The Strangeness and Non-Strangeness of Higher Mathematics

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Mathematicians don’t easily get excited. When my Shabbos-after-mincha chavrusa (Torah study partner) Dr Barry Simon told me with some urgency that I must read a fascinating article in the current issue of the New Yorker about a reclusive Jewish mathematician in St. Petersburg, I took him at his word. The article was a fascinating journey into a world few of us ever see – the Olympian reaches of world-class mathematics.

Grigory Perelman solved the Poincaré conjecture, a mathematical puzzle around one hundred years old, with significant potential application. Mathematicians of stellar performance have devoted their careers to it. This huge accomplishment clearly called for the mathematician’s form of the Nobel – the Fields Medal, awarded every four years. Perelman turned it down. No one had ever done that before. Perelman explained. “It was completely irrelevant for me,” he said. “Everybody understood that if the proof is correct then no other recognition is needed.”

Perelman is forty years old, served in academic positions in the United States, but returned to St. Petersburg, likely to work on the Poincaré conjecture. He gets all the solitude he wants there, where he lives with his mother. (His father made aliyah some years ago.) It is not only recognition that he manages without. Returning to his old job at the Steklov Institute, he is paid less than a hundred dollars a month. (He told a friend that he had saved enough money in the United States to live on for the rest of his life.) He dresses simply, lives simply, without the accoutrements of success or comfort. He can go for days without checking his email. None of the toys that intrigue the rest of us matter to him as much as pursuing mathematical knowledge.

Perelman’s story is woven into those of other mathematicians, including those with very contrasting styles. Their jockeying for recognition appalled Perelman – to the point that he felt the need to withdraw from the company of peers consumed by ego. The offer of the Fields was his Rubicon. “As long as I was not conspicuous, I had a choice,” Perelman explained. “Either to make some ugly thing” a fuss about the math community’s lack of integrity “or, if I didn’t do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit.”

The authors do not treat him as some sort of freak, despite his rather unusual habits and demeanor. They treat him with bemused detachment, but their respect for his quixotic integrity shines through. They cannot help but respect someone whose search for knowledge is complete and real.

Unlike Dr Simon, I am far from a world-class mathematician. I have long forgotten the difference between an integral and a differential, and hardly expected myself to feel at home with the characters in this story. So why did I feel a mounting sense of deja-vu as I read on?

In our community there are thousands of Perelmans. There are indeed thousands of problems as fascinating and intractable as Poincaré’s. Some are in the Rambam, some in the Ketzos, some in R’ Akiva Eiger. There are no Fields Medals awarded to those who work on them, and often produce results of stunning elegance. Unlike Perelman, these people pursue knowledge monomaniacally, but manage to raise beautiful families at the same time. Like Perelman, they spurn many of the comforts that others take for granted, and find satisfaction in knowledge itself. For the most part, their pursuits are non-competitive, and delight if they can offer a piece to a solution that others will complete.

Like Perelman, they are often misunderstood and under-appreciated, even mocked by others.

Those who can read about Perelman and find his single-mindedness something to celebrate, should pause and reevaluate their attitudes towards the young men in Kollelim who are his Torah analogue.

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39 Responses

  1. Henry S. says:

    Rabbi Adlerstein, if you liked this aricle, try reading to one at the attached link.
    http://www.cs.elte.hu/erdos/NY-Times.html

  2. cvmay says:

    Interesting comparison between the Math genius and Kollel members, but the equivalency is not up to par. We are comparing a spiritual aspiration with an academic search for excellence. Both are aspiring goals to achieve. Caren V May

  3. Bob Miller says:

    Aaron,

    Not that last paragraph—-I thought you were talking about my last paragraph in Comment #30 which pointed out your lack of evidence to support your claim that day school 7th graders in general and Kollel members in general lacked the needed math and English skills.

    As for your condescension toward these two groups shall I call it something else, such as pity or disdain?

  4. Aaron says:

    Bob, you’re straining the context of what was written.

    * In our community there are thousands of Perelmans. There are indeed thousands of problems as fascinating and intractable as Poincaré’s. Some are in the Rambam, some in the Ketzos, some in R’ Akiva Eiger. There are no Fields Medals awarded to those who work on them, and often produce results of stunning elegance. Unlike Perelman, these people pursue knowledge monomaniacally, but manage to raise beautiful families at the same time. Like Perelman, they spurn many of the comforts that others take for granted, and find satisfaction in knowledge itself. For the most part, their pursuits are non-competitive, and delight if they can offer a piece to a solution that others will complete.
     
    * Like Perelman, they are often misunderstood and under-appreciated, even mocked by others.
     
    * Those who can read about Perelman and find his single-mindedness something to celebrate, should pause and reevaluate their attitudes towards the young men in Kollelim who are his Torah analogue.

    Does the hyperbole also extend to the number of “problems as fascinating and intractable as Poincaré’s”. Or can we de-hyperbolize both the Perelmans AND the Torah problems to more closely match the count of Perelman-level mathematicians? You either have an “analogue” or you don’t.

    Explain how “hard evidence” could refute your OPINION that I was condescending? You could always claim you aren’t satisfied. Give me “hard evidence” to refute my claim that there isn’t a leprechaun behind you as you read this, which disappears when you look for it.

    Hyperbole? Love ’em. In my family we have a saying: “If I ever fail to overstate the case, please call an ambulance.”

  5. Bob Miller says:

    Aaron commented (#31) on my comment #30:

    “Concerning your calling me “condescending”, re-read your last paragraph.”

    I kinda like it. In fact, you must, too, in a way, because you didn’t offer hard evidence to refute it.

    In context, the “thousands” mentioned by Rav Adlerstein were not meant to represent thousands of Kollel members on Dr. Perelman’s level, but thousands addressing very knotty issues. A little hyperbole should not send you to the moon.

    Credit my initial, pretty good grounding in English, science and math, to my eight years at the Jewish Foundation School of Staten Island, which is surely within your “Orthodox day school spectrum”.

  6. Ori Pomerantz says:

    Do we respect Perelman because of his achievement, or because of the personal sacrifices this achievement took? Imagine I were to do the same, and spend my days humbly trying to prove that NP=P (a famous unsolved problem in computer science). Because I am nowhere near Perelman’s level, I would die with NP=P still an open question.

    Would I be worthy of respect, or a fool who wasted his G-d given potential to do some good in the world in favor of persuing a dream totally unmatched by his talents?

    * Note: I’m not saying anybody else is a fool, or that there are people in Kollel unable to learn Torah in the same way I’m unable to prove NP=P. I picked an extreme example on purpose, to ask if the point is the achievements or the sacrifices that enable SOME people to achieve them.

  7. hp says:

    “I submit that you don’t focus on me the person. Rather, focus on the validity of what I say, and factor my messaging into the cumulative messaging of this blog. Make sense?”

    Comment by Jewish Observer

    I think that the individual credibility and honesty of posts are what comprises the whole. The whole is as strong as its parts.

  8. Jewish Observer says:

    “In this instance, however, you could not be more wrong”

    – I bet I could if I really tried

    “In the United States, there is no side factor like mandatory army service before entering the work force”

    – This is incorrect (though I do allow that you could be more incorrect). You are totally discounting societal expectations. This is not a criticism; just a reality. If you come from the heimishe velt you necessarily will go to kollel, much as e.g. George Bush was expected to go to college, whether or not it was what he would have wanted. When I was a bochur I was once chatting with my roommate in Mir about our futures. He told me he planned to go to Kollel, so I asked him why. He responded – that’s what everybody does. He is not a bad guy. He is davka a good guy. He was just being very honest. You can believe what you want to believe.

    Anyeway, if disagreeing with your version of reality makes me wrong, then by definition I can’t win this argument.

  9. Aaron says:

    Bob,

    Extrapolating Stuyvesant and MIT secular skills to anywhere in the orthodox day school spectrum is specious. What part of “In our community there are thousands of Perelmans.” don’t you understand? Thousands. Had that sentence been written “In our community there may be Perelmans.” there’d be nothing to object to.

    I didn’t mean to downgrade ability. I mean to downgrade the emphasis on accelerating and idolization of gemara mental pyrotechnics by those who haven’t been grounded in building the equivalent of a safe campfire. Less with quality is superior to quantity.

    I’m saying that kids who haven’t mastered pre-algebra and composition skills before they graduate high school wasted vast amounts of time, effectively trying to slice their way through the material without ever having removed the hard plastic bubble wrap from their knife. If gemara were withheld for 6 more months until those neural paths were solidly paved, the subsequent quality of learning would more than make up for the earlier delay. And it’s BECAUSE I believe that those kids are capable which infuriates me about the present system. If those kids can’t write a coherent English paragraph about the daf they were learning all week in 9th grade, you’re going to have a hard time convincing me they have a clue about what they’ve learned. I’m not asking for William Safire English. Business letter simplicity would suffice.

    Concerning your calling me “condescending”, re-read your last paragraph.

    Thousands. That’s a claim exceeding three orders of magnitude more Perelmans than there are actual Perelmans. It’s that simple.

  10. Bob Miller says:

    Aaron, regarding your comment #26:

    I agree that there is value in grounding students in English, math, and logic, which I saw plenty of at Stuyvesant HS and MIT. I don’t agree that Rav Adlerstein was trying to compare the level of all or most Kollel members in their field with Dr. Perelman in his.

    Your earlier comment #14 seemed to downgrade 7th graders and Kollel members not for lack of proper training, but for lack of ability. If you didn’t mean to demean their ability, please say so.

    You have not brought evidence beyond your limited personal experience to substantiate your broad claims about either group. Before launching into sweeping accusations and recommendations, first do your homework.

  11. Yaakov Menken says:

    The reason why that is objectionable, JO, is because every reader already has received an unrealistic, negative portrayal of frum society via the general media. In a vacuum, perhaps one could say that we paint too rosy a picture. Far more often, however, what we are doing is poking holes in the negative portrayals on the positive side.

    In this instance, however, you could not be more wrong. How do you imagine that learning in Kollel *became* a normative behavior for our community? Thousands of young men and women made a conscious decision to sacrifice current and future income potential in order to learn Torah. In the United States, there is no side factor like mandatory army service before entering the work force — and yet American and Israeli kollelim are filled with young men, all of whom could be in work training or getting jobs.

    They may not have the genius of Perelman, but they are making a comparable sacrifice in terms of their economic advancement. No matter what level of support they may get, it is not going to be what they could get in the workforce. They certainly deserve our respect.

    Focusing upon the minority who stay in Kollel “because they have nothing better to do” is an inappropriate denigration of the majority, who could go into the business world tomorrow and make a decent salary.

  12. Jewish Observer says:

    “JO- I know you strive to be honest about the shortcomings of bnei torah. At the same time, it’s important to be honest about their very spiritual and special accomplishments. One way to do that is to refrain from offering critisism consistently- it changes honesty to something else. In order to be the conscience of a society, one needs to be honest with oneself as well.”

    – good point, respectfully presented and well articulated.

    my response: if we forget who says what, but view the totality of comments on this blog from a portfolio point of view, the overall messaging here is one of self lauding based on an unrealistic portrayal of frum society. my dosage of reality does not even begin to dilute the potency of the messaging. This blog – from mu point of view – is about ideas, not about judging the posters or their motives. I submit that you don’t focus on me the person. Rather, focus on the validity of what I say, and factor my messaging into the cumulative messaging of this blog. Make sense?

  13. Bob Miller says:

    High-level, intensive Torah study is a noble and valuable thing that many talented people pursue despite their potential to make more money and achieve more fame doing something else. Not all in full-time learning have (or need to have) the very highest level of talent. However, full-time learning is not for everyone without exception. These learners should not be, and rarely are, full of themselves.

    As for the economics, we will see over time how much mass participation in full-time learning is or is not practical, and any necessary adjustments will end up being made. Doom and gloom predictions by people who really want the enterprise to fail, and who look down on the participants anyway, do not add to the discussion. For some who are Orthodox or think they are, the word Kollel is like the red cape to the bull. Like, they should get a life!

  14. Aaron says:

    Bob,

    If you asked the 7th grade of that yeshivah (I substituted in the other class, too, so I taught every 7th grader that year), I doubt you’d find one that would call me “condescending” as a teacher. As a commenter on a blog, maybe.

    Concerning developing the English skills to write a business letter or the math skills to balance a checkbook or understand how a spreadsheet works, those are issues of literacy and numeracy, not even remote bias toward limudei chol. If you can’t calculate area, you can’t determine the minimum amount of schach you need for a sukkah of given dimensions. If you can’t calculate volume, you can’t determine if a mikveh is kosher. If you don’t understand remainders, you can never determine if 4 years from now is a Jewish leap year or not. Are we content with being Jewishly innumerate? If one can’t write a coherent paragraph, that’s pretty damning and overwhelming evidence of an inability to structure and reproduce what one has learned.

    Better to learn less, well, than lots, poorly.

    Yes, I’d hold back every student from progressing in gemarah until he did solid B-level work in pre-algebra. Until then, their brains simply aren’t mature enough for Talmudic logic. In the long run, it’s no big deal if they get to gemara a year or two later (except to the egos of the parents!). Math is probably the ONLY field they’ll have until they reach reach the age of 18 where there are no grays and machlokes. If you’ve never worked on a problem where there is only one unambiguous answer, your mental blade has never touched a whetstone.

    I regret there are many of you who had uninspired math teachers who made the material tedious. That doesn’t mean the material isn’t necessary for developing critical thinking skills.

    Anyone who can’t do pre-algebra is far from understanding even the fundamentals of Rabbi Yishmael’s hermeneutical rules. Lacking these tools, progress in gemara is stringing beads — memorizing stories — hardly learning with the ability to apply the reasoning. Perelman-quality learning? Spare me.

    Note that I’m not even suggesting proficiency in algebra, geometry, trig or calculus. The vast majority of well-educated Jews can survive nicely in life without ever opening a book about these subjects.

    Get yourself a copy of Innumeracy by John Alan Poulos and learn the practical ramifications for being poorly grounded in math. If you don’t know enough math to raise a skeptical eyebrow to inquire (or at least ask a more math-proficient friend) about Torah Codes or environmentalist claims that the world is overpopulated (did you know that you could easily fit all 7 billion of the world’s people into a 30-mile cross-section of the Grand Canyon–not as sardines, but each person in his own 20′-sided cube!) you’re vulnerable to all kinds of specious arguments.

    You want the kids to ace pre-algebra and enjoy it? Get a Rosh Yeshiva to courageously stand up at a PTA meeting, stare down the parents, and say that the school policy is that the first gemara can’t be opened before proficiency in pre-algebra. My guess is that most kids will be motivated to know that material in as little as 100 days. Those that find the pre-algebra more difficult, twice as long, still less than one schoolyear. And you’ll have BETTER subsequent gemara learning by those boys as a result!

    Returning to my main point… Why should one accept a claim that there are more real or potential kollel “Perelmans” than there are in university math departments?

    Moreover, “Perelmans” are born, not made. Ask most world-class mathematicians and those who knew them and their potential was already obvious before such future stars hit puberty.

    Most mathematicians good enough to be paid to be math professors aren’t even world-class — maybe the equivalent of a Triple-A baseball player, good enough to be paid to play and better in their field than most people will ever know, but hardly stars. The bulk of tenured competitive university mathematicians are the equivalent of major league baseball players… who warm the bench. Only a third of these are daily starters, the quality to draw an audience. Only a third of these are stars whose names a kid living in the same city would know a decade after they retired. Only a third of these are potential Hall of Famers. Few Hall of Fame baseball players hold all-time offensive or defensive records. THOSE are baseball’s Perelmans, the kind of rare-in-a-generation players for whom peers stand in awe.

    It does us no good to assert that every Triple-A baseball player is a budding Babe Ruth nor to claim that there are many Perelmans in the kollel system.

    That being said, the sheer joy of being in either game, Torah or baseball, is meaningful to the participant. The advantage of Torah learning, however, is that we don’t peak at the age of 27 and that our superstars continue and improve scandal and steroid-free for twice and three times as long.

  15. hp says:

    JO- I know you strive to be honest about the shortcomings of bnei torah. At the same time, it’s important to be honest about their very spiritual and special accomplishments. One way to do that is to refrain from offering critisism consistently- it changes honesty to something else. In order to be the conscience of a society, one needs to be honest with oneself as well.

  16. HESHY BULMAN says:

    JO – As you like.

  17. Jewish Observer says:

    “JO – like I said …”

    – s/b “as I said…”

  18. Jewish Observer says:

    However, the message would have increased credibility if you did indeed identify with the “we” that you refer to, as in “bnei torah”

    – if a prerequsite for “identifying with the we” is to being dishonest about who we are, then it is not my goal. Our – and torah’s honorability stands on its own and does require whitewashing.

  19. HESHY BULMAN says:

    JO – like I said, “sadly, there are those in our midst who simply can’t accept etc.” Incidentally, I’m an equal-opportunity “Glory Shedder” – more than willing to shed glory on any segment of our Am Segulah deservous of such.

  20. hp says:

    why don’t we (bnei torah) focus on others’ glory and improve our own behavior to the point where others are singing our praises. pointing out ones own greatnesses is never good form

    Comment by Jewish Observer — August 29, 2006 @ 11:03 am

    JO- Your point is well taken. However, the message would have increased credibility if you did indeed identify with the “we” that you refer to, as in “bnei torah”, at least some of the time. When your posts consistently shed bnei torah in a less than flattering light, it’s difficult to take a call from you for bnei torah to improve seriously.

  21. Jewish Observer says:

    “there are those in our midst, who simply can’t accept that there is indeed, even in our own cynical age, some great glory”

    why don’t we (bnei torah) focus on others’ glory and improve our own behavior to the point where others are singing our praises. pointing out ones own greatnesses is never good form

  22. Jewish Observer says:

    “intense higher learning with no hope, in most cases, for either monetary reward or even “Kavod” alone – virtually unheard of in the secular world – is almost commonplace in our world”

    – the flawed implication is that if it is not for kavod; it is driven solely by noble intentions. imagine an alternate reality where working were the de facto cultural next step for young charedi marrieds. do we honestly believe that the same percentage would be going to kollel? being truthful about the way things are is not tantamount to cynicism. if there were less self delusion and self promotion there would be less criticism.

  23. easterner says:

    the kollel system cannot work when the whole haredi society is expected to essentially tobe post-doc fellows for an unlimited amount of time on someone else’s dime. imagine if 50,00,000 americans decided to be History PhD candidates, without intention to get a PhD , or just to study history for study’s sake. of course this economic model would come crashing down— as haredi society in Israel will continue to do [since the kollel students ie every haredi boy over 18– essentially sends a bill to a society that hates his way of life…not a viable model]….if wealthy individuals want to support this model, it works well. but if this is seen as an entitlement, an impediment to a shidduch etc then it cant have a good end….

  24. Bob Miller says:

    Regarding Aaron’s comment #14 above:

    1. Who says that the slice of life he saw in his 7th grade class is typical of other such schools and communities in general?

    2. Who says his class gave math or English composition the same weight and attention as its Torah-related studies? (By the way, I’m not suggesting that math and English proficiency is unnecessary).

    3. A condescending attitude reduces one’s effectiveness as a teacher.

  25. Baruch Horowitz says:

    “Like Perelman, they spurn many of the comforts that others take for granted, and find satisfaction in knowledge itself.”

    The fact is that avreichim who participate in the Kolel System deserve praise both for opportunities given up, as well as for accomplishing things that are necessary for the spiritual health of the Jewish People. This is separate from and unrelated to the issue of whether the Kollel system needs improvement in different ways, or whether long-term Kollel study is viable as an only option for the majority of Orthodox Jews.

  26. Aaron says:

    If the quality of learning in kollel can be predicted from 7th grade pre-algebra from “our community” (my personal experience with boys expected to be future kollel students), I have even less confidence than before reading this in the likelihood of kollel parallels to state university (aka non-elite college) math majors with a B average and much less (by orders of magnitude) Perelmans. Does mathematics NEED a vast momentum of third-rate math students who really have no business plugging away in the field after the age of 21? We properly tell math students who aren’t world class to get a life and go into practical worldly applications. Do we need a subsidized class of B and C kollel students?

    A born American kollel student who can barely write a coherent paragraph in his mother tongue suitable for a business letter can hardly convince me of clear reasoning ability in Torah. Someone who writes at C level in his mother tongue is probably doing sub-C thinking in Talmud. I’ve fantasized about imposing the SATs, especially essay questions, on the American rabbinate and publicizing the results so that parents can see just how crippled the vast majority are in fundamentals.

    “Publish or perish” works for academia. Anyone who has read Thomas Kuhn’s “The Structure of Scientific Revolutions” should see an obvious beneficial application of this practice to Torah. Maybe it’s time to consider the equivalent of published “thesis papers” for admission and continuation of kollel subsidies?

    The value of kollelim is not in the product produced, certainly nothing as quantifiable as that of university science departments whose accomplishments are published and reviewed by outsiders, but in the value of Torah learning lishma. Does that deserve subsidy or being promoted as more worthy targets for shidduchim for our daughters than the frum professional who has gemara and mussar seders and maximizes the few hours per week that can be devoted to learning? Are we allocating our resources in the best way?

  27. Ezra says:

    **** Re your last sentence: Those who can read about Perelman and find his single-mindedness something to celebrate, should pause and reevaluate their attitudes towards the young men in Kollelim who are his Torah analogue.

    You miss a critical point. While both Perelman and kollel learners are singleminded, only the kollel learners are dependant on others (ultimately all of us) to support their interests. Let people study torah all they like, but go be like Perelman. Go to work, save up, then study as you live a modest life. Now THAT would be a good lesson! Sadly, today’s young men are only too happy to be a financial drain on society. And they display a holier than thou attitude to boot!

  28. JZ says:

    The cream of our kollel scholars toils altruistically in the pursuit of Torah knowledge much like Perlman, but goes one step further: It puts up with raw antipathy and condescension from its fellow Orthodox Jewish brothers. Reb Yitzchok, no matter how cleverly you package your praise for the kollelman, you are simply waving red meat.

    May Hashem bless our kollelim with strength and success. May we all merit to appreciate the blessings our kollelim have brought the remnant of our nation.

  29. HESHY BULMAN says:

    Comments submitted here with nuanced criticism of the Kollel system as it exists today are quite beside the most seminal point of this posting, which is that intense higher learning with no hope, in most cases, for either monetary reward or even “Kavod” alone – virtually unheard of in the secular world – is almost commonplace in our world. Sadly, there are those in our midst, who simply can’t accept that there is indeed, even in our own cynical age, some great glory to be found amongst even a segment of Klal Yisroel. I would urge these individuals to spend some little time in the Batei Medrash of Yerushalayim.

  30. Jewish Observer says:

    “Although not all Kollel people are brilliant geniuses, many are”

    – percentage?

  31. Harry Zelcer says:

    The article was fascinating until I got to

    “In our community there are thousands of Perelmans.”

    Then I realized that the article was not really about Perelman.

  32. tzvee says:

    Perelman published his proof. It was scrutinized by the greatest minds in his field and validated as correct. The equivalent in the Yeshiva context would be a kollel boy who published a sefer which was studied by the greatest gedolim and validated as outstanding. Without such validation we cannot know if the intellectual side of kollel study is productive.

  33. HILLEL says:

    Brilliance aside, what is so engaging about Perelman is his unassuming modest nature.

    Although not all Kollel people are brilliant geniuses, many are. And ever more are unassuming Talmidei Chachomim who devote their lives to Torah, just as Rav Aharon Kotler desired when he reestablished the Kollel system in America in Lakewood, New Jersey.

    All American–an even non-American–Jews are greatly indebted to Rav Aharon, ZT”L, for this great achievment. It is this pool of devoted Torah scholars that help maintain our Torah environment and supply us with our Rabbonim and Torah teachers.

    And, without modesty, I would assert that the achievment of even the most average true Torah scholar dwarfs Perelman’s achievements in significance.

  34. S. says:

    I didn’t say that I agreed that grappling with a R. Akiva Eiger was an equal intellectual feat with solving a hundred year old math puzzle. I’d say that solving a similarly challenging puzzle is comparable.

  35. Lumpy Rutherford says:

    “If you have learned much Torah, do not give yourself credit, because for this [purpose] you were created.”

    Pirkei Avos, Chapter 2, Mishna 8

  36. Jewish Observer says:

    “I believe R. Adlerstein’s contetion is that they essentially all are, because they are all engaged with the challenging material.”

    Comparing Perelman to the rank and file kollel members would cause – among those familiar with the kollel system – diminished awe for Perelman’s achievnments.

  37. S. says:

    >the challenge is how to identify those kollel men who are his analogue from within the larger group of kollel men

    I believe R. Adlerstein’s contetion is that they essentially all are, because they are all engaged with the challenging material.

  38. Seth Gordon says:

    In order to work full-time on pure mathematics, you need more than an interest in mathematics; you need to be one of the most outstanding mathematicians of your generation. (Or, like Dr. Perelman, you need to live frugally in the United States for a while and then take your savings to Russia.) Note that many of the people mentioned in the New Yorker article were involved with Princeton’s Institute of Advanced Studies, which is unusual for not requiring its scholars to even teach any classes. This freedom from all other responsibilities is an honor reserved for a very small elite.

    What kind of standard of Torah knowledge does someone have to achieve before they are allowed to learn full-time in kollel?

  39. Jewish Observer says:

    “reevaluate their attitudes towards the young men in Kollelim who are his Torah analogue”

    the challenge is how to identify those kollel men who are his analogue from within the larger group of kollel men