Category Archives: harvard

I don’t work at a finishing school

David Brooks, in the New York Times:

On the left, less viciously, we have elite universities that have become engines for the production of inequality. All that woke posturing is the professoriate’s attempt to mask the fact that they work at finishing schools where more students often come from the top 1 percent of earners than from the bottom 60 percent. Their graduates flock to insular neighborhoods in and around New York, D.C., San Francisco and a few other cities, have little contact with the rest of America and make everybody else feel scorned and invisible.

It’s fun to track down a fact. More from the top 1% than the bottom 60%! That certainly makes professoring sound like basically a grade-inflation concierge service for the wealthy with a few scholarship kids thrown in for flavor. But it’s interesting to try to track down the basis of a quantitative claim like this. Brooks says “more students often come,” which is hard to parse. He does, helpfully, provide a link (not all pundits do this!) to back up his claim.

Now the title of the linked NYT piece is “Some Colleges Have More Students From the Top 1 Percent Than the Bottom 60.” Some is a little different from often; how many colleges, exactly, are that badly income-skewed? The Times piece says 38, including five from the Ivy League. Thirty-eight colleges is… not actually that many! The list doesn’t include Harvard (15.1 from the 1%, 20.4 from the bottom 60%) or famously woke Oberlin (9.3/13.3) or Cornell (10.5/19.6) or MIT (5.7/23.4) or Berkeley (3.8/29.7) and it definitely doesn’t include the University of Wisconsin (1.6/27.3).

We can be more quantitative still! A couple of clicks from the Times article gets you to the paper they’re writing about, which helpfully has all its data in downloadable form. Their list has 2202 colleges. Of those, the number that have as many students from the top 1% as from the bottom 60% is 17. (The Times says 38, I know; the numbers in the authors’ database match what’s in their Feb 2020 paper but not what’s in the 2017 Times article.) The number which have even half as many 1%-ers as folks from the bottom 60% is only 64. But maybe those are the 64 elitest-snooty-tootiest colleges? Not really; a lot of them are small, expensive schools, like Bates, Colgate, Middlebury, Sarah Lawrence, Wake Forest, Vanderbilt — good places to go to school but not the ones whose faculty dominate The Discourse. The authors helpfully separate colleges into “tiers” — there are 173 schools in the tiers they label as “Ivy Plus,” “Other elite schools,” “Highly selective public,” and ‘Highly selective private.” All 17 of the schools with more 1% than 60% are in this group, as are 59 of the 64 with a ratio greater than 1/2. But still: of those 173 schools, the median ratio between “students in the top 1%” and “students in the bottom 60%: is 0.326; in other words, the typical such school has more than three times as many ordinary kids as it has Richie Riches.

Conclusion: I don’t think it is fair to characterize the data as saying that the elite universities of the US are “finishing schools where more students often come from the top 1 percent of earners than from the bottom 60 percent.”

On the other hand: of those 173 top-tier schools, 132 of them have more than half their students coming from the top 20% of the income distribution. UW–Madison draws almost two-fifths of its student body from that top quintile (household incomes of about $120K or more.) And only three out of those 173 have as many as 10% of their student body coming from the bottom quintile of the income distribution (UC-Irvine, UCLA, and Stony Brook.) The story about elite higher ed perpetuating inequality isn’t really about the kids of the hedge-fund jackpot winners and far-flung monarchs who spend four years learning critical race theory so they can work at a Gowanus nonprofit and eat locally-sourced brunch; it’s about the kids of the lawyers and the dentists and the high-end realtors, who are maybe also going to be lawyers and dentists and high-end realtors. And the students who are really shut out of elite education aren’t, as Brooks has it, the ones whose families earn the median income; they’re poor kids.

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Pandemic blog 9: The Class of 1895

I was wondering about what the last major pandemic, the Spanish flu of 1918, looked like in real time, so I looked at the 25th anniversary report of the Harvard Class of 1895, published in June 1920 and written in 1919. To my surprise, the flu is barely mentioned. Henry Adsit Bull lost his oldest daughter to it. A couple of classmates worked in influenza hospitals. Morton Aldrich used it as an excuse for being late with his report. Paul Washburn reported being quite ill with it, and emphasizing that it might be his last report, demanded that the editors print his curriculum vitae with no editorial changes. (Nope — he was still alive and well and banking in the 1935 report.) I thought 1894, whose report was written more in the thick of the epidemic, might have more to say, but not really. Two men died of it, including one who made it through hideous battles of the Great War only to succumb to flu in November 1918. Another lost daughter.

But no one weighs in on it; I have read a lot of old Harvard class reports, and if there’s one thing I can tell you about an early 20th century Harvard man, it’s that he likes to weigh in. Not sure what to make of this. Maybe the pandemic didn’t much touch the lives of the elite. Or maybe people just died of stuff more and the Spanish flu didn’t make much of an impression. Or maybe it was just too rough to talk about (but I don’t think so — people recount pretty grisly material about the war.)

Back to the present. The Wisconsin Supreme Court ordered all jury trials halted for two months for the safety of jurors, witnesses, and officers of the court; an extremely overwrought dissent from Justice Rebecca Bradley insists that if a right is in the constitution it can’t be put on pause, even for a couple of months, even in a pandemic, which will be news to the people in every state whose governors have suspended their right to assemble.

CJ made a blueberry bundt cake, the best thing he’s made so far, aided by the fact that at the Regent Market Co-op I found a box of pectin, an ingredient I didn’t even know existed. Powdered sugar there was not, but it turns out that powdered sugar is literally nothing but regular sugar ground fine and mixed with a little cornstarch! You can make it yourself if you have a good blender. And we do have a good blender. We love to blend.

Walked around the neighborhood a bit. Ran into the owner of a popular local restaurant and talked to him from across the street. He’s been spending days and days working to renegotiate his loan with the bank. He thinks we ought to be on the “Denmark plan” where the government straight up pays worker’s salaries rather than make businesses apply to loans so they can eventually get reimbursed for the money they’re losing right now. (I did not check whether this is actually the Denmark plan.) Also saw my kids’ pediatrician, who told me that regular pediatrics has been suspended except for babies and they’ve closed the regular clinic, everything is consolidated in 20 S. Park.

I’ve been spending a lot of time thinking about different groups’ COVID projections, claims and counterclaims. I’ll write about it a little in the next entry to show how little I know. But I think nobody knows anything.

Tomorrow it’ll be two weeks since the last time I was more than a quarter-mile from my house. We are told to be ready for another month. It won’t be that hard for us, but it’ll be hard for a lot of people.

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Elif Batuman, “The Idiot”

What a novel!  The best I’ve read in quite a while.

One thing I like:  the way this book takes what’s become a standard bundle of complaints against “literary fiction”:

It’s about overprivileged people with boring lives.  Too much writing about writing, and too much writing about college campuses, and worst of all, too much writing about writers on college campuses.   Nothing really happens.  You’re expected to accept minor alterations of feelings in lieu of plot.  

and gleefully makes itself guilty of all of them, while being nevertheless rich in life and incident, hilarious, stirring, and of its time.

Maybe “hilarious” isn’t quite the right word for the way this book is funny, very very funny.  It’s like this:

“Ralph!” I exclaimed, realizing that he was this guy I knew, Ralph.

Whether you find this funny is probably a good test for whether The Idiot is gonna be your thing.

Given this, it’s slightly startling to me that Batuman wrote this essay in n+1, which endorses the standard critique, and in particular the claim that fiction has been pressed into a bloodless sameness by the creative writing workshop.  They bear, as she puts it, “the ghastly imprimatur of the fiction factory.”

What kind of writing bears this stamp?

Guilt leads to the idea that all writing is self-indulgence. Writers, feeling guilty for not doing real work, that mysterious activity—where is it? On Wall Street, at Sloane-Kettering, in Sudan?—turn in shame to the notion of writing as “craft.” (If art is aristocratic, decadent, egotistical, self-indulgent, then craft is useful, humble, ascetic, anorexic—a form of whittling.) “Craft” solicits from them constipated “vignettes”—as if to say: “Well, yes, it’s bad, but at least there isn’t too much of it.” As if writing well consisted of overcoming human weakness and bad habits. As if writers became writers by omitting needless words.

So what’s weird is that Batuman’s writing is exactly the kind that the creative writing workshop leaps to its feet and applauds.  OK, there’s no leaping in creative writing workshop.  It would murmur appreciatively.  Her sentences are pretty damn whittled.  Also clever.  Scenes don’t overspill, they end just before the end.  Batuman’s writing is both crafted and crafty — but not anorexic!  Anorexia isn’t denying yourself what’s needless; it’s a hypertrophy of that impulse, its extension to a more general refusal.

Batuman is really excellent on the convention of the literary short story cold open, which is required to be:

in-your-face in medias res, a maze of names, subordinate clauses, and minor collisions: “The morning after her granddaughter’s frantic phone call, Lorraine skipped her usual coffee session at the Limestone Diner and drove out to the accident scene instead.”  …. A first line like “Lorraine skipped her usual coffee session at the Limestone Diner” is supposed to create the illusion that the reader already knows Lorraine, knows about her usual coffee, and, thus, cares why Lorraine has violated her routine. It’s like a confidence man who rushes up and claps you on the shoulder, trying to make you think you already know him.

Her paradigmatic offender here is the first line of Michael Chabon’s The Amazing Adventures of Kavalier & Clay:

In later years, holding forth to an interviewer or to an audience of aging fans at a comic book convention, Sam Clay liked to declare, apropos of his and Joe Kavalier’s greatest creation, that back when he was a boy, sealed and hog-tied inside the airtight vessel known as Brooklyn New York, he had been haunted by dreams of Harry Houdini.

about which she says:

All the elements are there: the nicknames, the clauses, the five w’s, the physical imprisonment, the nostalgia. (As if a fictional character could have a “greatest creation” by the first sentence—as if he were already entitled to be “holding forth” to “fans.”)

To me this all starts with One Hundred Years of Solitude, which all of us writers read the hell out of in high school, right?  Surely Batuman too?  No kid can read

Many years later, as he faced the firing squad, Colonel Aureliano Buendia was to remember that distant afternoon when his father took him to discover ice.

and not say, oh, that’s how you do it.

Anyway, I’m mostly with Batuman here; once she shows you how it works, the trick is a little corny.  Maybe I already knew this?  Maybe this is why I always preferred the first line of, and for that matter all of, Chabon’s The Mysteries of Pittsburgh to Kavalier & Clay.  Here’s the opening:

At the beginning of summer I had lunch with my father, the gangster, who was in town for the weekend to transact some of his vague business.

In medias res, yes — but not so overstuffed, just one piece of information (the gangster!) presented to start with.  No names.  The word “transact” — boy, there’s nothing I like more than a perfect placement of a boring word.  I think it’s a lot like the first line of The Idiot:

“I didn’t know what email was until I got to college.”

Except Chabon focuses on rhyme (summer-father-gangster) while Batuman is all scansion — perfect trochees!


Of course there are a lot of reasons I’m predisposed to like this.  It’s about bookish, ambitious, romantically confused Harvard undergrads, which Batuman and I both were.  There are a lot of jokes in it.  There are some math scenes.

There’s even a biographical overlap:  Batuman, wrote her college novel right after college, just like I did.  And then she finished her Ph.D. and put the manuscript in a drawer for a long time, just like I did.  (I don’t know if she carried out the intermediate step, as I did, of getting the book rejected by every big commercial house in New York.)  And then at some point in the run-up to middle age she looked at those pages again and said words to the effect of “This is not actually that bad…”

So let me say it straight; The Idiot makes me think about the alternate universe where I stayed a novelist instead of going back to grad school in math, a universe where I spent years working really hard to sharpen and strengthen the work I was doing.  This is the kind of novel I would have been aiming my ambition at writing; and I still wouldn’t have done it this well.  The existence of The Idiot releases me from any regrets.

(I don’t have many.  Math, for me, is fun.  Writing fiction is not.)





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Why would anyone want to become a security analyst or portfolio manager?

In today’s Wall Street Journal, Jason Zweig frets about the popularity of index funds:

If investors keep turning their money over to machines that have no opinion about which stocks or bonds are better than others, why would anyone want to become a security analyst or portfolio manager? Who will set the prices of investments? What will stop all stocks and bonds from going up and down together? Who will have the judgment and courage to step in and buy during a crash or to sell during a mania?

First of all, it hardly seems like the entire stock market is liable to become one big Vanguard fund:  as Zweig says later in the piece, “indexing accounts for 11.5% of the total value of the U.S. stock market.”  Big institutional actors have special needs which give them reason to actively manage their funds.  And an institution like Wisconsin’s pension fund, which manages about $100b, isn’t giving away 2% of its money per year to a manager, the way you or I would.  (This document says we spent $52.5 million in external management fees in 2013; percentagewise, that’s less than I give Vanguard for my index.  Update:  I screwed this up, as a commenter points out.  Our external management fees increased by $52.5m.  They present this as a substantial percentage of the total but I can’t find the actual amount of the fee.)

But second:  am I supposed to be upset if it becomes less attractive to become a portfolio manager?  One out of six Harvard seniors goes into finance.  Is that a good use of human capital?

(By the way, here’s a startling stat from that Harvard survey:  “None of the women going into finance said they would earn $90,000 or more, compared to 29 percent of men in finance.”  Is that because men are overpaid, or because we lie about our salaries the same way we lie about sex?)




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Math Bracket 2015

March Math Madness is here!  Presenting the 2015 math bracket, as usual prepared by our crack team of handicappers here at the UW math department.  As always, remember that the math bracket is for entertainment purposes only and you should not take offense if the group rated your department lower than the plainly inferior department that knocked you out.  Under no circumstances should you use the math bracket to decide where to go to grad school.

Math Bracket 2015-page-0Lots of tough choices this year!


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10,000 baby names of Harvard

My 20th Harvard reunion book is in hand, offering a social snapshot of a certain educationally (and mostly financially) elite slice of the US population.

Here is what Harvard alums name their kids.  These are chosen by alphabetical order of surname from one segment of the book.  Most of these children are born between 2003 and the present.  They are grouped by family.

Molly, Danielle

Zachary, Zoe, Alex

Elias, Ella, Irena

Sawyer, Luke

Peyton, Aiden

Richard, Sonya

Grayson, Parker, Saya

Yoomi, Dae-il

Io, Pico, Daphne

Lucine, Mayri

Matthew, Christopher

Richard, Annalise, Ryan


Christopher, Sarah, Zachary, Claire

Shaiann, Zaccary

Alexandra, Victoria, Arianna, Madeline


Grace, Luke, Anna

William, Cecilia, Maya

Bode, Tyler

Daniel, Catherine

Alex, Gretchen

Nathan, Spencer, Benjamin

Ezekiel, Jesse

Matthew, Lauren, Ava, Nathan

Samuel, Katherine, Peter, Sophia

Ameri, Charles


Andrew, Zachary, Nathan

Alexander, Gabriella


Andrew, Nadia

Caroline, Elizabeth

Paul, Andrew

Shania, Tell, Delia

Saxon, Beatrix


Nathan, Lukas, Jacob

Noah, Haydn, Ellyson


Leonidas, Cyrus

Isabelle, Emma

Joseph, Theodore

Asha, Sophie, Tejas

Gabriela, Carlos, Sebastian

Brendan, Katherine


James, Seeger, Arden

Helena, Freya

Alexandra, Matthew


If you saw these names, would you be able to guess roughly what part of the culture they were drawn from?  Are there ways in which the distribution is plainly different from “standard” US naming practice?


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Math bracket 2013

And here it is, the annual NCAA bracket produced by awarding each game to the school with the better math department.  Of course, these judgments are for entertainment only, and were produced by a group, so if you find any of the picks absurdly wrong, those were the ones I didn’t make.

Go Crimson!

MathBracket 2013

Update: A great first day of play for the math bracket — Harvard and Berkeley advance over higher-seeded opponents and we’re in the 55th percentile of the ESPN Challenge.

Update: Second day less good as UCLA is the first of our final four to get eliminated, and we drop into the low 30s.

Update: Bracket in disarray, with only Duke remaining from the math final four. On the bright side, the math faculty at Florida Gulf Coast University includes Eric Insko, a student of my collaborator Julianna Tymoczko, and an undergrad alum of UW-Madison. So that explains nicely why they’re doing so well.

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The life and opinions of a college class

I always thought of pre-WWII Harvard as a place that paid some lip service to educating the common man while mostly functioning as a finishing school for preppies.  But was it so?  The very interesting Life and Opinions of a College Class, which reports the results of an extensive survey offered to the Harvard Class of 1926 on the occasion of their 25th reunion in 1951, tells a more complicated story.  I learned there that:

  • Only 54% of the class had fathers with a college degree; 26% of the class had fathers who had not finished high school.
  • Only about half the class went to private high school.
  • 17% were Jews.  (But only 8% were Catholic!)
  • 29% of the class worked at an outside job during the school year to support themselves.

(But note:  in the appendix, we learn that while half the class came from public high schools, the officers and class marshalls were entirely drawn from the preps.)

Nothing here really tells us whether the families of the Harvard students had money, though the fact that 70% of those families were Republicans might offer some clue.  Certainly they were rich by 1951, with a median income almost four times the national median.  (That would amount to about $180,000 today — I wonder how that compares with the current incomes of the class of 1988?)

Already in 1951, proponents of the liberal arts were anxious about becoming antique in a world ruled by science:

Only 13 percent were sufficiently prophetic of the shape of things to come to prepare in any of the physical or human Sciences; another 10 percent chose Engineering and/or Mathematics.

But one alum stuck up for tradition:

Admitted this is an age of specialization, then a boy should go to M.I.T. and do it up brown.  If he is going to Harvard, let him get a good liberal grounding which I think will make him a better citizen, and then concentrate later when he can put his whole mind on it.  He will undoubtedly be surpassed by many of the trade school boys but he will have something they will never have and to hell with his dinner pail.

One of my favorite moments in the book is the list of responses to the question, “What is the biggest mistake you have made in life?”

The catalogue of miscellaneous major blunders includes:  ill-advised speculation in 1929; getting back into the market too soon after the crash; failure to sell short; overeating; starting to smoke; neglecting the home for business; voting for Franklin D. Roosevelt and not voting for Franklin D. Roosevelt; wasting time; taking too little part in community life; too much diversification of interests; relying too much on the advice of older people; placing too much confidence in business associates; joining the Communist party; too much sex in earlier years; buying too large a house; drinking too much; a youthful indulgence in arson; and, in one instance, misappropriation of funds.

The irrevocable change brought about by the Civil War

From the Harvard reunion book entry of Edward Learoyd Cutter ’06, a coal dealer in Boston, concerning his vacation trips to Charleston, SC:

We have been extremely fortunate in knowing a few of the old plantation families, and in having been included in some of their good times, which has given us a viewpoint that few Northerners can ever have.  When one sees and understands a little the irrevocable change brought about by the Civil War, one cannot escape the sensation of guiltiness for having been born a Yankee.

Was this a respectable view to assert in public in 1931?  If so, when it it start being respectable to talk this way (surely it took some time after the end of the war) and when did it stop?

Possibly relevant is the testimony of Cutter’s classmate, Floyd Andrews Brown, of Deposit, NY:

I am now in the my thirteenth year as clerk of the Board of Education, a matter in which I take some pride by reason of having survived the period when every other elective or appointive officer in the village, township, and school district was at least in sympathy with, if not an active member of, the Ku Klux Klan.  This domination of a community by the Klan, now happily past, is a fair measure of the benightedness of the section of rural New York in which I seem fated to spend my declining years.

Aside, directed mainly at Harvard coevals:  Whatever happened to Bridget Kerrigan?

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Barry Mazur wins the National Medal of Science

As the old joke goes, “Who’s that guy next to Mazur?”

Barack Obama, Barry Mazur

Barry Mazur, my Ph.D. advisor, was awarded the National Medal of Science last week.  It’s hard to overstate the extent to which his work and his outlook have affected the direction of number theory.  And of course my own way of doing math is substantially colored by my time studying Barry’s mathematics,  and my very good fortune of working closely with him as a student.  It seems to me that it must be transparent to anyone who talks to me that I was Barry’s student.  He taught me to see mathematics as a unified whole, he taught me that forming good questions was as important a part of progress as settling on answers, and he taught me how to say “It is what it is,” which has entered my idiolexicon as a kind of mu-like mantra.  Maybe the most important lesson I learned from him is that in mathematics it is very useful to be interested in everything.  I’m just one of 54 students Barry has advised, and I’ll bet all of us would say similar things about his influence.

Lately (on top of his continuing busy schedule of proving theorems!) Barry has been thinking very deeply about what we are doing when we think we know something.  See “What is Plausible?”, which considers the difference between gathering evidence for “all ravens are black” and gathering evidence for the Riemann hypothesis, and features guest appearances by the Cohen-Lenstra conjecture and the analogy between function fields and number fields, two of my favorite topics.  (Note to self:  “Why do we and why did we find the Cohen-Lenstra conjecture plausible?” would be a good future post.)

Via Brian Conrad, here’s a link to video of the ceremony.

I gathered a couple of reminiscences from people who worked with Barry before I knew him.

Dick Gross:

The memory of Barry’s graduate courses and seminars when I arrived at Harvard as a student in the early 70s is indelible. Barry was working through the ideas in his great paper on the Eisenstein ideal, and every talk he gave was an opening into a beautiful new world.

It’s not an exaggeration to say that the next generation of number theorists came out of his overcoat.

Ken Ribet:

My real relationship with Barry began toward the end of my last year at Harvard, when I explained my thesis to him and we realized that we had many mathematical interests in common.  My thesis was about Galois representations attached to abelian varieties, and Barry’s Eisenstein ideal paper was at least partly in the same subject.  (That article covers a lot of ground!!)  I communicated with Barry quite a bit over the next few years, when I was in Princeton and in Paris.  We sent letters back and forth, and we had face-to-face discussions.  I made some tiny contributions to the Eisenstein ideal paper by pointing out to Barry a few things that he hadn’t yet come to grips with and by finding a mistake in Barry’s initial discussion of Eisenstein primes mod 2.

For me, the Eisenstein ideal article is one of the great landmark articles of all time.  It introduced a plethora of new techniques and solved a number of important problems.  One takeaway from the article for me was Barry’s insistence on studying objects just as they are, in the most delicate possible way.  Shimura would study quotients of Jacobians of modular curves by replacing them by isogenous varieties on which full rings of integers could operate.  Barry’s idea was to study the Hecke ring just as it is and not to replace it by its normalization.  What a great idea!  He also introduced the perspective of studying Hecke rings as objects of commutative algebra.  He proved (in most cases) that they’re Gorenstein, for example.  Another takeaway is that your work is not finished until you’ve sorted out every detail.  Barry wasn’t content with a result that was true outside of some finite set of primes; he insisted on going down into the exceptions to see exactly what happens there.

A central contribution of Barry’s paper was to prove that many Hecke modules that are generically of “rank N” (N= 1 or 2) are actually locally free of rank N.  One way to describe my “level-lowering” theorem is to say that, in the simplest case of representations of prime level, I prove a statement analogous to Barry’s for the one Hecke module whose local freeness he didn’t discuss.  This is the character group of the torus in the Neron reduction of the Jacobian of X_0(N) at the bad prime N.

If I’m not mistaken, Barry won two major AMS prizes for the same article — the Eisenstein article.  He won the Cole Prize when it was published and then the Steele Prize for an article of enduring value a couple of decades after it was published.  I don’t know any other example where a single article was honored by multiple AMS prizes.






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