Ferment
VolXII #4
September 9, 1998
Editor, Roy Lisker
8 Liberty Street # 306
Middletown, CT. 06457
aberensh@lynx.neu.edu
rlisker@yahoo.com
 

Note: A tribute was presented to me on my 60th birthday (September 24th, 1998) in the form of a webpage. It 
contains photographs and news clippings  about me going back to the  activism of the 60's; also writings, and 
commentary from Kenn Thomas, editor of Steamshovel Press, (free wheeling political conspiracy magazine 
published in St. Louis.)  It's better than any resume I've ever put together on my own. Internet access is at 
http://www.umsl.edu/~skthoma/royalien.htm.
 

"A Beautiful Behind"
Book Review:
Sylvia Nasar: A Beautiful Mind, a biography of 
John Forbes Nash, Jr.; Simon & Schuster, 1998;  $25;  
ISBN: 0-684-81906-6 I.
        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 s
ick 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   - 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 research papers 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. II. 
        John Forbes Nash, Jr. 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,  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 typical 
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 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.   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,   
although he's never received them. Justice and politics 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 the student simply wrote down his name rather than ' My name 
is ________'  , 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); 
the solution to the isometric embedding problem  (1954-56); and his work on 
bounding estimates for multi-dimensional parabolic partial differential 
equations  (1957) .  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 fiancŽe, 
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,   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, usually by deceit, 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:
                        (1) The obsessive-compulsive calculation of solutions 
to problems and  equations. This goes on relentlessly , even in dreams.
                        (2) 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. , 
brandishing that day's copy of the New York Times, walked into 
something resembling the above in the mathematics lounge at MIT. In a 
strong 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 . Even so do Polonius,Gertrude, Claudius  go to their deaths.
        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.    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 experience as a "mathematics consultant for 
the arts" has revealed to me that  numerologists  ascribe horrendous 
"significance" to the number 23.   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 intractably difficult conjecture in 
all  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. 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.   His second son,  John Charles Martin  , having been 
born in the interim , his wife  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. In less than a year he would be undergoing 
insulin shock treatments at Trenton State Hospital.
        In some respects he was lucky . In this and subsequent 
incarcerations, doctors who raised the spectre of electroshock therapy were 
successfully  thwarted by Nash's friends, family and colleagues,  who managed 
to convince them of the obligation of protecting Nash's grey matter for the 
good of humanity. I myself have  reason to be grateful for such type-
casting. There is no doubt that the quasi-prodigy status that I acquired 
at the age of 15, when I was skipped out of 10th grade into a graduate 
program in mathematics at the University of Pennsylvania, was a 
principal influence  on the decisions of my various doctors not to put 
me through electroshock therapy during my own brief bouts with psychosis in 
1957 and again in 1973. Being labeled a "genius" has definite 
advantages: don't knock it. 
        There was a temporary remission of his symptoms in 1965 . In 1967 
he returned to his family , now living in Roanoke , Virginia. In the 3 
years he stayed with them his mind was totally inflamed,  engulfed by 
delusions of an intensity beyond anything he'd known up to that point. It was the 
worst period of his ordeal. 
        In 1970 he returned to Princeton. His mother had died and his 
sister could no longer take care of him. On the threshold of homelessness, his 
ex-wife Alicia Larde, though no longer married to him, invited him into  
her  house in Princeton Junction.  He had good reason to be grateful to her: 
Nash never had to move into the New England Home for Little 
Wanderers. 
        Nash's return to Princeton initiated his transformation from the 
local genius of the 50's to the genius loci of the next 2 decades. As 
the  "Phantom of Fine Hall"  , he wandered through the rooms and corridors of 
the Princeton mathematics department, wild, unkempt and harmless, 
obsessed with numerology, chalking cryptic messages on the blackboards. 
Some of them were prophetic . On a blackboard in the basement corridor 
linking Jadwin and Fine Halls, this message was uncovered in 1970  :
" N5 + I 5+ X5 + O5 + N5 = 0 "
        His condition was indeed pitiful, his reason, ( according to any 
reasonable definition thereof), unhinged, and to some he served as an 
ambulatory object lesson to those who would offend the gods through 
forcing their intellects to dizzying heights at the cost of their 
immortal souls. This role actually turned him into a far more interesting human 
being than the one who, in those bygone days, divided his time between 
crapping on his students, working for 12-hour stretches on the isometric 
embedding theorem, then walking across the Harvard Bridge late at night 
to fuck Eleanor . 
        All through the 60's and beyond,  even in  times when he was most 
extravagantly deranged, friends and  colleagues  kept trying to line up 
teaching positions for him, at the University of Michigan, Northeastern 
University, MIT, Princeton. The salvation of a genius seemed to them 
well worth the price of killing all joy in mathematics for generations of 
undergraduates. The general attitude of the mathematics community is 
best summed up by this quote from a member of  Nash's legion of hero-
worshippers, the mathematician Donald Spencer:
	"When I look at the human race all over the world, I think there's 
zero reason for humanity to survive. We're destructive, uncaring, 
thoughtless, greedy, power hungry.  But when I look at a few individuals, 
there seems to be every reason for humanity to survive. [Nash] was worth 
doing the very best for."   (op. cit., pg. 304  )  Spencer fails to tell us in 
what particulars Nash differed from his description of the rest of the human 
race;  but I know what he means:  All hail the eubermensch  .
        The following  example suggests that in some ways  John Nash's 
outlook on the world was wiser  in his mad period than in his  previous 
sane state.  After his return from Paris in 1960,  Oskar Morgenstern 
offered him a high-paying consultant's job as a game theorist. The deal 
fell through when Nash refused to fill out the W2 forms: he could not because 
he was  a citizen of Liechtenstein. Apparently John Nash differed  from 
most of the  world around him in at least 3 respects: he was a genius; 
he was mad; and he had a sense of humor.
        John Nash's remission from 'schizophrenia'    began around 1983. 
By 1992 he was once again, in a manner of speaking, sane. He has remained 
so ever since , and we can only hope that his condition has stabilized. 
In 1994 he was awarded the Nobel prize in Economics for the clever take 
he'd done on Game Theory  in his thesis of 1948, (a document of such awesome 
importance for the fate of mankind that no-one has ever thought it worth 
the effort to publish it ) . John Charles, after demonstrating real 
promise  in college,  has also been crippled by severe mental illness for most of 
his life. His story is perhaps more tragic than his father's, in that he has never 
had a chance to develop  his potential. Given that society as  a whole has 
absolutely no conception of what is genuinely productive, it may be that 
only the supreme deities know the definitions of usefulness , meaning 
and fulfillment in life.
        John Stier and his father have established strained relations.  If 
we can believe Nasar, Nash still treats his son badly, but no longer 
irresponsibly. Guilt casts a long shadow. 
        This concludes our obviously unbiased summary of the life  of John 
Forbes Nash, Jr.  We now turn our attention to the literary merits of  " A Beautiful 
Mind". The fatuousness of Nasar's mentality complements that 
of  the community she describes, but she is on her own when she plummets 
to levels of ignorance where it does not normally tread. 

III.

        The most benign of all the charges that one might level against  A 
Beautiful Mind   is that Nasar, almost without exception,  garbles every 
mathematical example or explanation she presents . By itself  that would 
not be a serious failing: she is not a mathematician and the book is not 
about mathematics. What is rather strange  , given the hundreds of 
mathematicians she's interviewed , is that none of them took the time to 
correct her mistakes. Mathematicians tend to be an insolent and 
condescending clan. They may have glanced at the manuscript and, with a 
silent sneer, concluded that her intellectual powers were insufficient 
to the task. Still,  it is odd that Simon & Schuster did not assign or hire an 
editor with a good mathematics background to weed out the more obvious 
errors.
        Starting on page 52 she elaborates her  history of the origins of 
modern mathematics. In the 1920's, she says, David Hilbert made 
Gšttingen in Germany the center of a "drive" to axiomatize mathematics. 
His disciples, arriving at our shores during WW2, continued his crusade 
to its eventual triumph in Princeton in the 40's. It is a charming fantasy 
but has nothing to do with the history of mathematics. Quote:
        " The axiomatic approach ... was in its heyday at Princeton in the 
late 1940s. Nash's paper [ The Bargaining Problem,] is one of the first to 
apply the axiomatic method to a problem in the social sciences.  "
        Commentary : there never has and never will be an "axiomatic 
method  ", in mathematics or any other science. An axiomatic exposition  
of human nature was the magnificent achievement of Spinoza in the 17th 
century. She herself, starting on  page 12, raves  about the way  Nash's 
intuitive artistic mind operates by flashes of insight and is impatient 
with proofs that must be laboriously derived, often by others. 
        On page 68  she quotes a conjecture posed by Nash that was  worked 
on by John Milnor. The book's version goes like this:
        " Let V  be a singular variety of dimension k, embedded in some 
variety M, and let m equal G(m  ) the Grassmann variety of tangent k-
planes to M. Then  V  lifts naturally to a k-dimensional variety V  
included in M. Continuing inductively, we obtain a sequence of k-dimensional 
varieties. Do we eventually reach a variety V which is non-singular?"
        Here is the correct version: 

" Let V0   be a singular variety of dimension k,  embedded in some smooth 
variety M0 , and let M1 = Gk (M0 ) be the Grassmann variety of tangent 
k-planes to M0 . Then V0 lifts naturally to a k-dimensional variety V1 contained 
in M1 . Continuing inductively, we obtain a sequence of k-dimensional varieties 
V0<-- V1  <--V2 <--.... Do we eventually reach a  variety Vq which is 
non-singular?"   ( John Milnor, Mathematics Intelligencer,, Vol. 17, #3, 
1995) 
        Nasar's version is gibberish. Even someone who doesn't understand 
what the statement is saying can see that she drops all of the indices 
from Milnor's version, so that V0 , V1,  V2 ,.... , and  Vq all become "V". 
M0 and M1 become "M"  , ( sometimes "m" ). The fact that these indices 
distinguish between different entities is vital to making sense out of the 
statement.
        On page 85 she refers to von Neumann's basic game theory result as 
the "stunning min-max theorem  " . No more stunning than 6,000 other 
theorems. Can I give you my new proof of the stunning Pythagorean 
Theorem? 
        On page 128 she reveals to us that "manifolds were a new way of 
looking at the world.  " No more so than rap poetry, multi-culturalism 
or color television!  She herself states in another place ( pg. 157)  that 
the concept of a manifold has been around for a century, that the important 
conjecture proved by Nash's isometric embedding theorem was stated by 
SchlŠfli in 1870. 
        On page 140 she presents an example of Nash's habit of putting 
unsolved conjectures on  examinations. She claims that it isn't known if 
a certain sequence ( the successive iterates of the decimal expansion of _) 
has more than one limit point. In fact  because _ is an irrational 
number, it has an infinite number of limit points. The real question must 
have been whether the limit point set was countable or uncountable. 
        On page 157, she announces that "Riemann discovered examples of 
manifolds inside Euclidean spaces.  " Yes; they're called doughnuts. All 
references to the life of  George Bernhard Riemann are preceded by the 
catch-phrase  "the sickly German genius" ; which  could , of course,  
also be used to characterize  Adolf Hitler.
        Further along on the same page she utterly garbles a description 
of a "Klein Bottle". In her hands it becomes an ordinary cylinder. 
        On page 157 she confuses an embedding with an isometric 
embedding. This is not serious: many details are ignored or incorrectly 
stated with are apparent to a mathematician, but her discussion does 
convey the flavor of the idea to an informal audience. 
        On page 201 however she produces the most thorough garbling of de 
Moivre's Theorem I've ever seen: "  e equals i to the _ minus -1   ". 
That is to say, either e = i _____ or e = i _ - 1  . The correct equation is    
e i_ = - 1  . 
        On page 217 she garbles something as elementary as the definition 
of a differential equation.
        On page 230 she informs all of us that mankind has yet to prove 
the Prime Number Theorem, a result known to all mathematicians that was 
proven over a century ago.
        On page 231 she asserts that 4-dimensional geometry and non-
Euclidean geometry are the same thing. On page 336 she reveals that she is 
on shaky ground even in high school algebra. A formula such as "A to the 
fourth plus B to the fourth "  is quoted as an example of "deep abstraction 
of the sort that real mathematicians perform.  "
        As has already been stated, I don't fault her very much for these 
mistakes, although it is rather sad that she never  gets anything right,  
doesn't know what she's talking about, and could have easily corrected 
all these mistakes by consulting a mathematician. One wonders why, since 
she expresses such unbounded veneration for mathematics, she didn't 
bother to check at least one of her mathematical examples carefully . 
The answer of course, is that deification is rarely appreciation, and hasn't 
got much to do with respect.
____________
        We now shift our attention to a domain where her sins are more 
numerous and more consistently  egregious: her embarrassing infatuation 
with  'genius'. This obsession permeates every paragraph, often  every 
sentence. One can begin almost anywhere and arrive at the same place, 
but we have chosen to focus on three aspects of the phenomenon : 
        (1) The density of the application of words such as  "genius" and 
its many synonyms; 
        (2) Shrewd observations about the traits geniuses allegedly 
possess 
        (3) Adulation of the  sexual characteristics of  geniuses.  
(1) Synonyms for Genius         
        The very first sentence of "A Beautiful Mind", opens with
"John Forbes Nash, Jr. - mathematical genius  " . The first sentence of 
the second paragraph begins " The young genius from Bluefield, West Virginia  
". The first sentence of the third paragraph begins with "Genius, the 
mathematician Paul Halmos wrote...  " 
        Within the first 3 pages, genius or synonyms for the same idea, 
are used 15  times. In this same space she invokes this welter of 
attributions: 
        ".... the eminent geometer Mikhail Gromov..."
        " ... great mathematical intuitionists.. ( Riemann, Poincare, 
Ramanujan)..."
        " ..the high priests of twentieth century science ( Einstein,  von 
Neumann, Wiener) ..."
        "...supermen like Newton and Nietzsche..."
        "... the great Hungarian-born polymath, John von Neumann..."
        This emulatory verbiage grows in quantity and density until page 
52, at which point her style virtually collapses under the weight of 
flatulent hype:
        ".... Kurt Godel, the Viennese wunderkind of logic..."
        "... Hermann Weyl, the reigning star of German mathematics..."
        ".. Einstein, the biggest star of them all..."
        "... Einstein ,..the pope of physics..."
        ".. Einstein, a world cult figure ..."
        " ... a bright light from the new generation, von Neumann..."
        " ... Princeton stars .. Hermann Weyl and John von Neumann.." 
        "...Princeton...the new Gšttingen..."
        " ... two young geniuses of Hungarian origin, John von Neumann ... 
        and Eugene Wigner..."
        "... William James, the preeminent American philosopher..."
        "...Norbert Wiener, the most brilliant American-born mathematician 
        of his generation ..."
        "..[Harvard's] legendary chairman, G.D. Birkhoff ..."
        "... [Harvard's] brightest young stars... Marshall Stone, Marston 
Morse and Hassler Whitney ..."
        " ...Harvard, once the jewel of American mathematics ..."
        "... the .,... critical mass of geniuses"
        " the .. German mathematical genius, David Hilbert ..."
         Like the media  bombardment of advertising clichŽs for detergents 
and automobiles, the words quickly lose all meaning and fade into the 
background. Staples of her vocabulary include:
        .... Geniuses; giants; stars; superstars; supermen; bright young 
stars; crops of young geniuses; Olympian auras; Olympian perspectives; 
Olympian speech; intellectual Olympus ; Olympian detachment ;  high 
priests; popes; intellectual elite ; mathematical elite; social elite; 
Catholic elite ; hotshots;  fair-haired boys; bad boys; golden boys;   ; boy 
wonders ; wunderkinder ; royalty; brilliant academics; brilliant young geniuses; 
undeniable brilliance ; royalty ; authorities ;  idols ; leading lights;  
the most worthy;  aka Great Man  (capitals)  ; Nobel Laureate (capitals) ; King 
( capitalized ); visionaries; powerhouse departments; behemoth state 
universities; hothouse atmospheres .....
        The writing style drips with this fatuous slop .  One might be 
tempted to conclude from a perusal of this catalog that the  book was targeted 
only for super-market shopping carts. However,  when she is not writing about 
mathematics, mathematicians or universities, when she covers life in the 
mental hospitals, or Eleanor and John Stier's struggles for survival, or 
Nash's wanderings about Europe, the writing improves remarkably, 
becoming informative and even enjoyable. The unfortunate fact of the 
matter is that, as a writer per se , she is really quite good. It can 
only  be the ideological universe that she inhabits that is deplorable. 
____________

         (2) Theories of Genius

         Paul Halmos' theory  of  two kinds of geniuses appears on page 
12: 
        " We can all run, and some of us can run the mile in less than 4 
minutes; but there is nothing that most of us can do that compares with 
the creation of the G-minor fugue." 
        The comparison is redolent with paradigm-worship; as much as I 
admire J.S. Bach, I think he might rather resent being type-cast as some 
kind of academic  evidence of the existence of genius. Few musicologists 
would make such a statement: they would see Bach in the context of an 
extraordinary age of musical culture lacking which this fugue could not 
have been written. Halmos claims for himself the special ability to 
dissect a 'genius' out of the body of the vitality of an age in which was 
conducive to the production of great music.
        The quotation from Halmos establishes a tone of eugenic fascism 
that underlies the book like the deep structure of a Schenkerian 
analysis of  Bach's G-minor fugue! To wit: (i) There is a special class of persons 
called 'geniuses'. (ii) Experts like Nasar and Halmos can tell us who they are 
(iii)  They are born, not made (iv) Their names circle the roofs of high 
schools and teaching colleges; 90% of them are Europeans; 99.99% of them are 
men. (v) They are worth more than the rest of us (vi) One must apply 
different standards of morality to them (vii) Since there is no hope for 
the rest of mankind, we must enslave ourselves , heart and soul, to this 
saving remnant.
        Yet when one carefully examines  the list of traits Nasar believes 
typical of geniuses, they turn out to be tired reruns of cliches 
traceable to the cult of the romantic hero of the early 19th century: 
geniuses are  Napoleanic; they are 'men of sorrows' like Christ; or hedged 
about with eccentricity like Beethoven; they are lonely as Frankenstein's 
monster, indeed, they suffer torments of loneliness; sometimes, like Nietzsche 
it drives them mad; they are above petty morality, like Raskolnikov. 
        Quote, page 24: , "...rejection is the price that genius must pay. 
" Nasar  also has the  tendency of taking very ordinary traits, found in 
millions of people, and treating them as traditional signs of the 
presence of genius: 
        On page 15 she notes that " Many great scientists and philosophers 
... have had similarly strange and solitary personalities.   " Among 
them she includes Rene Descartes, Ludwig Wittgenstein, Immanuel Kant, 
Thorstein Veblen, Isaac Newton and Albert Einstein. From the witty 
Veblen to the ponderous Kant, from the humanitarian Einstein to the 
misanthropic Newton,  a more diverse gang of rowdies is hard to imagine. 
If they had anything is common it was a tendency to introversion:
 ( translation, they thought a lot) . She does not display for us the 
sampling methods whereby she derives a statistical correlation of genius 
with introversion. 
        On page 69 she writes:  " a strong compulsion to learn by doing is 
one of the most reliable signs of genius. " And , I would hazard to guess, 
94% of the human race.
        In the spring of 1949, while still a graduate student at Princeton, 
Nash  " astounded everyone by inventing an extremely clever game.  " The 
game was called, surprisingly , "Nash", sometimes "John". This, to Nasar  
is, " ...the first hard evidence of genius.   " In fact, ( as she admits), the game 
was invented independently two years earlier by a clever Dane 
named Piet Hein. It was called Hex and marketed by Parker Brothers. She 
does not however assert that the invention of Hex was the first hard 
evidence of Piet Hein's genius! Hein is better known to the public for 
his collection of charming child-like cartoons, "Grooks". 
        In the same way, in talking about Nash's work on parabolic non-
linear differential equations, she uses the work "genius" three times in 
five sentences. Then she concedes that the same ideas had been published 
independently a few months earlier by an obscure Italian mathematician 
named Emilio  DeGiorgi ; but she doesn't call him a genius even once.
        On page 128 she is impressed by the fact that Nash "works 
backwards in his head.  " Elementary, dear Watson. 
        On page 174 there is this revealing sentence which shows that she 
has made an exhaustive study of the history of the genius personality: 
" Matches between egocentric and childish men and self-abnegating and 
maternal women abound in the history of genius.  " Well, you don't have 
to be a genius to be egocentric and childish, but it helps. 
        Going even further on  page 199  she attributes even his choice of 
a marriage partner as evidence of genius: " It was part of Nash's genius 
to choose a woman who would prove so essential to his survival.  " What 
about Eleanor Stier? 
        Sylvia Nasar is not alone. Without much difficulty she has uncovered  
Nash fan-club , more knowledgeable of mathematics than she , who 
trumpet the same tedious cant:
        "Nash} is the most remarkable mathematician of the second half of 
the twentieth century',  Mikhail Gromov:  page 12.  What ever happened 
to Thom, Gelfand, Grothendieck, Weil, Wiles, Conway, Witten, .....and 
all my mathematician friends, whom modesty dares not allow me to list?
        " No one has a right to rob a genius of his freedom!  "   Adriano 
Garsia,  hearing that Nash had been incarcerated in McLean, pg 257
        "It blew my mind that someone who gave the appearance of being so 
simple could be a genius.  " Jean-Pierre  Cauvin, pg. 284
        "  I drove down to Trenton State...The attendant kept calling him 
Johnny. I told the people there, "This is the legendary John Nash." I 
kept thinking, my God, those shrinks! Who's going to figure out what's wrong 
with a genius?  "  John Danskin, on his first visit with  Nash at 
Trenton State mental hospital, page 291. 
        "Everybody wanted to help him. He was a mind too good to waste."
Fagi Levinson. pg. 318 . Why not just help him because he's a friend in 
trouble? 
       And the statement by Donald Spencer, quoted above, which renders 
explicit the eugenic fascism which is clearly at the core  of these 
observations.  Nash seems to always have had the ability to assemble 
followings of idol worshippers,  less interested in what he has actually 
accomplished than in reveling in the intangible mystique of the man,  
his talents , his domineering personality, his mental instability or his 
sexual prowess: David Gale,  Lloyd Shapley, John Danskin, Donald Spencer, 
Donald Newman,  Mikhail Gromov, Jacob Bricker, Paul Cohen, Frank 
Wilczek   , Ariel Rubinstein,  Jorgen Weibull, etc....
        ( To be continued over one or two more articles. As the material 
is already assembled, this review will be sent out to Ferment's subscribers 
in  two -week intervals.) 

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Vol. XII #5
September 24, 1998
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Book Review:(Part II)

	Sylvia Nasar: A Beautiful Mind, a 
biography of John Forbes Nash, Jr.; Simon & 
Schuster, 1998;  $25;  ISBN: 0-684-81906-6
	The first article of this series concluded with some 
remarks on the pervasive  "genius infatuation" of  A 
Beautiful Mind. We continue with a visit to  Sylvia 
Nasar's  meditations on  the  erotic charms of a genius. 
	Her views on  psychiatry and schizophrenia lay the 
foundation for her theories of the causes of John Nash's 
insanity, and for its remission.  A final essay on the  
many uses of the word importance in mathematical 
discourse includes a  short assessment of the 
importance of Nash's work for mathematics, science, 
history, and all civilization.
<<<>>>
	It may have been from an intention of enlivening public interest in 
her subject, that Sylvia Nasar never passes  up an opportunity to remind 
us of the uniqueness of  John Nash's sex appeal. Her frequent references to 
his cute legs seems to suggest that these continue even today to dominate 
all other attractions. On page 196 Joyce Davis,  classmate of Nash's ex-
wife , recollects 50 years after the fact that it was indeed his legs which 
attracted Alicia to Nash, to which she adds: "He looked like Rock Hudson." 
I encourage readers of A Beautiful Mind to browse through the 
photographs grouped after page 224 , to see if, in any of them, John Nash 
bears the least resemblance to Rock.  
	On the same page Nasar startles  us with the revelation that even 
the name  "John Nash" has the power to arouse sexual desire. Its twin 
monosyllables, explains , ÒJohnÓ followed by ÒNashÓ, signify some kind of 
high-born Anglo-Saxon ancestry: anyone who thinks IÕm making this up is 
invited to consult the passage in question. In context, it seems to indicate 
that  Alicia  would have turned down her nose at some fellow ethnic suitor 
with a name like  Ò Jose Domingo Loyola Gonzalez  Rivera de  San Miguel 
y Salamanca  Ó  !  Warding off the implication that she   herself   considers 
Alicia to be a member of some sort of sub-standard ethnicity, Nasar  
assures us that although Alicia was born in El Salvador, her roots sink 
deep into the humus of  royalty. 
	Page 191 is certainly the most depressing - shall we rather say 
appalling- performance in the entire book. After setting the tone of high 
pulp with the sentence  "Alicia glowed like a hothouse orchid. "  Nasar  
reveals that  noble blood runs in Alicia's veins, Romanov or Hapsburg, 
sheÕs not sure which,  and, for good measure, Bourbon as well. Side-
stepping  possible ties to Prince Norodom Sihanouk or the dynasty of Ibn 
Saud, this pretty much covers the terrain.  From the footnotes  we learn  
that this entire  fabric of legend reflects  the beliefs of uncle  Enrique L. 
Larde. In his  son's self-published book    , the assertion is made  that 
Enrique is the post-Mayerling bastard son of Archduke Rudolf. I did some 
work for vanity presses in the 60's, and  I immediately recognized the kind 
of  testimonial that  provides the bread-and-butter of those shysters. 
	 Sylvia Nasar also suspects that these cobwebs of Enrique's brain 
may not be credible - all to the good, given that Alicia didn't inherit the  
Hapsburg nose/chin connection -   so she digs up additional support for her 
thesis , that  the Harrison-Lopez- Arthes -Larde  family fits snugly  into  El 
Salvador's  "social elite" . She knows this because, back in the 30Õs, it   
Òmingled with [El Salvador's] presidents and generals.    Which, if true,  
can only mean that :  (1) they were among the 300 families owning 98% of 
the nation's wealth, and,   (2) they were welcome to come and go at the 
homes of card-carrying Nazis.
	And Nazis they were in those days! From 1932 until 1944, the year in 
which the Larde family fled to the United States, El Salvador was ruled by 
a real loony-bunny of a  fascist dictator,  General Maximiliano ( "El Brujo")  
Hernandez Martinez  . After a coup-dÕetat in which he  ousted the elected 
government of Arturo Araœjo, Martinez consolidated his power with La 
Matanza  , a massacre in which 30,000 people were murdered  in 2 months. 
Martinez soon established close diplomatic relations with Germany, Italy, 
Spain, Japan and of course the United States. El Salvador's army was 
trained by German colonels, its air force stocked with planes from Italy:
	Ò In January 1932 Martinez permitted local elections to be held with 
the participation of the Communists ... After the Communists  had won the 
vote  [in certain districts ] the generals refused to allow them to take office. 
The Communists called for an uprising ... the uprising came to grief due to 
the division between the pure wage owners and the colonos   and worker-
peasants. The generals butchered between twenty and thirty thousand 
workers.
	Martinez found a modus vivendi   with the Salvadoran bourgeoisie. 
The military kept the office of President and the politically important 
ministries, while the key positions in economic policy were filled by 
representatives of the bourgeoisie..  ( El Salvador, Central America 
in the New Cold War; Grove Press, 1981 ;Harold Jung, "Class 
Struggle and Civil War in El Salvador ",  pg. 73  ) 
	It is significant that the Larde family waited until 1944 to escape,  the 
year in which Martinez was forced out of office by a coalition uniting left- 
and right-wing elements. The rise to prominence of which Nasar speaks , 
had to be  bound up with this  modus vivendi  . 
	This is not to imply that the Lardes were, or are, fascists, ( except for 
uncle Enrique, who seems to fit the part ) ; yet such connections hardly 
qualify them as aristocrats, or upper class, or distinguished, or elite, or 
whatever. Nasar continues  through several pages to imply that they do . 
On page 193  she relates , in hushed tones of awe, that "Admission   [ to 
Marymount High School for Girls in New York] was based strictly on    
families' social standing; the El Salvador ambassador wrote Alicia's letter 
of reference, attesting to the Lardes family social position. 
	While  establishing  the claims of Prince John and Princess Alicia to 
the thrones of the Romanovs, Hapsburgs, Bourbons and, presumably, 
Plantagenets, Nasar takes time out to  ogle Nash's physique.  At age 20, 
she writes, (page 67) : 	
		"He had the build, if not the bearing of an athlete, 'a very 
strong, very masculine body', one fellow graduate student recalled. He 
was, moreover, 'handsome as a god', according to another student." 
	Lest we think that Nasar is merely quoting citing 50-year old 
recollections of former class-mates, she adds: 
	" His high forehead, somewhat protruding ears, distinctive nose, 
fleshy lips and small chin gave him the look of an English aristocrat."
	Imagine what Daumier would have done with  that recipe !  In 
between  she casts  a few side  glances at other mathematicians,  telling us 
that (page 71) " John Milnor ..was..tall, lithe, with a baby face and the body 
of a gymnast. Milnor was only a freshman but he was already the 
department's golden boy."    And that (page 73)  Emil Artin, refugee 
mathematician from Germany,  looked like a 1920's German matinee 
idol. "
	Back to Nash. On page 149, she reminds us  that  "Nash was built 
like a Greek God. " The legs surface again in a few places, even, on page 
385, at the age of 70.  Nasar's personal opinions, free from the protective 
coloration of quotation marks, emerge,  resplendent in shameless 
nakedness  when ,  on page 196,  she  calls him  "A genius with a penis." 
Here is the exact quote:
	"It was his good looks, however, that made Alicia's heart beat 
faster, 'A genius with a penis. Isn't that what we all want?' an actress once 
quipped, and the quip captures the combination of brains, status and sex 
appeal that made Nash so irresistible."
	I guess I'm bemused, and more than a little flattered, to learn that 
mathematicians have any sex appeal at all,   It makes me want to consider 
going back to doing mathematics full time. I doubt that I'd be able to  
reconcile the effort involved in  fighting off all the women eager to get at 
me, with the long hours required for my research. 
<<<>>>
Psychiatry
	The topic of "schizophrenia" is treated at some length in  "A Beautiful 
Mind" . In the first article I stated that "schizophrenia" is known abroad as 
"the American diagnosis." My source for this refers to the 50's, (the period 
of Nash's first hospitalization) , and  I'm sure it's still true today. Here is 
the  reference:
	"...a given patient might be diagnosed quite differently from one 
country to another...The English call almost any kind of emotional trouble 
'neurosis', said Henri Ellenberger, the great historian of psychiatry, in the 
mid-1950s. 'The French apply the diagnosis of feeblemindedness very 
liberally.' As for the Swiss, 'The French say that the Swiss diagnose 
schizophrenia is 90 percent of the psychotics and 50 percent of the 
normal.'"
	But nobody used the diagnosis of schizophrenia more often than the 
Americans. Schizophrenia was the great foible of American psychiatry. ..In 
one study, 46 American psychiatrists and 205 British psychiatrists watched 
a videotape of "patient F", a young man from Brooklyn who had a 
hysterical paralysis of one arm and a mood fluctuation associated with 
alcohol abuse. Afterward, 69 percent of the Americans diagnosed 
"schizophrenia", 2 percent of the British     ( pg. 296, Edward Shorter, 
"A History of Psychiatry", John Wiley and Co, 1997) 
		Sylvia Nasar's theories of schizophrenia are no worse than the  
fantasies current  in modern psychiatry. Since she is a  painstaking  
referencer, one need only consult her footnotes to learn the sources of her 
ideas. For the most part they come from the books cited in her 
bibliography. These writers emphasis the genetic theories of 
schizophrenia and the neuroleptic drug regimes in use today. 
	 Although Nasar does not regard psychiatry with my acerbic 
skepticism, she should not be charged with accepting  all of its dogmas at 
face value. Here is her description of psychiatry  as practiced at McLean's 
hospital at the time of John Nash's first incarceration:
	Fagi [Levinson] recalled that Alicia's pregnancy was thought to be 
the culprit. It was the height of the Freudian period-all things were 
explained by fetus envy. [Paul] Cohen said :  "His psychoanalysts theorized 
that his illness was brought on by latent homosexuality." .....Freud's now 
discredited theory linking schizophrenia to repressed homosexuality had 
such currency at McLean that for many years any male with a diagnosis of 
schizophrenia who arrived at the hospital in an agitated state was said to 
be suffering from Ôhomosexual panic.'"   ( pg. 259) 
	This, together  with the above citation from Edward Shorter, implies 
that American doctors considered the density of repressed homosexuality 
in American society to be greater than that of England by a factor of 35 ! 
Which, combined  with the oft-quoted figure of 1% for the percentage of 
schizophrenics in the human race, plus  the ratio of 6 to one for the 
population of the United States over that of the United Kingdom , implies 
that........
		Mazel Tov! 
	If Nasar's picture of the symptoms and causes of schizophrenia lacks  
coherence, this is only  because the contemporary psychiatric identifier ,  
"schizophrenia",  is not coherent. Drawing from the  books of such  
psychiatric authorities, Nasar spreads the following list of "schizoid" 
symptoms across the pages of "A Beautiful Mind":
	...The "schizoid state"   is characterized by a sense of meaningless 
and futility.' 
	...John Nash was exceptional because "Men of scientific genius, 
however eccentric, rarely become truly insane", 
	...  schizophrenia has a genetic basis and 'tends to run in families'
( Most of the literature in defense of this assertion  can be traced to a single 
research finding,  the Copenhagen twins study done in  1995 ,  a 
remarkable example of shoddy science. See Peter Breggin, "Toxic 
Psychiatry", St. Martin's Press, 1991, pg. 97  ) 
	... Schizophrenia  'leads to a lifelong pattern of social isolation and 
indifference to the attitudes of others' . 
	... consistent with her reactionary , even monarchist tone, she 
explains on page 271 , more or less, that radical political activity  'has long 
been a hallmark of a developing schizophrenic consciousness.' This 
assertion, if true, stands in stark contradiction to  the one just above it. 
		... 'voices... are the most characteristic delusion of 
schizophrenia.' . What this  statement says is that when a patient tells his 
psychiatrist  that he's hearing voices, the  psychiatrist is likely to write 
down a diagnosis of 'schizophrenia'. 
	....schizophrenics are 'insensitive to physical pain'  . 
	Finally, on page 258, we are provided with a bargain - basementful 
of symptoms: 
			...simultaneously grandiose and persecutory beliefs - 
tense, suspicious behavior - relative coherence of speech - ( relative to 
what? To other mental diseases? To what one ought to expect? To normal 
people?) - blankness of facial expression - extreme detachment of voice - 
reserve to the point of muteness ......
	By now we begin to realize that the word 'schizophrenia' is  a grab-
bag  into which one is welcome to throw anything that may be considered 
abnormal. This conclusion is evaded by Nasar's  psychiatric experts 
through the use of  traditional political loopholes of the form:
	 Symptoms vary so much between individuals and over time for the 
same individual that the notion of a 'typical case' is virtually non-existent 
	 ...self-contradiction is also characteristic of schizophrenia, every 
symptom being matched by a 'counter-symptom...' , and so forth. 
	Finally, as if to exculpate psychiatry from its  vagaries , a former 
psychiatrist of  Nash at  McLean Hospital suggests , (page 318, footnote 
36) , that Nash may not have been suffering from Ôparanoid schizophrenia 
at all, but Ôbipolar disorderÕ: Ò The quality of ...two papers   [written 
between 1965 and 1967] - the first of which geometer Mikhail Gromov 
called 'amazing' - constitutes the single strongest reason for questioning 
NashÕs diagnosis of paranoid schizophrenia.  
	 Being both everything and nothing, 'schizophrenia' can  be 
conveniently employed to say everything and nothing. Nasar's account of 
modern psychiatric dogma is competently done, though I feel that she 
takes too much of it at face value. Unfortunately, she then abandons her 
doctrinal moorings to wander far out to sea with numerous theories, all of 
a sentimental, ad hoc or silly character, about the causes for Nash's 
insanity  and its long-postponed remission in the late 80s. Most of these 
theories are her own, some were proposed by Nash's colleagues. Nash's 
own theories shed an interesting light on his character. Among them we 
find:
		.... teasing in elementary school  ( page 188)
		.... the stress of teaching  ( page 125. Proposed by Nash himself)
		....  fear of being drafted into the Korean war  ( page 126)
		.... the horrible stories his father made of about what would 
happen if the Japanese invaded West Virginia. ( page 36)
		....  McCarthyism at MIT  ( page 154)
		....  dismissal from RAND after his arrest   ( page 188)
		....  because Emilio di Giorgi published his research on 
parabolic partial differential equations a few months earlier than his own  
(page 220. This theory was proposed by mathematician Gian Carlo-Rota )
		....  agonizing too much over the contradictions of quantum 
theory   ( page 221. Another Nash theory )
		.... the rejection of his amorous advances  by young  logician 
Paul Cohen  ( page 243)
		....  his failure to win the Bocher Prize  ( page 243)
		.... the humiliation he  was exposed to  after the presentation of 
his proof of the Riemann Hypothesis  ( Quote:, page 232:  Nash's 
compulsion to scale this most difficult, most dangerous peak proved 
central to his undoing.) 
	Apparently  unaware of what she was doing, Sylvia Nasar 
systematically followed each  account of every misfortune or setback 
suffered by Nash, with a statement to the effect that this was probably the 
cause of  his mental collapse. It must be admitted that, given that 
"amateur" and "professional" psychiatry overlap so completely in our own 
day, her list of theories stands up fairly well against "fetus envy",  
'homosexual panic' and the like. 
	Nasar's views on the causes of his remission are grouped together in 
the 20 pages starting at page 335. Here she claims that Princeton 
functioned as a therapeutic community.   The assertion is not 
unreasonable , although 20 years does seem like a long time for therapy to 
reveal its benefits  .  There exist mathematics departments that are 
dangerous for certain kinds of people, functioning as negative potential 
wells,  in which they risk getting stuck in  stable regimes  for decades, 
sometimes their entire lives. The department at Stanford University 
apparently had that effect on Ivan Streletsky. His 20 years sojourn in its 
doldrums led to a major tragedy in the early 80s  with the brutal murder of 
his thesis adviser .   
		This Twilight Zone phenomenon is known to everyone who has 
spent a fair amount of time wandering about the mathematics community, 
yet I've never seen it described in published accounts . My own encounters 
with it have been  at  U. Pennsylvania, M.I.T. and U.C. Berkeley. It's very 
easy, by the way, to get typed as one of these individuals . They acquire a 
reputation as  fixtures  hanging  around in the lounges and libraries. They 
may  show up at lectures and colloquia  where they tend to ask questions 
that have no connection with the subject matter. The public  reaction to 
their remarks  on these occasions hovers between a suppressed laugh and 
an embarrassed silence. 
	Beyond making fun of them, few  persons take much  interest in their 
situation.  Nobody does anything for them. They may live with their 
families, like Nash did, or have some other form of guaranteed income. 
Basically, provided they don't run interference with the grinding of the 
wheels of the great theoremizing engine, they're allowed to rot. Sitting 
alone in the departmental  reading rooms, they appear to be off in a world 
of their own,  perhaps with a math book or article on their lap or the table 
before  them, perhaps with nothing at all. 
	An unhappy young man whom I got to know,  fitting this description,  
installed himself  as the Òphantom of the MSRI ( Math Sciences Research 
Institute)  during the  years 1983 to 87 when I lived in Berkeley. At that 
time he was in his 20Õs. When I came back for a visit in 1996 he was still 
there, essentially unchanged. The staff and administration of the  MSRI 
are very aware of his presence.  I doubt that anyone has ever suggested  
constructive ways to help him.  It's not their style.  High-principled 
decisions to respect others' privacy are sometimes the easiest way out 
for those who just don't give a damn.  Gangrene no doubt sets in 
elsewhere as well, ( I recall a few 'phantoms' around the NE Conservatory 
in the 80's. Of course there will always be administrators who think that 
anyone who isn't paying money to the institution is a phantom.) , but I 
suspect that  it's only in mathematics where such situations are allowed to 
continue indefinitely,  without anything being done about them.  
	John Nash fit this category, with the very important difference that 
he had something to recover back into. Sylvia  Nasar is certain that the 
"gentle manner" of his ex-wife Alicia Larde, "played a substantial role in 
his recovery." Alicia adds her own comments: (page 342)  "Did the way he 
was treated help him get better? Oh, I think so. He had his room and 
board, his basic needs taken care of, and not too much pressure. That's 
what you need: being taken care of and not too much pressure."
	The issue is controversial, isn't it?  Since Nash's marriage, the birth 
of their son, and Nash's first mental breakdown all occurred in the late 
50s, one could argue, ( with as little scientific foundation), that it was the  
marriage itself that caused his illness, and that it took him thirty years to 
recover from  it!  Strongly motivated persons often thrive in situations in 
which basic needs are guaranteed. Many however go to seed , turning to 
alcoholism and self-justifying abusiveness or violence  for lack of 
meaningful work. Still others may coast along for 20 years or more under 
such a regimen, getting neither better nor worse. All 3 elements seem to 
have been at work  in Nash's case.  
	These speculations of Nasar's are at least reasonable. On  page 336, 
however, she makes the bizarre assertion that Nash's dabblings in 
Cabbalistic numerology kept his grey matter intact :
	"The immense effort   [ of calculating and writing down 
numerological messages]   may have played a role in preventing Nash's 
mental capacities from deteriorating."
	Her remaining suggestions are brought together in a single 
paragraph on page 353. All reveal a peculiar shallowness of perspective:	
	" ..... high social class ....  "  ( A constant refrain, although no 
evidence is provided anywhere in the biography to show that NashÕs social 
class is higher than anyone else's . )
	" ...  high IQ ...  "( Has anyone  established a meaningful correlation 
between IQ and recovery from mental illness? )
	"... high achievement ...  " ( ditto. Our unlucky friends, Robert 
Schumann, Vaslav Nijinsky, Jonathan Swift,  Vincent van Gogh, Friedrich 
Nietzsche , Antonio Salieri , John Ruskin ,Georg Cantor, Kurt Gšdel ?..... )
	" ... no schizophrenic relatives ...   "  ( what about  grandfather 
Alexander Nash?  ( page 26) :  " a strange and unstable individual, a neÕer-
do-well, a drinker and philanderer who either abandoned his wife and 
three children ... or, more likely, was thrown out."  ) 
	"... disease acquired in 3rd decade .. " (Although Nasar's own  
documentation of  Nash's  borderline  pathology in his  20s. is excellent.)  
	This somewhat arbitrary list is followed by  ruminations on the role 
of hospitalization,   psychogenic drugs, and even  Nash's rejection of them. 
Everything and its opposite somehow contributed to his spontaneous 
remission.  Nash's own theory appears to be the most sensible:
	I emerged from irrational thinking , he said in 1996, "ultimately, 
without medicine other than  the natural hormonal changes of aging." 
____________
On the Importance of  
"Importance"
in Mathematics	 
Take a hecatonicosihedrigon and multiply by four
A sexicosihedrigon plus half as many more:
Put in some polyhedrigons whose gaps suggest a 
minus
And you'll have a polyhedral-
perpendodicahedrinus!

-  ( Luran W. Sheldon, NY Times, 1910,   in honor of William SidisÕs 
lecture on 4-dimensional geometry at Harvard at the age of 11) 
	What is mathematics? Although mathematics is largely about values, 
that is to say numbers and their many generalizations, mathematicians 
tend to believe that mathematics is value-free. That this is far from the 
truth is seen by the fact that the science lay dormant for a thousand years 
between the time of Diophantus in the 3rd century  G.R.    and the revival 
of learning in the 13th. Still, most of us agree that numerical value, moral 
worth, and pragmatic usefulness ought not be confused.
	At the same time, "importance" is the word most  abused  in  
mathematical discourse . As part of their professional equipment, 
mathematicians are required to have a sense of  what is  "important" in the 
history of mathematics, in contemporary mathematics, and certainly in 
their own field. Sensible people do not  work for very long on a difficult 
problem that they did not consider  "important". Why the properties of 
prime numbers  should be considered more "important" than the 
mathematical prodigy  William Sidis's encyclopedic knowledge  of the 
properties of  trolley car transfers is not  easy to put into words. 
	The uses and interpretations of the word "important" vary so much 
from one person to the next that, were mathematicians as perspicacious as 
they should be,  they would  recognize  how arbitrary it has become, and 
discard it as meaningless. Here, for example, is a short list of statements 
made by his colleagues about the value of Nash's research:
	"The embedding theorem .... is one of the most important   pieces of 
mathematical analysis in this century. " John Conway. ( Although not an 
analyst,  Conway is a great mathematician. I suspect him of making  this 
comment  because it sounded at the time like the right thing to say.)
	"[Nash's work on parabolic differential equations] .. which many 
mathematicians regard as Nash's most important  work ."  ( Sylvia 
Nasar. She doesn't tell us who they are, but  they presumably  work in the 
field of partial differential equations.)  
	"The concept of a Nash equilibrium n-tuple is perhaps the most 
important    idea  in non-cooperative game theory." Economist P. 
Ordeshook. ( Notice the "universal qualifier" perhaps! Lots of  people feel 
that Game Theory   is "not important". ) 
	"Let me describe an important application [ of the manifold-real 
varieties paper of 1951] " John Milnor. 
	( The application, the Artin-Mazur Theorem , is  important to   the 
theory of dynamical systems. One can  find mathematicians who think that 
the  field of  dynamical systems is "not of much importance". )
	"During these three years [ 1945-48, when he was still a teen-ager] , 
Nash completed an important   piece of work on bargaining. " ( Harold 
Kuhn, mathematical economist at Princeton. ) 
	"It gives me great pleasure to chair this seminar on the importance 
of John Nash's work on the occasion of the first Nobel award that 
recognizes the central importance   of game theory in current economic 
theory." ( ditto. How "important" is current economic theory?) 
	"In the short period of 1950-53 John Nash published four brilliant 
papers in which he made at least three fundamentally important 
contributions to game theory." John Harsanyi, co-recipient of the Nobel 
prize in economics, 1994. 
		Without going into the details, everyone of these statements 
attributes a different meaning to the  word "important". One is reminded 
of the story about the  student employed by  Thomas Kuhn's  to proof-read 
the original manuscript of  his "Structure of Scientific Revolutions". He 
told Kuhn  that the word "paradigm" was being used in 64 different ways! 
	The valuator, or validator  "important" cannot be dropped from 
the meta-vocabulary  because it is the very pillar, the spine of the entire 
enterprise: what sane  person would spend weeks, months, even years, on 
a mathematics problem unless he ( and, increasingly, she )  thought it was 
important? The word determines careers, causes quarrels, ruins 
friendships, alienates the profession from the public,  and vice-versa . 
	One example: after Louis  DeBranges of Purdue proved the  
"Bieberbach Conjecture"    around 1986, he  barn-stormed the nation, 
ranting and bullying conference audiences  for not giving him  the credit he 
deserved. No one , he fumed , thought that anything coming out of  Purdue 
could  be  "important"!  He finally descended into that black Slough of 
Despond,  his  own "proof' of the Riemann Hypothesis. 
	When a  lecture presented  in a  research department is poorly 
attended, there are usually two reasons for it: the first is  that it's on a 
topic the department deems "unimportant". In 1997 I attended a lecture 
given by  a woman whose very name is revered in applied mathematics, 
Olga Ladyshenksaya . Only a devoted handful  were present at her talk.  
Applied mathematics is considered of  "no importance" at Berkeley.
	The second reason is that it's too specialized topic,  with  so esoteric a 
vocabulary  that only a few  can  understand it. Some people may be sitting 
in  anyway, though uncomprehending :  the subject is "important"! 
	A life in mathematics conditions people  to apply the powerful 
law of contradiction to many situations, even where  inappropriate. It is 
easy to over-generalize but many  mathematicians strong in 
computational ability and the gift of pattern recognition  will be lacking in 
the kind of  judgment that weighs alternatives, decision-making of the sort 
that is done by doctors, judges, politicians, etc. in their professional 
activity.  The same criticism applies of course to their perceptions of the 
value, meaning, worth, or "importance" of  their own fields . Such  notions 
can be inflexible,  biased, often  unreliable.
	 It is easier to say what is important in applied mathematics, because 
one can speak of its effect on the field of application.  A new way of 
computing solutions to the Navier-Stokes equation will be deemed an  
"important" advance if these solutions lead to a deeper understanding of 

hydrodynamics, oceans, clouds, tornadoes, jet streams, etc. Thus the 
concept of the fractal   is very important from the viewpoint of applied 
mathematics, though pure mathematicians see it as just slightly above the 
obvious. If one now defines pure mathematics as applied mathematics in 
which the field of application is mathematics itself, it becomes  easier to 
decide matters of relative  importance. Observe that discoveries of  
applied mathematics are not directly   evaluated . It is in  the effect   of 
these results on the field of application that importance resides.  Ingenuity 
of reasoning, prolonged labor of computation, high levels of abstraction, 
extensive command of knowledge count for little . "By their fruits shall you 
know them" is the only reliable criterion for judging the "importance" of 
advances  in any scientific field.  
	Take  the two well-known theorems of Fermat. His last theorem  is a 
conjecture. It might have been made by anyone, but because it was made by 
Fermat, mathematicians took a look  at it. Formulating  it required no 
particular insight; it's  the kind of  conjecture anyone might make after 
reading a book on number theory.  Its importance is incontestable: it lay 
the ground for 4 centuries of incredible effort. 
	Fermat's   little theorem  is also "important". This states that , 
where p is a prime and a is any positive integer. It can 
be proven by any talented high school student who's learned something 
about congruences in his course on the "new math". It is also among the 
most frequently employed  tools in Number Theory.
	"Nash equilibrium" is even easier to "prove" than Fermat's Little 
Theorem.  It gave economists the feeling that they were doing something 
useful. They therefore considered it very important;  and to many people, 
Sylvia Nasar among them, a Nobel Prize proves that a result is important.
	Freudian psycho-analysis, the  paradigm of a pseudo-science, is 
likewise important because it shaped world civilization for a century, The 
movie Jurassic Park was extremely important for Paleontology because it 
led to increased funding for  dinosaur research. The flap of that butterfly's 
wing in the Amazon was also  very important because it caused all the 
dreadful floods in China we've been reading about. 
		The adjective "important" when applied to mathematics 
ought to  be given essentially the same meaning that it has in  other 
sciences. There are five of these: 
	I. Tool-making: methodologies for  problems solving   	
	II. Discoveries
	III.  Solutions of outstanding unsolved problems 
	IV. Introduction of new  concepts
	V. Practical applications
	(I. )  In terms  of problem-solving methods  ,  Nash's and diGiorgio's 
papers on higher dimensional parabolic partial differential equations are  
indeed important. 
	( II. ) Discoveries   in mathematics are like Vaughn Jones' discovery of 
the "Jones polynomial"  in Knot Theory, or Euler's discovery of the 
properties of the number e = 2.718281828É.., or Feigenbaum's discovery of 
the universality of the "Feigenbaum constant",__ . Nash has, to date,  not 
made any discoveries of this nature  . 
	(III.) John Nash is unquestionably one of the great problem-solvers of 
history. The isometric embedding theorem is  an "achievement" 
comparable,  in mathematical terms, to batting 65 home runs. Surprisingly, 
it does not require that much of a command of mathematics to read his 
papers . Nash did not cultivate an encyclopedic knowledge of 
mathematics, or even of his area. He was rather like a mountain climber 
who, rising to a certain height, decides that he needs oxygen or an ice-ax, 
goes back to base camp to get them, then returns to the assault. Nash  only 
learned what he needed to attain his objectives. It's amazing how much he 
did with so little, particularly when he is compared to  those  who know 
enormous amounts of mathematics  but never do any notable research. 
	(IV.) Nor did Nash introduce any new concepts: things like  
"transfinite number", "category derivatives", "fractal", "topos", "group",
"manifold" , etc. These  are  ideas   that  illuminate the whole domain of 
mathematics . Another example is the idea of "probability" developed by 
Pascal and Fermat. The closest that Nash ever came to inventing a concept  
is the "non-cooperative game",  a variant  on the "cooperative game". 
	In arguing that Nash was (is)  or was (is) not a genius, one needs to 
look at all five of the above categories and judge him separately relative to 
the requirements of each. This already shows how unprofitable the label of 
"genius" is, mathematics being a field so rich in its  diverse aspects that it is 
very difficult to judge the worth of discoveries without relating them to the 
purpose for which they were intended. Although it may be possible, in 
thought,  to separate brilliance from the results of brilliance, it remains a 
futile exercise that is best carried out by journalists and their public, who 
will always be in need of miracle-workers and wizards to inspire them in 
their journey through this trackless wilderness of earthly existence. 
	Mathematics is a monumental ediface. Some  are the architects, 
others work on its construction. Still others design the wallpaper, decor, 
furniture, etc. If the word "genius" be applied to all of them, what term can 
we reserve for the Master Builders: Pythagorus, Brahmagupta, 
Archimedes, Descartes, Newton, Laplace. Gauss, Riemann, Galois, Jacobi,  
Kowalewski, Hilbert , Grothendieck ...? 
	John Nash's remarkable gifts have been attested to by everyone 
qualified to understand them. Nor ought one discount his heroic 
accomplishment  in rising above a prolonged ordeal of terrible suffering to 
return to the world of rationality, however fragile that world itself may 
seem. Unrelieved flattery is not complimentary, and its real , often hidden 
intent may yield destructive consequences.

____________
____________








 





	
	
	
 The Crown Prince Rudolf. His Mysterious Life After Mayerling; Dorrance, 1994
 I. Gottesman, Ò Schizophrenic Genesis: The Origins of MadnessÓ, W.H. 
Freeman, 1991 ; G. Winokur and M. Tsuang, ÒThe Natural History of Mania, 
Depression and SchizophreniaÓ American Psychiatric Press, 1996 ; L. Sass, 
ÒMadness and ModernismÓ, Basic Books, 1992; E. Fuller-Torrey, ÒSurviving 
Schizophrenia, A Family ManualÓ, Harper & Row,1988

  Favorable as it might appear in comparison with the length of time for a 
classical psycho-analysis. 
 Gregorian Reckoning 
 The Prodigy, Amy Wallace; E.P. Dutton,  1986  
 Ô blind luckÕ, some mathematicians claim , anxious to discredit its ÔimportanceÕ. 
#0...