poorly learned and reconstruction of the cgs system (dis- entism of H. G. Wells and with the pos- poorly dressed up in a phoney physical tance, mass, and time) on the basis of itivism of the Vienna Circle (the reign- language. But his faith in a few men a random walk. Another, which Dan ing philosophy of his time), but in his whom he considered great remained Mauldin has recently proved true, is the actual thinking he was closer to the phe- unshaken: Einstein, Fermi, Brouwer, existence of a limiting energy distri- nomenoIogy of Husserl and Heidegger. President Truman. bution for systems in which energy is His knowledge of philosophy suffered redistributed through particle collisions. from his habit of scanning without read- Thinking back and recalling the ideas, ing. He seldom read a book from top to insights, analogies, nuances of style that Stan Ulam’s best work is a game bottom; more often he would handle it I drew from my association with him played in the farthest reaches of ab- long enough to pick out the main point, for twenty-one years, I am at a loss to straction, where the cares of the world sometimes after correcting a few mis- tell where Ulam ends and where I really cannot intrude: in set theory, in measure prints, and then literally toss it away. begin. Perhaps this is one way he chose theory, and in the foundations of math- I once set up a little test of his under- to survive. ematics. He used to refer to his volume standing of existentialism, by way of of collected papers as a slim volume of teasing him. I gave him a collection of He could not bear to see unhappiness poems. It is just that. poems written by Trakl, the first exis- among his friends, and he went to any As a mathematician, his name is most tential poet in German. Stan read them lengths to cheer us up when we were likely to survive for his two problem all and was visibly moved. I will al- down. One day, we were driving to- books, which will remain bedside books ways regret not being able to hold his wards the J6mez Mountains, along the for young mathematicians eager to make attention long enough for him to get the stretch of straight road that starts right their mark by solving at least one of basic idea of Husserl’s phenomenology. after the last site of the laboratory. I felt them. He also wanted to be remem- He would have liked it. depressed, and drove silently, looking bered for those of his insights that found straight ahead. I could feel his almost substantial practical applications, such Those of us who were close to him physical discomfort at my unhappiness. as the Monte Carlo method, for which at the end of his life (Bednarek, Beyer, He tried telling some funny stories, but he will share the credit with Metropolis Everett, Mauldin, Metropolis, Myciel- they didn’t work. After a minute of si- and von Neumann, and the bomb, for ski, Stein, and I, to name a few) were lence, he deployed another tactic. He

Lo> Alumos S1 /en[’e Speclal Issue 1987 knew I had been interested in finding out just how much physics he really knew, and that I had unsuccessfully tried to quiz him. Now he launched on a description of the Planck distribution (which he knew I didn’t know) and its role in statistical mechanics. I turned mound, surprised at the thoroughness of his knowledge, and he smiled. But a few minutes later he again fell silent, and the gloom started all over. After a minds have been discouraged from a pause that was undoubtedly longer than career in science by reading such un- he could bear, he blurted out: “You are realistic portrayals of the scientist as a not the best mathematician I have ever saint. Moreover the presumption that met, because von Neumann was a better “good” behavior (as interpreted by the one. You are not the best Italian I have biographer) is a prerequisite for success ever met, because Fermi was a better in science betrays a lack of faith in sci- one. But you are the best psychologist ence. Lastly, one should tell the truth, I have ever met.” This time I smiled. even when such a truth belies our ideas It was his way of acknowledging our of how things ought to be. friendship. He knew that I could see Stan Ulam was lazy, he talked too through his weaknesses, through his much, he was hopelessly self-centered laziness, through his inability to do any (though not egotistical), he had an over- prolonged stint of work. He knew that powering personality. But he bequeathed I discounted those weaknesses, and that us a view that bears the imprint of depth I saw, beyond them, the best of his per- and elegance, one that enriches our lives son. That he appreciated. and will enrich the lives of those who come after us. For this he will always be remembered. ¤ o other period of civilization has been so dependent on hypocrisy Nfor survival as the belle 4poque, Gian-Carlo Rota is a Professor of Applied the Victorian Age. It has bequeathed Mathematics and Philosophy at the Massachusetts us a heritage of lies that we are now Institute of Technology. He has served as a consultant to the Laboratory for over twenty charged with erasing, like a huge na- years. tional debt: the image of the hero as the fair-haired boy, and the sharp parti- tion of all people into “good guys” and “bad guys.” These false illusions must tIow make way for biographies in which ambiguity, duplicity, and the tension of opposites are seen as the fundamental forces that drive every person. The prejudice that the scientist, as a seeker of the truth, is immune from the passions of the world and is capable of doing no wrong, a prejudice prop- agated for over a century by bigoted biographers, has done harm. One shud- ders to guess how many talented young

32 [.1)s Aiumi)., S[ien[ <. Special l\ sue 1987