This is a bad book: bad in its social philosophy, bad in its conception, bad in its scholarship, of bad mentality. It is intellectual biography reduced to the level of pulp fiction. However, it's a bad book about an important subject. As this subject is rarely written about, this may make the book important. Furthermore, the badness of the book is closely tied to the importance of its subject, and the importance of its subject has something to do with the importance of the word "important" in the meta-vocabulary of science , that is to say, the language scientists employ when talking to one another about science . I hope later to devote a section of this review to my insights on this important matter.
The concerns of this biography ought to concern us for many other reasons as well, reasons which for the most part, probably never occurred to its author : A Beautiful Mind is the story of how the unstable psyche of an intelligent man, the mathematician John Nash descended , under the encouragement of the irresponsibility and corruption of an appallingly sick professional community, within the decadent institutional frameworks of a sick civilization, into a psychotic breakdown lasting 30 years.
I herein break with the self-reinforcement of tradition, in calling John Nash an intelligent man , not a genius ; though many people would argue that there has been considerable evidence for the latter, but not much for the former. My own opinion is that Nash is not, and never was, a genius: the arguments will be grouped in the final section of this review. It makes some sort of sense to say that Archimedes, Gauss, Newton, Poincare and Einstein were geniuses (Along with various women and non-Europeans who never had a chance to prove that they were geniuses because they never had a chance to do mathematics. ) though I do not willingly undignify such accomplished beings with this trashy label. John Nash has never walked with them on their august promontory. Before the onset of his misfortune, between 1948 and 1958, Nash produced a steady stream of mathematical researchpapers of a high quality, nothing that anyone need feel ashamed of. Among the general public, raised on a diet of journalistic drivel, there are plenty of people who think that anyone who does research worth publishing in mathematics is a genius. And Nash was better than most.
We need only retain the word, 'genius' in the vocabulary to describe an historical phenomenon dating back to the Enlightenment that has inflicted immense damage on our civilization. It is not going too far to say that the mystique of genius as it was applied to John Nash - by colleagues, university administrations, Cold War think tanks, journalists, friends, male and female sexual intimates, and inevitably, by Nash himself - was a major contributing factor in the destruction of Nash's life and mind. Indeed, a more woeful saga of make-believe , spoilage, vanity, ignorance, insensitivity and exploitation is scarcely to be imagined.
Although Sylvia Nasar, via this book, places herself at the head of the groupie pack , her narrative gift and the thoroughness of her research go far to undermine her monument to 'genius infatuation' . Those of us able to read between the lines will value it for its documentation of the pitiable moral character of the American mathematics community in the latter half of the twentieth century.
This review is divided into 3 parts. The first is a precise of the life and career of John Forbes Nash, Jr. The second discusses the merits and demerits of Nasar's biography. The third will be a general meandering on mathematics, mathematicians, and the value of Nash's mathematical opus.
John Forbes Nash, Jr.( When there is no ambiguity, he will be referred to generally as 'Nash', or ' John Nash' . However, since his father's surname was John, and both his sons, (by different women) , are called John, ambiguity may manifest itself in many ways . ) was born in 1928 in Bluefield, West Virginia. His father, J.F. Nash, Sr., was an electrical engineer, his mother Virginia an elementary school teacher. In 1945 he won a Westinghouse scholarship to Carnegie Tech, majoring in chemical engineering. The chairman of the mathematics department at this time was John Lighton Synge,(Sylvia Nasar incorrectly states that he was the son of the playwright John Millington Synge. ) the noted relativist from the Institute for Advanced Study in Dublin, Ireland. Under Synge's guidance, Nash's outstanding talent for mathematics quickly manifested itself, and in 1948, Nash was offered scholarships from both Harvard and Princeton. He chose Princeton, although he has ever afterwards felt diminished by not being able to call himself a Harvard man.
In the 1930's and 40's Princeton University set out, in typically American fashion, to create a world class research center through infusions of huge amounts of money. The predictable result was a nightmare. Princeton's reputation at the time was that of a finishing school for jocks from the deep South. They were being sent there for the business contacts and social veneer that might later prove useful in professional life. More specifically,
"During the 19th and early 20th century Princeton University was a seed-bed for the education of southern white leadership. As a member of the class of 1928 once put it, 'Princeton is popular through the south because it is the one eastern school which does not enroll negroes.' Throughout much of its history the university has been described as a northern town that has its spiritual heart in the south. The social attitudes that prospered in the south were given free reign and support at the university and the town that sustained it." ( Web page of The Historical Society of Princeton)
By the end of WWII , Princeton's mathematics department was, if little more commendable, very different from the rest of the university. Exceptional mathematical talents, prodigies and whiz-kids recruited from all over the country were immersed in a mathematics pressure cooker, whipped into shape by the bully tactics of Solomon Lefschetz and others. This was to be a factory, unique in scientific history, for churning out mathematics theorems like automobiles from a Detroit assembly line.
" On Nash's second afternoon in Princeton, Solomon Lefschetz rounded up the first-year graduate students in the West Common Room. He was there to tell them the facts of life, he said, in his heavy French accent, fixing them with his fierce gaze. And for an hour Lefschetz glared, shouted, and pounded the table with his gloved, wooden hands, delivering something between a biblical sermon and a drill sergeant's diatribe." ( A Beautiful Mind, pg. 58 )
The social life of Princeton University thus precessed erratically between the barracks life of the genius incubator and the drunken brawls of the 'true sons of the Confederacy'. The enormous differences between the groups at the polar extremes are obvious, but one should also note their similarities; callowness, rudeness, arrogance, inadequate or failed socialization, and a conviction of superiority over the rest of the human race, the jocks because of their breeding, the whiz-kids because they knew they were smarter than everybody else.
It is clear that Princeton University of the late 40's served to catalyze Nash's life of mental illness. Its' unwholesome artificiality was compounded by an additional factor: the enforcement by the Cold War of tendencies to conformity, personified by the Princeton faculty and administrators, including math department inhabitants like right-wing hawk, John von Neumann.
In 1944 John von Neumann and Oskar Morgenstern published their Theory of Games and Economic Behavior . This treatise, and its subsequent editions of 1947 and 1953 , lit-up the halls of academic economics like a big light-bulb. This was due in large part to the promulgation of the paradigm of the "zero-sum, two person game" , which enables anyone to talk at great length about economic behavior, but has never had any application to situations encountered in the real world. Since Game Theory could thereby reduce much of economics to a Theoretical Game, it was highly fungible, which means that it could be readily adapted to such purposes as writing PhD theses, awards , honors, promotions and tenure, all in the name of the fatuous elaboration of the what-might-be-if-only . This being the oldest 'game' in academic life, Game Theory won its place in the living tradition that goes back to the scholastics of the Middle Ages, next to psycho-analysis, structuralism, the New Criticism, linguistic analysis and deconstructionism.
In 1948 the twenty-year old Nash noticed that, by a slight modification of von Neumann's initial assumptions to include the notion of the 'non-cooperative game', one could treat each pure strategy as an independent coordinate in a multi-dimensional Euclidean space. This opened the way to the application of classical 'fixed point' theorems ( Brouwer, Kakutani), to prove the existence of equilibrium solutions ( situations in which no player can change his strategy without reducing his pay-off).
Not every game has a Nash equilibrium point; not every equilibrium point constitutes an optimal strategy for anyone; and since Nash uses existence rather than constructive proofs, the only way to find these points in most cases is by trial and error. Uselessness thereby being pushed to a higher level, the result was hailed far and wide as the undeniable manifestation of "genius". The Nash legend was born.
His insight was clever, but the actual mathematics involved is a triviality. Almost half a century later it was this footnote to an otherwise exciting mathematical career that would, in 1994, earn him the Nobel prize in economics. Any evidence that would lead me to concede that the Nobel prize has any real meaning would have upset me.
As a general rule, the Nobel prize in physics is a fairly accurate indicator of the priorities of the science, the Nobel prize in literature is totally capricious, while the Nobel prize in economics is consistent in its emulation of mediocrity. ( I refer interested parties to my Chant to honor the Nobel Prize of Gerard Debreu who proved Reaganomics by Pure Mathematics. Available directly from the author for $5 ) Nash's prize does not provide a counter-example. On the other hand, he has deserved most of the prizes awarded to mathematicians , The Fields medal, Bocher prize, Crafoord prize, etc. , although he's never received them. Merit and honors come together at best by accident.
Nash joined the faculty of MIT in 1951 , where he remained until quitting in 1959. From Nasar's account we learn that Nash carved out a special niche for himself in the pantheon of the world's worst mathematics instructors. Students in his classes were regularly derided and ridiculed. He called them "stupid" and "idiots" - to be fair, he didn't treat his colleagues any better. He ignored both questions and requests. He was fond of springing mid-term exams without prior notification. On a moment's notice he would turn his classes over to unprepared graduate students and hop off to the West Coast to cruise with his network of boy-friends. He was fond of placing classical unsolved conjectures, ( including Fermat's Last Theorem), on final exams, and questions like 'What is your name?' If student XZ simply wrote down his name rather than writing out ' My name is XZ ' in full , Nash deducted 25% points from the grade.
Although Nash was tottering on the brink of insanity by the winter of 1958, MIT's math department voted in January of 1959 to grant him tenure. This indicates the utter contempt in which it held its' students. There is a mythology which would have us believe that the granting of tenure at American universities is based on 4 factors: teaching ability, research, getting along with colleagues, and community service. Nash provides a paradigmatic example of the elementary truth, that research alone counts: this being the only factor for which his record was not abysmal. Perhaps, even as the mental hospital kept Ezra Pound out of the penitentiary, so MIT kept John Nash ( temporarily) out of the mental hospital. What is more mysterious than the way of the genius?
In the early 50's, Nash also did some thinking of the unthinkable for the RAND corporation, the Cold War think tank in Santa Monica. The military's addiction to game theory has a lot to do with why the US persisted in and ultimately lost the Vietnamese war. John Nash, John von Neumann, John Milnor, Donald Spencer, Lloyd Shapley and other gamers from Princeton were not adverse to taking money from the government for 'research' that they well knew amounted to little more than esoteric fooling around.
In 1955 Nash fell into a clumsy entrapment 'strategy' designed by the Santa Monica police department for catching homosexuals, and was summarily dismissed from RAND. Sylvia Nasar, with her admirable thoroughness, devotes an unbelievable amount of space to tracking down every one of Nash's homosexual liaisons. At the same time , A Beautiful Mind says almost nothing about his tastes in art, music, poetry, literature, philosophy, religion, cooking, flowers, wall paper, sports, etc. When his politics is discussed, it is only with reference to his insane delusions of the 60's and beyond. The words 'Civil Rights' and 'Vietnam' do not appear in the index. All does indeed look jaundiced to the jaundiced eye.
It was in the period of his employment by MIT that Nash produced the 3 remarkable results that make him famous among mathematicians:
the differentiable manifold-real algebraic varieties papers (1952);
These will be discussed in a separate section which can be skipped by the amathematical or anti-mathematical reader.
In 1953, John David Stier was born to Eleanor Stier and John Nash. Further commentary on this event is limited by my dependence on the account Sylvia Nasar's biography, the number of factual errors of which is of the same order as magnitude as its number of footnotes. Given her extensive documentation , we can assume that when she does make a mistake it is not a deliberate lie. Although the intellectual level of her discourse rarely rises above a television talk show ( Geraldo or, at best, Oprah Winfrey), one ought not forget that most of the social life of mankind, including that of great geniuses, is conducted at this level. By observing the world from a low perspective she is able to connect with the low behavior that people actually exhibit, which has the effect of making many of her observations reliable .
Sticking with Nasar's story, John Nash's interest in Eleanor Stier seems to have been restricted to going to bed with her. He refused to marry her. It appears that he was too ashamed of her poor education and too vain of his ' superior social class' ( a fiction that Nasar relentlessly invokes) , to introduce her to any of the MIT illuminati. That his son, John Stier, migrated through two dozen foster homes before the age of 12, ( including refuges with delightful names like the " New England Home for Little Wanderers"), seems never to have ruffled him: why concern yourself with a mewling brat when you're busting your balls to give the world an isometric embedding theorem? Recall that for the first three years of John Stier's life, Nash was raking in a king's ransom from his work as a RAND consultant.
Eleanor Stier found the nerve to sue him for child support in 1956, after she surprised him in his apartment together with his fiancee, Alicia Larde. Up until that moment she had continued to live and sleep with him: he did, after all, have a beautiful behind.
His mental collapse ended a decade of astonishing productivity in mathematics. Between 1964 to 1966 he rallied somewhat to produce a handful of lesser results, after which, as far as we know, ( and the history of science is full of surprises, though not so many as nature itself ) , he has done nothing notable in his fields . His teaching career was over by 1959, which is something of a shame, as it should have ended in 1951.
His manner of going insane was utterly admirable. Whatever nobility there is in the man surfaced in this period. One might even argue that his "genius" never deserted him, but merely changed fields from non-linear partial differential equations to guerrilla theatre. That most of his colleagues were too spaced out to recognize the Hamlet in their midst is entirely their fault, not his.
The first hard evidence of insanity proclaimed itself on the afternoon of January 20th , 1959 ( Nasar, op, cit., pg. 241 ) in the lounge of the mathematics department of MIT. Setting the scene requires that we now devote a few paragraphs to the description of a typical afternoon in the common room of a typical mathematics department at a major university, something that can only be understood from direct experience. Further , it must be savored, studied, mediated in tranquillity, pondered in fascination.
As a class, (by which the author means that there are many exceptions to the standard model, for which we must be thankful.) research mathematicians are competitive, rude, introverted, irritable and poorly endowed by disposition or training with the conventional social graces. It is a noisy silence, rather than voluble discourse, that fills the corridors and common rooms of research departments. People in divergent disciplines, logic and differential equations for example , use such incompatible vocabularies that they, literally, have nothing to talk about. Persons in somewhat similar fields, with overlapping vocabularies but perhaps a slightly different focus, may experience severe culture shock , similar in many respects to that of the average American tourist wandering about London, when they try to communicate with one another.
Persons in exactly the same area of research also don't tend to talk to each other. On one level they may be concerned that others will steal their ideas. They also have a very understandable fear of presenting a new direction of inquiry before it has matured, lest the listening party trample the frail buds of thought beneath a sarcastic put-down.
When an idea has developed to the point where they realize that they may really be onto something , they still don't want to talk about it . Eventually they want to be in a position to retain full credit for it . Since they do need feedback from other minds to advance their research, they frequently evolve a 'strategy' of hit-and-run tactics, whereby one researcher guards his own ideas very close to the chest, while trying to extract from the other person as much of what he knows as possible.
Above everyone's head at a gathering of mathematicians hangs the scimitar of exposure of ignorance . Say you get into conversation with someone who brings up the concept of a "Riemann surface". You decide to risk all by confessing that you don't know what a Riemann surface is. The words are barely spoken when already the eyes of almost everyone else in the lounge is fixing you with a look of long-suffering, malevolent and self-righteous disgust . Never mind that your field is mathematical logic, or discrete semi-groups, or computability, or combinatorics, in which the concept of a Riemann surface rarely, if ever, enters. You are now forever type-cast as ignorant . Excessively insecure individuals, notably graduate students, may even start wondering aloud, ( behind your back naturally), what somebody like you is doing in their great department in the first place.
Because just about everyone fears lest his ignorance be disclosed, people rarely open their mouths for any purpose other than that of speaking innocuous banalities. Or sometimes they may venture to talk about other subjects altogether, music, or politics, or Elizabethan drama. Yet one must be careful not to do too much of this, since there are some sorts who may begin suggesting that he's covering up his ignorance of 'real mathematics' by vaunting his knowledge of something else. Furthermore since many mathematicians do not cultivate interests outside of mathematics, such conversations on complementary subject matter soon peter out.
Departmental teas tend to be held around 3:30 or 4:00, just before the afternoon seminars and colloquia. People sit apart, or in little groups, their minds consumed by calculation:
The obsessive-compulsive calculation of solutions to problems and equations. This goes on relentlessly , even in dreams.
The calculation of how much of what one thinks or knows may be safely revealed in a room of many potential enemies and few allies.
At those times the climate of a mathematics lounge will be crippled by an oppressive and surly silence. Conversations will be punctuated with long, vacant silences, abstract gazing at the empty walls or out the windows, and excessive caution in speaking out. Hostility in all of its forms, subtle or crude, is omnipresent. Indeed the atmosphere may be so thick with tension that only a saber could cut it.
On the afternoon of January 20th, 1959, John Forbes Nash Jr. , (that is to say, the department genius) brandishing that day's copy of the New York Times, walked into something resembling the above in the mathematics lounge at MIT. In a strident voice he announced that he'd discovered that the little box in the upper left-hand corner of the front page ( the off-lede) carried a message from outer space aliens to the governments of Earth, which he alone was able to decipher.
Pandemonium reigned long after he'd left.
It's probably the only correct way to deal with such people. Most of us haven't got the guts to pull it off ; Nash did only because he was going crazy. Subsequent events would reveal that there was considerable method in his madness, though few people in the community got the message. Its' basic response appears to have been to try to help him get back to normalcy; no-one seems to have seen anything wrong with the way of life that produced his condition .
Nash then ventured into the domain of Mail Art, a genre much cultivated by the Dadaists and Surrealists. A letter sent to the French mathematician, Claude Berge written in 4 different colors of ink complained that his career was being ruined by aliens from outer space. It was; I happen to be acquainted with several of those aliens personally.
His next bold act of emancipation was the rejection of an attractive job offer from the University of Chicago. (Chicago's was the dominant mathematics department in America from 1947 to 1959, not Princeton as Sylvia Nasar, ( and the Princeton cheer-leaders) would have us believe: cf. Saunders MacLane, "A Century of Mathematics in America", Part II, AMS, 1989; page 126 )
He wrote back thanking them for the offer, explaining that he could not accept it because he was about to be crowned Emperor of Antarctica. Most of us never get the chance to write such a letter. We can be grateful to Nash for rising to the occasion.
Around the same period, one of his personal friends, the gentle Eugenio Calabi visited MIT and gave a lecture. Nash walked into the seminar room in the middle of his talk and started ranting at a student named Al Vasquez because he'd discovered a photograph of himself on the cover of Life Magazine, thinly disguised as Pope John XXIII. Nash had just discovered numerology: ( My own work experience as a "Mathematics Consultant for the Arts" has shown me that numerologists ascribe horrendous "significance" to the number 23.It is , among other things, one of only two numbers ( the other being 3001), that cannot be expressed as a sum of less than 9 cubes. ) Calabi ignored the disturbance, the audience ignored it. Only Vasquez, apparently, realized that something was amiss.
This doesn't surprise me, since I've often witnessed similar things at mathematics lectures . One example: in the early 90's a famous Russian geometer was invited to UC Berkeley to give a series of lectures. His audience was so large that we had to be moved to the auditorium of the Bechtel Engineering Building. The stage on which he was standing was pitch-black. He assiduously covered 4 blackboards with equations, of which no-one in the audience could see so much as a decimal point. Yet such was the veneration in which the man was held, that nobody had the audacity to suggest that the stage lights be turned on. It was, in every sense, the 'Emperor's New Math' . In fact there was one exception - after 15 minutes of this bizarre performance, I was the one who stood up, left the auditorium, and roamed the building looking for a janitor. Of course, for the five minutes that I was gone, I was missing perhaps the most precious distillations of his wisdom. She came back with me, walked onto the stage, and turned on the lights. Seating myself once again , I'd the impression that I'd upset numerous members of the audience with the crime of distracting them from their distraction.
On the afternoon of February 28th, 1959, at Columbia University in New York City , like Samson chained in the temple of the Philistines, John Nash finally brought the walls crumbling about everyone's head, not the least his own. He did this by presenting his stream-of-consciousness proof of the Riemann Hypothesis , the most intractable conjecture in all of mathematics. It was guerrilla theater at the acme. By that evening, most of the mathematics community between Boston and Princeton knew that Nash was mad. But so what? The only victims of his madness would be undergraduate students, disposable cannot fodder in the best of times.
However , by the end of April, Nash had been committed to McLean Hospital in Belmont, Greater Boston. Something had to be done; I don't fault people for turning to mental asylums in serious emergencies. They may at times be the only thing that the primitive psychiatric medicine of our society has to offer. If you're dying of malaria in the Amazon jungle, and the only remedy the local Native Americans have to offer is rattlesnake dung, you take it. The commitment was done by his wife, Alicia, the MIT administration, and the MIT psychiatric staff.
He shared a room with Robert Lowell, who wrote poetry that hardly anyone reads, but who is famous nevertheless. Their co-habitation provides one of the narrative's moments of high comedy. As a regular feature of their daily routine, Lowell and Nash's room filled up with staff, students and other worshippers of genius. As the twin gurus expanded fulsomely on their delusions, ( most of the fulsomeness being Lowell's ) , the reverent crowds wrote down every word dropping, like sea-gulls darting for herrings, from their lips.
Upon his release from McLean, Nash resigned his tenured post at MIT. This was to his credit , as he could probably have hung on there for the rest of his life and gotten away with doing nothing. There is a 'genius alcove' on the 4th floor of the MIT mathematics department where few dare to tread.(I tried it once. ) His second son, John Charles Martin , having been born in the interim , Alicia left him in the care of his mother-in-law and took Nash to Paris.
There he embarked on what appears to have been the one truly noble gesture of his entire career: the renunciation of his American citizenship and self-declaration as a "citizen of the world", in the manner of Gary Davis.
That it didn't work was only because the governments he had to deal with were as crazy as he was. It is characteristic of certain forms of insane behavior that they would be considered sane in a sane world; but since it isn't, they aren't. John Nash's realization that nationalism is an outmoded, ignorant and destructive delusion aroused degrees of paranoia in many respects comparable to his own, in the officialdom of France, Luxemburg, Switzerland, Liechtenstein and East Germany. On April 21,1960, he was rounded up by the French police in his apartment on the rue de la Republique, escorted to Orly airport and put on a plane bound for the United States. Less than a year later he would be undergoing insulin shock treatments at Trenton State Hospital.