Tuesday, May 25, 2010

He wrote a lot, now people are writing about him

This entry is not written by me - this is an e-mail which was sent to all friends by Colm Mulcahy (or how readers of MAA columns know him -"Card Colm"). He knew Martin Gardner personally. Here is his interview with Martin Gardner in 2006. There are lots of other interesting links in Colm's message, so I wanted to share them with you.

An intellectual giant, brilliant expository writer and one of the great American men of letters of the 20th century has died, aged 95.
A great friend to mathematics, physics, computer science and philosophy, all of which he wrote about extensively (also religion).  He knew Salvador Dali, Roger Penrose and M. C. Escher personally, and helped to popularize the latter's mind-boggling art in the US.   He also played a major role in popularizing origami in the West.
http://www.scientificamerican.com/article.cfm?id=scholars-and-others-pay-t (yes, that url is correct!) includes this quote:
"So it is a very sad day to think that such a person is gone, and that so many of us owe him so much, and that so few people—even extremely intelligent, well-informed people—realize who he was or have even ever heard of him. Very strange. But I guess that when you are a total non–self-trumpeter like Martin, that's what you want and that's what you get. And so perhaps it's all for the best that he remains sort of hidden behind the scenes, known only to a special set of people." Douglas Hofstadter
Winning Ways (Academic Press, 1982), by Berlekamp, Conway & Guy, is dedicated to "Martin Gardner, who has brought more mathematics to more millions than anyone else."
He was a leading light in the (disjoint?!) worlds of magic & scepticism also.  See James Randi’s heartfelt words here: http://www.randi.org/site/
Martin was named by MAGIC Magazine as one of the 100 most influential magicians of the twentieth century.  (See http://turnermagic.wordpress.com/2010/05/24/a-final-comment-on-martin-gardner/ also.)
His best seller was The Annotated Alice In Wonderland (1960).
Fun fact from one of his very numerous books: "If you shrank the Earth to the size of a billiard ball and dried it off, it would be smoother than a billiard ball."
I had the great honour and pleasure of getting to know Martin over the last decade, first via letters and on the phone, and then visiting him three times “in retirement” in Oklahoma.  A sweeter, more modest, self-effacing man you can hardly imagine.  He could talk knowledgably for hours on end about a bewildering variety of subjects, generally curious and probing, always full of fascinating trivia and deep insights.  He could sit silently for 15 minutes as both of us tried to think through something.  Delightful company, every time.  I never could persuade him to play the saw for me (and I tried).  He was so famous, yet so shy.
What follows is both an introduction to him for those who didn't know about his amazing influence, with links to obits/appreciations/video and more, and also (excuse the presumptuousness) a handy one-stop-shop for some of these items for those who DID know him to some degree. 
At the very end are some brand new suggestions from his family as to how to make a contribution in his honor (and a suggestion from me for those who had the good fortune to visit him in his final years in Norman).
He was next to impossible to get a good photo of.  He’d freeze up when he saw a camera coming, the frequent chuckles would fall silent, the mischievous twinkle in his eye wound vanish, and he’d look a little stiff and almost uncomfortable. As his son Jim remarked to me in an email this morning:
Dad was not a big picture guy (well, actually he did quite well with getting the "big picture" of things; I should have said not a big photo guy - LOL).
Truth be told, Martin was a “big picture” guy very early on. A story he told me a few years ago: he worked for Univ of Chicago press office right before enlisting in the Navy, circa 1941, and "was privy to some insider Manhattan Project stuff” (my wording, I don’t recall his precise words anymore, though I may have it all on tape somewhere). In August 1945, he was on a destroyer when the news came through that "a spectacular bomb had been dropped on the Japanese" (my words, again). He said that he had a foreboding feeling that he was the only person on the ship who knew that the world was about to get much, much more complicated.
(there is a civilian photo from a few years later in which – to me -- he bears an uncanny resemblance to an impish Jim Carrey, but I can't find it on the web today)
Ironically, he did not like travel, and I gather that from 1945 on, he "stayed close to home" (Chicago, NYC, N. Carolina and finally back in his native Oklahoma).  I don't believe he ever went to the UK, or even Canada, after the war, despite having so many friends there, and indeed all over the world.  He said he never went back to Chicago after moving to NY, and never went back to NY after moving to Hendersonville.  In one sense his seemed to dislike looking back, preferring to move forward.
Once he settled into the assisted living community near his son Jim in Norman, OK, starting in 2004, he adopted a routine which rarely saw him deviate from the daily pattern of work in his room, meals in the dining room, and checking or posting mail. In the past few years in particular, he kept external trips to an absolute minimum, as far as I could tell, which was very smart in my opinion.  The risk of falling is high past 90! 
In a similar fashion, he kept the internet (and computer chess, an old vice of his) at arm’s length.  He had a lot of important work to do, he knew writing was his forte, and he organised his life to maximize his productivity in that arena.   We are all the beneficiaries of these choices, e.g., in the past few years alone he got through the revisions/updates for 5 of the 15 old classic collected Scientific American columns books (as well as a heck of a lot of other writing!).
Many assumed that he was a mathematician by trade, yet he never took a single mathematics class past high school.  Despite this, "Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children."  (I think that's a Persi Diaconis quote.)
He told me that he never gave a lecture in his life, and that he wouldn’t know how.  That's quite an inaccurate self-assessment from such a brilliant thinker and writer!
Three of his classic puzzles are here:
Author of close to 100 volumes, he published more books in the last year alone (including one on wordplay and another on G. K. Chesterton) than most people do in a lifetime.  Mind you, he started publishing (magic) at a very young age, back in 1930!
Prediction: he's not finished publishing yet. Knowing Martin, he's not going to let a little thing like death stop his output.  He was incredibly well organised, and planned ahead.  He may publish more in the future than most writers do in life.
He was arguably a deep sceptic who believed in god,  see:
A few months ago, he told me on the phone that he’d had a baffling visit.  Richard Dawkins had come by for a few hours, and Martin couldn’t for the life of him figure out why.  I suggested some obvious reasons, such as his own deep interest in religion and philosophy, not to mention his extensive publications and reputation in this area, but he remained unconvinced.  He said that the two of them had chatted for ages about this and that, and then Dawkins said he had to leave. They both realized that they hadn’t touched on theology at all, whereupon the guest sat down again and they went hard at it for an hour or so. He seemed chuffed that he’s had such a famous visitor!   He could still display an almost childlike innocence at 95 which was quite touching.
Martin got his own 4 minutes of fame on NPR yesterday:
(his biographer Dana Richards did a remarkable job of answering very general questions from Michelle Norris.  Full transcript provided if you can read faster than you can listen.)
Some obits and appreciations:
More obits on the way, including these (from folks who wrote to ask permission to use a photo of mine): The Economist (soon), Daily Telegraph (tomorrow), TIME Magazine (7 June issue) and China’s Modern Weekly (www.modernweekly.com.cn).
Not obits, but great stuff:
http://www.ams.org/notices/200506/fea-gardner.pdf (long interview with great photos)
("Martin Gardner wrote what became his most successful book because Bertrand Russell didn't have the time."  The last time his native city paid tribute to him in life?)
(even longer interview, includes pictures from his time in the navy)
A really worthy 45 minute Canadian TV programme on him from 1996: 
(The Nature of Things, also available on youtube in shorter, more digestible chunks. This includes TV footage from the 1950s!  Many big names in mathematics appear: Conway, Diaconis, Graham, Coxeter, etc. Also magicians Jay Marchall and Max Maven.  Watch this to find out what happens to marshmallows in a vacuum.... and learn of Martin's role in how a housewife with 5 kids (Marjorie Rice) confounded mathematicians with her breakthrough geometric discoveries in the 1970s.  Also: http://tessellations.home.comcast.net/~tessellations/ )
One of Martin’s last puzzles (from g4g9 website):
Write out the alphabet starting with J, namely

Erase all letters that have left-right symmetry (such as A) and count the letters in each of the five groups that remain.
From Martin's son Jim today:
"I've identified two foundations that individuals can sent gifts if they so choose. Dad, of course, would say none are necessary. But if anyone inquires, here they are:
 Martin’s Gardner's family has requested that anyone wishing to make a contribution in his honor may do so through either of these foundations:
     • The James Randi Educational Foundation, 201 S.E. 12th St. > Fort Lauderdale, FL 33316-1815, U.S.A. [ http://www.randi.org ]
     • The Mishawaka Foundation, 1 Brickyard Drive> , Bloomington, IL 61701 [ http://mishawakafoundation.org/ ]  "
A comment from me: If you've ever visited people in "old folks homes" you'll know that the quality of care and attention varies a lot.  On my three visits to Norman, I was very impressed by the people who worked in the Rivermont Retirement Community, and the support they provided for their extraordinarily active and independent guest, who probably generated more mail (incoming and outgoing) than the rest of the guests combined.  At mealtimes they always graciously accommodated Martin's visitors (who thereby got to find out where a large proportion of the world's brussels sprouts end up), and also cheerily obliged by snapping photos of Martin and his visitors.
Their care for all of their charges seemed exemplary, from what I could see.  It's often thankless, underpaid work.  I intend to drop the home a line, in old-fashioned MG style letter format, to express my appreciation of their kindnesses and dedication to providing dignified care to their charges, and of course to Martin in particular.
Their address is: Rivermont Retirement Community, 750 Canadian Trails Drive,Norman, OK 73072, USA.
A closing story, which for me sums up the sheer decency of Martin Gardner the man.
I think it was on my first visit there, in March 2006, as we returned from lunch in the common dining room to his private room. Per usual, he checked his mail box, and as we rounded the corner to his room there was a woman roaming the hall in a dressing gown. She was moaning softly and seemed distracted.  Martin nodded a friendly hello to her and we retreated to his room, and to the sofa far from the door.  He told me that she was often upset about things and cried a lot, that it was very sad. Sometime later we heard shouting outside, and after a minute, when it did not die down, we opened the door to investigate.  The woman seemed even more distressed at this stage, and was shouting angrily at the walls as she flailed around.  I went for help and when I returned with assistance, she had quietened down completely.  Martin was sitting down with her, saying comforting things, and she seemed quite reassured.  He remained with her for about five minutes, until he was convinced that her crisis had passed, and finally left her alone as she walked calmly back to her room.  It was a life lesson for me: sometimes a little kindness can go a long way even when we feel helpless and under-qualified to help.
The next time I visited him, in 2007, I asked how that woman was.  "She died a few months back," he reported sadly.  Then he added, "Curiously, I found out after she died that she was a retired mathematician.  Apparently quite a good one."
Martin didn't just inspire young mathematicians in public ways, through his writing, he touched some of them to the very end, in very private ways.
(He later told me that he thought that she was not local, but like himself had retired to the facility on account of  having an adult kid in the area.   He said he'd try to find out her name for me, but we never closed the deal there.)
Farewell my friend, it was one of life's GREAT treats getting to know you a little in person, spending some quality time with you in your oasis of thought in Norman, OK. 
               Colm Mulcahy

Sunday, May 23, 2010

Remembering Martin Gardner

When I first won math competition - it was in middle school - my math teacher gave me a small paperback, printed on cheap paper but with an amazing content - it was translation in Latvian of one of early Martin Gardner's books. It was in 1966. I never met Martin Gardner in person but I feel I have known him since then. It is for 43 years.
When I learned that he died yesterday, I had a feeling that I have lost one of my teachers. Gardner's books made me to realize that mathematics can be a fun. that there are much more in math than piles of algebraic formulas we had to memorize (I was lucky - it was easy for me!), I learned how to do some tricks with cards and other objects and learned about mathematics behind them. It taught me how to talk about mathematics. In 1967 I could not even dream that one day (2006) I will be invited to the most math                          fun math conference in the world - Gathering for Gardner - where I met most of the people I knew from Gardner's books. Thank you for the inspiration, Martin Gardner!

Obituary in New York Times 
A Flexagon for Martin Gardner
For 35 years he was writing columns for Scientific American
Discover magazine blog with many other people telling how much Gardner has inspired them

And here is what Martin Gardner's friend of 50 years wrote:


Written by James Randi 
Saturday, 22 May 2010 18:14
Martin Gardner has died.  I have dreaded to type those words, and Martin would not have wanted to know that I'm so devastated at what I knew - day to day - had to happen very soon.  I'm glad to report that his passing was painless and quick.  That man was one of my giants, a very long-time friend of some 50 years or so.  He was a delight, a very bright spot in my firmament, one to whom I could always turn to with a question or an idea, with any strange notion I could invent, and with any complaint or comment I could come up with.

I never had an angry word with Martin. Never. It was all laughs and smiles, all the best of everything.

Forgive me for writing this without any editing.  It's just as it occurs to me.

I can't quite picture my world without him, and just yesterday I printed up a new set of mailing labels for him, plus stationery, which didn't get mailed. For the last few years I supplied him with that small favor, assuring him that he should notify me when he ran out, but he never did, because he thought it was too much trouble for me. Only when I received a letter from him last week that was hand-addressed, did I know that it was time for another shipment to Oklahoma.

He was such a good man, a productive and useful member of our society, and I can anticipate the international reaction to his passing.  His books - so many of them - remain to remind us of his contributions to us all.  His last one was dedicated to me, and I am just so proud of that fact, so very proud

It will take a while, but Martin would want me to get on with my life, so I will.

It's tough 


How can this be true?
This is Martin Gardner's modified version of Curry's paradox. An extensive history and explanations are given in [Martin Gardner, 1956]. See also [Frederickson, 1997]. The picture made Daniel Takacs.

Tuesday, May 11, 2010

Shall we kiss?

Shall we kiss is the translation of French title for the movie Un baiser s'il vous plaît (2007) - 

It is a nice movie about feelings and responsibilities to people you are together with, but the mention of it found its place here because at least this is one movie where mathematicians are not showed the usual stereotype way. One of the main characters is a math teacher - couple times he is shown in a classroom with some high school algebra behind him. According the movie those should be different times with some time in between but the stuff on a board is the same - obviously those scenes where shot the same day...
The amusing episode is when this math teachers feels lonely and finds a girl on internet for certain services. When he arrives there, she first sends him to take a shower so that she can talk some math on a phone - in this place it was supposed to sound like a high level math but it was gibberish. Anyway - I thought it was nice to show that a woman - mathematician needs a second job... The movie is labeled as a comedy, may be that is why mathematicians in it look like real people.

Saturday, May 8, 2010

Seventy years in mathematics

While yesterday Cornell students celebrated Slope Day - the last day of classes for 2009-10 academic year, mathematicians gathered in 251 Malott Hall for the lecture "Seventy years in mathematics" which was also an opening for the 48th Topology Festival..

Audience was certainly more than 100 people, all seats were full and many were standing or sitting simply on a floor.

We all came to listen to a man who has spent 70 years in mathematics.
Here he is - Prof. Eugene Dynkin or as his original Russian name sounds Jevgenij Borisovich Dynkin. In couple days - on May 11 he will turn 86 and he is no retiring. While people were looking for seats in the packed room he was quietly looking through his slide and concentrating for his lecture as he had done countless times in his life.

He was born in Leningrad, now St. Petersburg in 1924 in Jewish family. In 1935 his father was declared "an enemy of the people", family was exiled to Kazahstan, and in 1937 his father was arrested. As his mother was told -"he was sentenced for 10 years without any rights of correspondence". Only after perestroika they learned that it was a code name used for those who were shot immediately. His mother with a teenage boy managed to return to Moscow and he graduated a year early from a high school with all A in his high school diploma. Holders of such diploma did not have to pass entrance exams in the university but they had to have an interview. Dynkin was lucky to have an interviewer Alexander Gelfond who immediately recognized teenagers talent in mathematics. 
In 1940 he became a student of the Department of Mechanics and Mathematics in Moscow State University or as it is known in the whole world - Mekhmat in MGU. From this year he counts started his life in mathematics.
Prof. Sofja Janovskaja noticed the talented freshman and took care of him, including taking him and his mother to live with her, so that he would be able to concentrate on mathematics.
And he really started to work very seriously. Two most memorable courses from the freshman year in MGU for him are linear algebra which Israel Gelfand taught in a spirit of functional analysis, and Kolmogorov's lectures in set theory. As Dynkin remembered - Kolmogorov had an obvious ability to overestimate his students. Dynkin admitted that he had trouble following Kolmogorov's lectures, but he decided to work harder. So he found Hausdorf's monograph on a set theory and studied it so that he would be prepared for the next lecture.
When Nazi German attacked Soviet Union in 1941, Dynkin evacuated to Perm (then called Molotov) and continued his studies there was couple years. He returned back to MGU in 1943, and that was a time when Gelfand seminars started.  

In one of those seminars Dynkin had to present something from Van der Warden's monograph but he could not understand the material. He started to approach in his own way, and the result was what is now called Dynkin Diagrams. When Dynkin in 1976 left Soviet Union, all algebra textbooks were edited to  "diagrams of simple roots" to erase his name. When asked how did he come with this idea he said - it was just so much simplier! This was not the only result he talked in his lecture about which I noticed that a great role to come up   with simple idea was his excellent background in elementary geometry. Even now he said - but those are the things that everybody knows! Not so true, unfortunately, for graduates of American high schools...
Until he arrived in USA, he did not know that these diagrams are widely used by physicists - in 1960-70 they were playing a significant role in mathematical aspects of particle physics.

The other seminar Dynkin started to attend as an undergraduate was led by Kolmogorov on Markov Chains.
This was another result obtained by an undergraduate Dynkin - Kolmogorov in 1945 had posed a problem of describing all eigenvalues of nxn stochastic matrices. Dmitriev and Dynkin partially solved it. The rest of it was added by the very talented student of Dynkin's - Karpelevich. More about him later. As Dynkin noted here about Dmitriev - Andrei Sakharov in his memirs called Dmitriev a mathematician who could solve any mathematical problem need to be solved when they were developing Soviet hydrogen bomb.

Eventually (with great help from Kolmogorov to overcome anti-semitism) Dynkin became Kolmogorov's graduate student and completed his PhD thesis Explicit form of Campbell-Hausdorf formula and its applications in 1948. He became an assistant professor in Mekhmat. he defended his second thesis in 1951 but could become a full professor only after Stalin's death when the situation in Russia eased. He was a professor in Mekhmat until 1968 when he was forced to resign for political reasons - he was transferred to the Moscow Central Institute of Mathematics and Economics. (In 1967 Dynkin signed a petition letter in defense of Yuri Galanskov and Alexander Ginzburg. ) Dynkin was invited to give a lecture in International Congress of mathematicians in 1962 held in Stockholm but he was denied visa, so he asked Kolmogorov to read his talk at the congress 

An hour has already passed - the usual time slot for talks -but Professor Dynkin realizes that he has covered only the first 15 years in mathematics. he has tried to explain his work in Soviet Union and his results very accessibly, mainly speaking to the large crowd of young people in the audience. 

About his move to USA he says simply - in 1976 I became a professor of mathematics in Cornell University. And then he adds - so people here know what I have been doing, let us just summarize 3 directions:
1. Markov processes as a tool in theory of random fields - this was inspired by quantum theory.
2. Superbrownian motion and its applications to partial differential equations.
3. In 2007 return to Lie algebras with enhanced Dynkin diagrams and Weyl orbits.
He wrote a monograph but at the end there was still an open question left. In couple years a very talented mathematician Benoit Mselati who he heard later became a banker, no word is he as successful in banking as in math yet.
Topology festival people are becoming impatient because the time of their banquet is approaching, and Dynkin says that his mathematical talk is about his 70 years is over, so people who have to leave can leave. But those who are interested to see some pictures can stay a bit. 

The second half of his talk is something about which his face really lits up - he can talk about his students and it is obvious that he is very proud about their achievements. Dynkin was in his senior year when he became a leader of his "math circle" - selected students from Moscow high schools who were interested and talented in mathematics. As he put it                      already earlier - there were two activities where people could feel free under Soviets - math and chess.

Dynkin apologizes for the quality of the slide but these are some of his first students. First from the left is F.I. Karpelevich (1927-2000) - one of his brightest students ever.

When Karpelevich graduated from high school he told Dynkin that he is not going to apply to university but instead will go to work in a factory. Dynkin was very disappointed and asked why, so Karpelevich explained that his family is very poor. He had two other siblings and a mother who cared for them as a single parent working a low payed job in a factory. (from Lie Groups and Symmetric Spaces:in memory of F.I.Karpelevich,vol.210)

In 1947 several participants of this first Dynkin math circle were admitted to the Department of Mechanics and Mathematics at Moscow State University and the circle transformed into the seminar "Selected Problems of Contemporary Mathematics" for freshmen. Under various names this seminar continued for several years. In 1955 it was divided in two "daughter seminars" - seminar in algebra and seminar in probability theory. Participants of these seminars were encouraged not only to solve various problems (several of them were previously unsolved problems) but also to prepare their results for publications. Karpelevich made his first serious contribution in mathematics when he was sophomore. Kolmogorov in 1945 had posed a problem about n x n stochastic matrices which partially was solved by Dmitriev and Dynkin, Karpelevich managed to find a final solution for this problem. His result was published in Russian and then translated in English and published in AMS Notices. He was one of the brightest students in his class, however after he graduated from the university in 1952 there was no chance for him to be admitted in graduate school because of him being a Jew, the State commission responsible for assigning jobs to university graduates ordered him to go and teach mathematics in Novocherkassk (at the level of community college). He became seriously ill there and was permitted to return to Moscow a year later. With his return he was able again to join Dynkin's seminars and eventually to complete his PhD work.

I am recognizing a teenager second in a lower row - I knew him in 1980 as Professor Vladimir Andrejevich Uspenskij when I was taking his class in algorithm theory in MGU during a semester I was there.

Dynkin is recognized by many of his students as a wonderful and engaging teacher, there are many mathematicians who grew out of his math seminars for high school students. It was his great disappointment to find out that this practice did not work when he arrived in Ithaca. He tried to organize a math circle in Ithaca High School in 1977 but students could not stay after school because they had to have their parents to drive them if they missed school bus. There was not possible to keep in touch after they graduated from the school because they went to different places. I can share this sentiment with Dynkin - there are nothing like bonds between students and teachers in former Soviet Union. It was something I missed in US also.
But that is another story.
This was a story about the man who yesterday celebrated his seventy years in mathematics.
Happy 86th birthday, Evgenij Borisovich!

Tuesday, May 4, 2010

Was it worth it?

Why do mathematicians are always portrayed as weird people? Are they more weird than others? Do they always have to be weird to become good mathematicians? Am I a real mathematician? Am I weird? Hopefully the answer to the two last questions is "no". But it can make another question - if I am not a real mathematician is it because I am not weird, or I am not weird because I never was a real mathematician?
I finished reading a book I wrote some in my previous blog.

I liked to read all those interviews Masha Gessen conducted - she really did a great research about Perelman. Somewhere she mentions that she thinks herself that the chances Perelman himself will read the book "are infinitesimal". I wish he would read and then he would be the one to say what he thinks about it. There are no pictures in the book which was a disappointment. I understand reasons - it is cheaper for a publisher to print just a text. So I tried to supply missing images with Google image search. The author wrote about St. Petersburg that the only time it is inhabitable is late spring meaning June and famous White Nights in St. Petersburg. The rest of the descriptions mentioning St. Petersburg are mostly - gloomy, rainy, cold, grey, windy...
 It has been a long time since I last was in St. Petersburg but I have been there with different weather conditions and for me it always has been one of the most beautiful cities - so it must be for Perelman too, otherwise he would have left with all the chances and offers he had over the years.
There used to be a difference in people who lived in St. Petersburg and in Moscow, it may still exists. I used to know people from both cities and they all said the same - if they lived in St.Petersburg, they could not possibly imagine to live in Moscow and vice versa.
I always liked St. Petersburg better. May be because of the romantic stories about "white nights" I heard since I was a child - we had in Latvia short nights in June but I always was jealous of St.Petersburg when at the same time it never really got dark - like in this picture with Troickij most (Trinity bridge) at 2am in June. Also St. Petersburg is next to Baltic Sea - the same as my native city Riga.

 For several summers in a row I used to take international students there for a short visit before they left home, and one of the "must-see places" was Hermitage.
 There were always long lines but I had my tricks how to get there early and avoid crowds. Everybody was going to see two Leonardo da Vinci paintings, so I knew to get my group there first so we can really enjoy them. I do wish that Gessen's book would have at least some pictures of St.Petersburg.
This is Lyceum 239 in St. Petersburg how it is called now, at the time Grisha Perelman went there it was School No.239 - "the graduates of this school thanked the school for opening their minds, for teaching them intelligence, erudition, and for giving them a head start in their higher education." (p.58). Perelman was there in so called "club class" - he and his classmates were from the Math Club trained by Rukshin for Math Olympiads. Perelman there was "allowed to concentrate on mathematics to the exclusion of - literally-almost everything else."(p.59).

In  his final year of the school Grisha Perelman scored a perfect score in IMO. As a winner of IMO he was entitled to enter university without entrance exams. The author of the book explains in great deal how hard it was for Jewish to enter universities. She draws on her personal experience - that of her parents and that they had "a chilling dread of trying to explain to your child that some of the world is so unfair as to make all hope futile".(p.65)
You do not have to be Jewish to have this experience, I had it also back in Soviet Union and I had in US also. Most of the time it has been not because you are not smart enough but because you are not from the "right family" or it may be said - you are not the right class - too low class, we, aristocrats, are the different bread...

 In a book it is some about this kinda of attitude also - when dirty fights are happening among mathematicians to become Academy of Sciences members. There is a mention about two very famous Russian mathematicians - Kolmogorov and Alexandrov - who went against their teacher Luzin in 1936 when Alexandrov desired the status of the member of the Academy of Sciences and perhaps that also helped them to cover up the fact of being a homosexual couple (it was considered criminal in Soviet Union).

Grisha Perelman's schoolmates and teachers remembered him being extremely honest. He always maintained high standards in school and in University, and later in the Steklov Institute. This is the picture of the old part of the university in St. Petersburg which was founded in 1724, construction of the buildings on  Vassilij Island was ordered by Peter the Great.

Perelman was lucky to have "guardian angels" looking after him during his university studies and also when he became a graduate student in Lenigrad branch of the Steklov Institute: "Rukshin shepherded him into competitive mathematics, Ryzhik coddled him through high school, Zalgaller nutured his problem-solving skills at the university and haded him off to Alexandrov and Burago to ensure that he practiced mathematics uninterrupted and unimpeded. Burago passed him on to Gromov, who led him out into the world."(p.111)

It is also mentioned in a book that all this time he had a caring mother around, so he even did not need to know about everyday chores.

I think that Grigory Perelman is a wonderful example of amazing results when talented person had dedicated teachers to support him. He was given all possibilities to think just about the mathematics and live the life the way he wanted. As a result he solved a great problem. He reached the top. And that is when he finally faced the reality of life, how things are going in this world, that you cannot be in isolation forever. And he realizes that the world is not the way he thinks it should be or wants it to be, so he turns back to the world.
Masha Gessen speculates that he had Asperger's symptom, that most of the mathematicians have it. I am not sure how appropriate is this part in the book - to talk about somebody's medical condition whether it exists or not, even if it is supported by famous psychologist Simon Baron-Cohen, cousin of famous actor Sacha Baron-Cohen.

I know couple other people who have become brilliant mathematicians because they also had devoted mothers who took care of them and they had great teachers. They are all men.

I have met successful women in mathematics who are referred as an examples that it is possible to have family and children and to be a mathematician with lots of publications necessary for academic advancement. It turned out - they also had mothers taking care of their kids (almost all the time) and doing all housework...

Is it really Asperger's symptom or is it this specific isolation from everyday life which makes mathematicians weird?

And when somebody like Perelman has reached his goal - he solved the problem nobody else could solve for 100 years - he is faced with all the realities at once and he is so disappointed that he announces that he quits mathematics.

The mathematical problem is solved but there is still a question left -
if this is a price to pay for it - was it worth it?  To realize that all this time spent in search of the solution of one problem no matter how great the problem was, was only to see how alone you are? Of course, million dollars cannot pay for that.

Money cannot buy the time that has gone...