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The 1980 Math Olympiad Program: Where are they now?

Brian Hunt: He was the #1 math team kid in our team (Montgomery County, Maryland). I think he came in first place in the international olympiad the next year (yup, here’s the announcement). We carpooled once or twice to county math team practices, and I remember that his mom would floor it rather than slow down when she came to a yellow light. I looked Brian up, and he is now a math professor at the University of Maryland. On Google scholar, his most cited paper is “Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter.”

Benji Fisher: He was quite a character, larger than life in some ways. He came in first place in the regional math competition (this required getting 8 problems out of 8 correct, which was difficult; maybe I got 4 correct that year, or maybe only 2?). I remember him (perhaps incorrectly) as a big guy with long hair in a ponytail. When I came to Columbia in 1996, I noticed that he was teaching in the math department. I gave him a call (“Hi, Benji, you probably don’t remember me, my name is Andy Gelman . . .”) and suggested getting together. He told me he was leaving Columbia to teach at the Bronx high school of science. We never did get together, nor did we speak again. I googled just now and here he is, mentioned in the NYT in 1981 (it says he could do the Rubik’s cube in 2 1/2 minutes, which was really the least of his talents at the time), then I found a linked-in page that says that he only taught high school for one year, and now he’s a web developer in Boston.

Jack Brennen: He and Noam were the two youngest kids in the Olympiad program. I and some others were 15, a bunch of the other kids were 16 or 17, Jack and Noam were only 14. Jack felt a bit of rivalry with Noam which was unfortunate because Noam was obviously the best of all of us. I did some googling and it appears that Jack is now a full-time software engineer, or at least he was as of 2011.

Andrew Gelman: I’ve written about my olympiad experiences before (see also here). I was probably about the 20th best out of 24. Had I practiced, I think I could’ve been 10th or 15th (then again, if everyone had practiced, maybe I would’ve been 23rd or 24th), but the important thing was that I realized there were other people better than me at this. I feel very lucky that I came to this realization and didn’t hit a dead end later on. At the time I was disappointed not to make it to the international olympiad but in retrospect it all worked out just right.

Gregg Patruno: A super-nice guy. That’s all I remember about Gregg: he was one of the top kids in the program and he was super-nice, very friendly. I was pretty shy at the time, I was younger than most of the other kids and mostly tagged along with the 3 others from Montgomery County. So I appreciated when some of the older kids were friendly. I googled and it appears that Gregg is a musician. More googling yields this page: it appears that Gregg is “a Vice President in the Fixed Income Division of Goldman Sachs.” That’s too bad.

Also I remember there were 2 or 3 participants in the training program who were from the Boston area. 2 guys and a girl, I think. Or maybe 1 guy and 2 girls. All 3 were, like me, near the bottom of the pack. Anyway, I remember that one of those Bostonians was really funny. Near the end of the four weeks, this guy was really stuck on one of the homework problems and he asked Gregg for help. He wrote up Gregg’s solution and then, at the end, put a long footnote with a citation to “Patruno, G., Solution to Problem 11 of Mathematical Olympiad Program,” etc. This joker (unfortunately, I can’t remember his name) was also amused by Gregg’s near-palindromic name and suggested that he change it to Grerg.

David Yuen: I don’t remember him well but I do remember his name, so that’s something. Here he is—he’s a professor of math and computer science. Most-cited paper appears to be “Linear dependence among Siegel modular forms.”

David Wollen: I remember him as a very comfortable guy, with lots of friends, I was envious of how at-ease he was. In the middle of the pack in terms of success on math olympiad problems. I can’t find him on the web but I do seem to be finding a David Wolland so maybe I’m misremembering the name. I remember that he went to Hunter College High School. In any case, Wollen or Wolland, I have no idea what he’s up to now.

Ken Zeger: He was the kid who was interested in engineering. All the rest of us cared only for pure math, he wanted to solve engineering problems. And here he is, he’s a professor of Electrical and Computer Engineering at the University of California. How cool is that? His most-cited paper appears to be “Closest point search in lattices.”

Dougin Walker: My roommate. Also from Montgomery County. Like me, a silly kid, also another guy who was trying his best but was no star. His distinctive name makes him easy to google! He appears to be a triathlete, and it looks like he’s a “principal” of the Watermark Group—a hedge fund?

Stephen Mark: A really mellow guy. The rest of us really cared where we ranked. Brian was a top scorer and that was important to him, Benji was a big shot and that came from his success solving math problems, Noam—well, Noam was not competitive with the rest of us, exactly, but he know how good he was—and I cared too. It’s all well for me to say, now, that I was lucky not to be among the best in the group. But, at the time, I did want to be the best. Not that I had any plan of how to get there, I just wanted to be #1. Or at least #2. Or #5, whatever. But Stephen (no, I can’t remember if he went by Steve, although I can only assume he did) just didn’t seem to care in that way, he was more aloof (in a good sense). The other thing I remember is that at one of the tournaments he wrote the anagram Peter Shmank on his nametag. And he was also from Montgomery County. And . . . that’s about it. I can’t find Stephen Mark on Google.

Hmmm, let me be clear on one thing. I’ve written how my mediocre performance on the olympiad training program pushed me to a new view of where I was heading in life, how I realized that (a) there were others who were better at math than I was, which led me gradually to the realization (b) that there were other things I could do. But this didn’t happen right away—even step (a) took awhile. I was in that program as a 10th grader and so I figured, sure, I’ll just get better each year. Every time I did a math competition I fully expected to get a perfect score and come in first place. The next year, I was pretty bummed when, after taking the national math test (from which the highest scorers got picked to do the olympiad), I didn’t score so high. Maybe I was in the top 100 in the country, maybe not, I can’t remember, but not in the top 8 or even the top 24, that’s for sure. And then the same thing happened in 12th grade. That was ok, I still did math team and was on the county math team at the regional competition, I still looked forward to these things. Which is fine: school sports would fall apart if only the very best kids participated (and of course there were lots of kids on the team who weren’t at my level, either). It’s funny in retrospect, though, to think that I kept sort of expecting I’d do better. And, again, I’m glad I didn’t do better. If I had, maybe I’d’ve gotten a math Ph.D. and now I’d be working at a hedge fund. Ulp.

Leonid Fridman, Zachary Franco: I remember only their names, and I think they were nice enough, also in that middle-of-pack range in math-problem-solving ability. Some googling appears to show that Zachary is now a medical researcher and does volunteer math coaching. I’m not sure what Leonid is doing.

Jeremy Primer: He was, like Patruno, one of the top kids but not the very top. I ran into him from time to time in grad school at Harvard; he was studying math while I was in statistics. My impression was that he was not so thrilled with it. What’s he doing now? Hmmm . . . “Jeremy Primer” shouldn’t be hard to Google . . . uhhhh, “Head of Research & Chief Risk Officer” at Tilden Park, looks like another hedge fund. He also worked at Goldman Sachs. Uh oh. I wonder if he stays in touch with Gregg? According to one online source, Jeremy was a “Harvard-educated maths genius whose computer models alerted the bank to how small levels of defaults would quickly turn apparently sound assets into junk,” leading Goldman to start selling off at the end of 2006. OK, whatever.

Dan Scales: Am I misremembering this name? I can’t find anything on Google.

Noam Elkies: Obviously the most talented math kid in the group (and thus, by implication, in the country); in retrospect, the most successful mathematician as well, maybe the top mathematician of our generation (not counting Stephen Wolfram ha ha ha). At the time, I don’t recall that we saw him as so brilliant; pretty much we saw him as being really weird. But, what can you say, we were all pretty weird and he had a lot going on in his brain. I ran into him a couple times in grad school. He’s now a math professor at Harvard. I haven’t looked him up in a long time. I guess I could—I could just walk over to his office one day. Maybe I should, although I don’t really know that we’d have much to talk about. His most-cited paper: “Alternating-sign matrices and domino tilings (Part I).” Hey, that’s got a bit of a Mel Brooks feel to it! And here’s Noam’s paper with the most math-team-like title: “On A^4+B^4+C^4=D^4,” which begins, “We use elliptic curves to find infinitely many solutions to A^4+B^4+C^4=D^4 in coprime natural numbers A,B,C, and D, starting with 2682440^4+15365639^4+18796760^4=20615673^4. We thus disprove the n=4 case of Euler’s conjectured generalization of …” It’s like a really really hard olympiad problem!

Sam Greitzer: The old guy who ran the mathematical olympiad program. A cranky, mean old man. On the other hand, I suppose he was doing it all on a volunteer or quasi-volunteer basis, and maybe you had to be a mean guy to keep a bunch of teenage boys under control. Still, he was not a pleasant person by any means. According to Wikipedia, he was born on August 10, 1905, so he was already 74 years old when I met him. A cranky old man indeed. I’ll give him a break. When I’m 74, I’ll probably have difficulty relating to 15-year-olds too.

Murray Klamkin: The second banana. Not so young himself, he was 59 when I knew him. More mild-mannered. According to Wiki, Klamkin “worked at AVCO, taught at SUNY Buffalo, and served as the Principal Research Scientist at Ford Motor Company,” among other things.

Mike Larsen: A former olympiad competitor who was serving as a coach. I think he was about 18. I don’t remember much about him, I suppose he (wisely) spent most of his time coaching the top kids, as the goal was to improve the national team, not to bring the laggards up to par. And, hey, here he is on Wikipedia! He teaches math at the University of Indiana. His most recent published paper: “Deformation theory and finite simple quotients of triangle groups I.” That, I’ll have to say, is the kind of thing we all imagined doing when we grew up. Pure math. You can’t get much purer than this.

OK, those are the names I can remember. But this is frustrating: I can only remember 15 kids out of 24. The closest to an official site I could find was this, which seems be from 2000 or 2001 and is on the Mathematical Association of America website. It has many omissions: it does not include me or most of my friends listed above!

P.S. I sent the above to Jordan Ellenberg, who added the following:

I [Jordan] have memories of lots of these people, though they’re a MOP generation older than me. Some disorganized thoughts.

Brian Hunt — I remember him as captain of the Montgomery County Math Team! I think 1980 or 1981 was the first time I went to ARML. I haven’t seen him in years and years even though we’re both in math academia.

Benji Fisher — left academic math a long time ago but wrote a very beautiful paper with Sol Friedberg that presents questions I still strongly feel need answers…. “long hair in a ponytail” fits my memory too. But was he also from Montgomery County? Weird that I would forget that!

Jack Brennen — remember the name, nothing else.

Gregg Patruno — he was the director of MOP by the time I went, when I was in high school! He was already working in the financial industry at that time. But great guy, “intense in a low-key way” if that makes sense; he really made me feel it was worth it to become ultra-strong at contest problems. I remember at one point the whole team went to Gregg’s house in Staten Island, the one and only time I’ve ever been there.

Leonid Fridman — he was a Harvard grad student when I was an undergrad. He founded a group called “The Society of Nerds and Geeks” and had an op/ed in the New York Times about it and was very briefly a national expert on nerds.

Noam: That A^4+B^4+C^4=D^4 paper was something he wrote in high school, I think! And people were like WHA-A-A-A-A-T? He is still an elliptic curves master (and master of many other things as well.)

Mike Larsen is a really good mathematician, who like Noam is very broad; I guess I would call him a group theorist but you could as well call him a number theorist, algebraic geometer, or many other things. He and I wrote a paper together about motives.

117 Comments

  1. Nick says:

    it appears that Gregg is “a Vice President in the Fixed Income Division of Goldman Sachs.” That’s too bad.

    What’s so bad about it? That he works for an investment bank or that VP is a pretty junior role? I hope the problem isn’t the former, because if you really remember him as a good guy, but have preconceived notions about what Goldman Sachs must be like, maybe you should update your priors.

    • Phil says:

      I’m not sure “preconceived notion” is the right term here; anyone who has been paying attention for the past ten years has quite a bit of information about what Goldman Sachs is like. The term “postconceived notion” might fit better.

      But, even if not Goldman Sachs in particular, some of us think that spending your professional career trying to squeeze out another basis point by playing the financial markets doesn’t sound like a very rewarding life. I’m in that camp myself; I’ll let Andrew speak for himself if that’s what he means.

      • Rahul says:

        Is it a more rewarding life to work on “Linear dependence among Siegel modular forms”? Or obsess about the “finite simple quotients of triangle groups”?

        I can imagine smirking at the one-basis-point-guys if my career was a UN-peacekeeper, or HIV-researcher or even a diesel-engine researcher or structural engineer.

        But pure math seems a strange reference point from which to judge Wall Street Modellers.

        • Patrick says:

          Well, people do math research because they are passionate about it. There’s no other way to be even a mediocre researcher.

          And if academia payed as well or offered as many good jobs these people would probably be doing that. In a sense, it’s a shame that people very skilled and passionate about something don’t end up doing it. And there are arguments that they add negative value… But I don’t really know about that.

          • Rahul says:

            Yes, but can people not be similarly passionate about Finance?

            In any case, I think one of our core problems today is the excessive glorification of kids following their passions.

            What do we do when the distribution of passions does not match the nature of problems we feel are important to “public good”?

            There’s no fundamental reason why we ought to be paying a smart kid the same $$ to do pure math as something else, just because it happens to be his passion.

        • Zack says:

          Pure mathematicians are scientists. They are trying to find a higher truth, and publish it for the world to advance us all. People who work at investment funds are trying to exploit various quirks of the market to make large amounts of money. There is about as significant a difference as you can imagine.

          • GC says:

            I would like to call bullshit on the above comment. No problem with the article as such. As an ex-scientist and as someone who is married to an ex-academic, I have seen the inner workings of academia, and I can honestly say that “finding a higher truth” is not what most academic gasbags are trying to do. While there are many academics who are genuinely talented, the majority are showmen who make a name for themselves by dint of hard self-promotion. I have found more merit-based hiring in industry than in academia. Academics have the privilege of doing something they are passionate about but to think they are not swayed by things such as money, popularity or petty jealousy is foolish. And the system tries to brainwash people into thinking they are failures if whatever reason (e.g., not wanting to move to the middle of nowhere, two-body problem, etc.) they do leave academia and end up leading a comfortable life.

    • Nick F says:

      I don’t see anything wrong with it. Except that Gregg saw no light of day. Strange and obsessive man. Very good modeller

      I worked for him for one month exactly. Shared an office with Jeremy Primer. The reason I went? Gregg had what I thought was the most interesting Bayesian prepayment model on the street. A continuum of borrowers. Pools with higher prepayment speeds lead to higher refi settings or higher turnover settings. Traders hated it. They called it s self-knobbing model. I thought it great for the brief while I was there.

      Anyhow Gregg was very smart but not very well adjusted I thought. He had an exceptional pallor in the days before sparkly vampires made pale cool! Jeremy was quite a decent guy and far more personable. Gregg later retired and did consulting work for them. I’d bet Jeremy knows his whereabouts.

      I saw nothing wrong in doing MBS prepayment modelling on wall St. Sure as heck beat trying to do the same in academia (this is where wall st quants are far better than academics). For me, it was far more productive than doing nonquasiconvex variational problems for phase transitions in materials where the math was cool but hard and the applications were just plain BORING. On wall st typically there are far too many interesting problems to have time to study. My experience with academia was too many people solving too few relatively uninspired problems.

      But nowadays academics can’t get enough of wall st. Quant finance programs are everywhere. And they fill all sorts of quant funds with recent grads who know virtually nothing about finance. It seems to keep math and cs programs funded though.

      • Rahul says:

        My mental model of modern Wall St., at least the parts that quants inhabit, is of one smart set of guys setting up very hard puzzles for another smart set of guys to solve with high stakes for the winner. Is that a bad model?

    • Andrew says:

      Nick:

      You ask why I said “That’s too bad” after learning that Gregg is a vice president at Goldman Sachs.

      Perhaps the best analogy is, what if you knew someone who was one of the top high school basketball prospects in the country, but instead of ending up in the NBA he made a career as a sports hustler, using trick bets to make money off suckers. This is not a perfect analogy, as this sort of sports betting is illegal, I guess, but the point is that it’s sad to see a great talent that is being used neither in its pure form or for scientific progress or the public good.

      • Rahul says:

        Andrew:

        Do you see all / most Investment Banking firms as hustlers? Or are you singling out Goldman Sachs, in particular?

      • Anon says:

        How about a different analogy. A beautiful girl is a cheerleader. However, she doesn’t want to be a cheerleader. She becomes something else, maybe she doesn’t stay as beautiful as she would have been if she stuck with cheerleading. Some other cheerleader tells her she used to be so much prettier when she was cheerleading.

        • Andrew says:

          Anon:

          Your analogy almost works but not quite.

          Here was my analogy:

          math olympiad = high school basketball star
          pro mathematician = NBA player
          Goldman Sachs VP = sports hustler

          Yours went like this:

          math olympiad = cheerleader
          pro mathematician = cheerleader
          Goldman Sachs VP = something else

          To make your analogy work, you need something like this:

          math olympiad = cheerleader
          pro mathematician = model
          Goldman Sachs VP = some career that involves using one’s beauty to hustle people.

      • BSM says:

        I’ll offer the disclaimer up front that I work in finance (though not at GS or any firm remotely like it).

        Andrew, I don’t know you, but through your writings I respect you as a smart person. I therefore find it disappointing that you cast such aspersions on a career path which you seemingly know vanishingly little about. As Rahul points out, you’ve seemingly equated anyone who applies their quantitative skill to finance to a hustler; on the contrary, there is a research to suggest that application of mathematics to finance has stabilized capital markets and resulted in lower costs to all participants [1][2].

        I also find it interesting that you bring up the “public good” and “scientific progress” while at the same time giving an implicit pass to web developers and software engineers who may or may not be working on things that you (or others) would deem valuable on those metrics. (To be clear, I think both are fine career choices.)

        I’d respectfully urge you to reconsider your position on applying mathematical talent to finance. Personally, I find it to be an immensely intellectually challenging field, and beyond that, a required role in any sufficiently advanced society that relies on capital markets.

        1. Angel, James and Harris, Lawrence and Spatt, Chester S. (2010). Equity Trading in the 21st Century. Marshall School of Business Working Paper No. FBE 09-10.
        2. Hendershott, T., & Riordan, R. (2009). Algorithmic trading and information. Manuscript, University of California, Berkeley.

        • Andrew says:

          BSM:

          Thanks for the info. I’m just giving my general impression, certainly not trying offer some sort of authoritative position on the matter.

          • Rahul says:

            I find hard to judge whether working on Siegel modular forms is better for the “public good” than, say, working out the details of a corporate merger.

            • Phil says:

              I think of working on Wall Street as something akin to being a professional gambler with your investors’ money. I have almost all of my money invested on Wall Street myself; I don’t have a moral/ethical problem with that as a career (or with being a regular ol’ professional gambler, either), and in fact I want the people who are involved with my investments to be smart enough and dedicated enough to do a good job at it.

              But if some smart guy said he likes to spend all day every day in a casino trying to make as much money as possible, I’d feel like he’s wasting his talents and to some extent wasting his life, and I feel the same way about people who spend all of their time trying to squeeze a few extra dollars out of everybody else who is trying to squeeze a few extra dollars. I don’t consider it unethical or immoral — certainly not inherently so — but I don’t see it as very productive. There’s plenty of unproductive academic work, there are smart people in ill-conceived startups, there are good musicians in bad rock bands, etc., etc., it’s not like talent isn’t being squandered in all kinds of ways. In all of those cases I think it’s a pity that those people don’t choose other (I think better) ways to use their talents.

              • Rahul says:

                Your gambler analogy is unfair I think. It only applies to a small part of what finance guys do. e.g. Mergers & Acquisitions, underwriting a stock issue, securities research, risk management, risk hedging instruments. These don’t seem very much like gambling to me.

      • Jonathan (another one) says:

        Suppose the NBA played before 100 fans. Indeed, suppose there were only a few thousand people in the entire world who could appreciate a basketball game. On the other hand, suppose sports hustlers, in the course of making a buck for themselves, ended up dissuading people from making foolish gambles altogether which, in their absence, would have been a substantial part of the economy.

        These analogies aren’t perfect either, but “market orientation and reward” is not synonymous with socially malign, nor is ascetic purity synonymous with the highest possible calling.

        • Andrew says:

          Jonathan:

          From what I’ve read about Goldman Sachs, I’m not so sure about your implication that their job is to “dissuade people from making foolish gambles.” But I appreciate you taking my analogy seriously, and that’s a good point about the 100 fans. Perhaps my NBA analogy missed the point, in that it’s not that I’d want Gregg Patruno to be proving theorems—he’s no Noam, after all! It’s just that, as Phil put it earlier in the thread, Goldman Sachs doesn’t have the best reputation. So I think the “sports hustlers” analogy captures what I’m getting at.

          • Jonathan (another one) says:

            Thanks, but you missed part of my point. I never said that dissuading people from making foolish gambles was their job. I said it was something that doing their job ended up causing. This was a hamhanded allusion to the single most famous quote in all of economics: “He intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was not part of his intention”

            • Andrew says:

              Jonathan:

              Let me preface this by saying that I know nothing about Goldman Sachs beyond what I’ve read in the news. But, conditional on that level of knowledge, my impression was that Goldman Sachs made money by ripping people off in various ways, essentially by luring people into foolish gambles.

              To say that ripping people off is a way of “dissuading people from making foolish gambles” . . . that doesn’t seem quite accurate! Any “dissuading” worth its salt would dissuade people before they make the gamble. If you say that they’re taking people’s money and then the people have no more money left to gamble, that hardly seems like a useful form of dissuasion.

          • Nadia says:

            Cathy O’Neil’s writing also inspires questions about whether it is honorable.

            http://mathbabe.org/2011/06/24/working-with-larry-summers-part-2/

      • Anonymous says:

        Who owns your mortgage? Who manages your assets? Do you own stocks, bonds? Who assists the companies who fill your Ivy League ivory tower liberal douche house with expensive consumer goods with their M&A? Have you ever been involved with running a business that needed financing? Are you a math genius too stupid to ever have learned the role of banks in modern society?

        • Andrew says:

          Anon:

          Your rudeness and profanity seems a bit over the top as a response to my reaction of “Too bad” that someone became a VP at Goldman Sachs), and of course I’ve never described myself as a math genius (as should be clear from the above post), nor do I know what a “douche house” is (but it sounds kinda gross to me).

          In any case, let me assure you that I think banks play a useful role in society. But it is also my impression that financial organizations (including Goldman Sachs!) have done a lot of harm too. You can say the same of universities, and you can feel free to say “Too bad” that I went to teach college instead of, say, working for a bank.

          If that’s your opinion, fine. Having such an opinion wouldn’t make you “stupid” or “butthurt” etc., it would just imply that you have a different sense of the world than I do. Which is fine. No need for the insults, dude.

      • Nick says:

        +1 metaphor

        I see where you are coming from, but I guess I’m a little more forgiving of people’s individual choices. Your analogy got me thinking of another metaphor that might be apt – a great Shakespearean actor who becomes an action movie star. Sure the world is worse off for his choice, but it’s his gift, and his choice to make. It’s very easy for me to say: he should use his gifts for the good of the world, and live a life of quiet poverty instead of cashing in, but I’m not sure it’s appropriate for me to say that. Since I will never have that choice, I’m not really sure what I would do in his place. (As you say, put aside illegality and morality and assume that whatever he does at Goldman Sachs is both legal and ethical)

        • Andrew says:

          Nick:

          I have no idea what whether Gregg does at Goldman Sachs is both legal and ethical–but to the extent that Goldman Sachs is a criminal organization (as some have claimed), this is a problem. That is, I don’t want to put aside illegality and immorality!

          Also, I’m not asking anyone to live a life of quiet poverty. Given that I live a life of comfort, that would be a funny thing for me to ask of anyone!

    • Anonymous says:

      I don’t get all the commotion. Andrew apparently believes, as does most of the rest of the human race, that top math genius is better spent doing something of permanent worth instead of being some hyped up actuary. Does anyone really believe we’d be worse off if 90% of the geniuses who went into creating mortgage derivatives or whatever had instead spend their time building/inventing/creating something useful or discovering something of permanent value?

      P.s. I have an advance degree in finance and have worked in finance, so save the blather about almighty important finance is.

  2. JSE says:

    Oops, Noam corrects me — he wrote that paper in grad school, not in high school. My mistake.

  3. Leila Schneps says:

    I remember both Mike Larsen and Benji Fisher from undergraduate days at Harvard. Mike was really nice, and good friends with a guy called Carlos Simpson who, if he wasn’t an Olympiad champion, should have been. Both are amazing mathematicians now. Benji came as a freshman when I was a junior, and boy was he vain and pleased with himself. (Not so big, but yes to the ponytail.) I remember him prefacing some remark he made to me once with “Pardon my hubris”. Even though he was super-bright it was obvious to me already that he was heading for a fall if he expected so much from himself. I don’t know why he quit research but probably he felt he wasn’t up to his own expectations.

  4. numeric says:

    When I was young you had to prove Fermat’s last theorem before you would even be considered for the Olympiad team, after walking uphill four miles each way to school in the snow. You had it easy.

    • CroMagnon says:

      You had proofs? What a luxury! In my day, we had only interpretive dance to explain theorems, and had to bang rocks together for accompaniment! You couldn’t even be considered for the Olympiad team until you’d brought enough mastodon to feed everyone! Walking uphill in the snow? Pshaw! We spent hours every morning pushing on the south side of glaciers, to make them retreat faster.

  5. Clyde Schechter says:

    Well, when I was young, the Olympiad was too–and the US did not participate in it. I had the privilege to be part of my high school’s math team when we won the New York City championship. The team had 5 members and 3 alternates. Either from renewed personal contact or internet search, I know about the career paths 7 of us have taken. Although most of us planned on it at the time, none of the 7 became a professional mathematician, though our numbers do include an epidemiologist (me) and a statistician. The rest are lawyers, educators in non-mathematical fields, and doctors, and the treasurer of a synagogue. The one about whom I have no recent information published problems in the American Mathematical Monthly into the 1970’s, but then the trail goes cold. (But he’s not in the social security death index, so not too cold.)

    This is at least, metaphorically, and probably in some quantifiable way, regression to the mean over time, is it not?

    For my part, the sudden realization, while in graduate school, that I was not Fields medal material came as a very hard shock, one that took me 3 decades to fully get over. While, like Andrew, I learned there were other things I could do with my abilities, it was a very long time before I accepted that being something other than a pure mathematician was not a failed life.

    Now in my senior years, I look back on my career with enormous satisfaction, and wake up eager to get to work every morning. I love what I do, and I’m proud of it. But I do wonder: had the recognition come earlier, as it did for Andrew, would I have ended up where I am now (but having felt good about it all along), or would I have diverted into some entirely un-mathematical path (as I did, briefly before coming back as an epidemiologist).

  6. Chris G says:

    > …. I realized that (a) there were others who were better at math than I was, which led me gradually to the realization (b) that there were other things I could do.

    Item (a) is my first month of grad school in a nutshell. (Actually, substitute “math and physics” for “math” but you get the idea.) Humility lessons aren’t much fun but I think most people – myself at least – are better off for them. That stated, it took a while for me to come around to Item (b).

    • Rahul says:

      +1 My first month of grad school was like that too.

      Gradually, I decided that since I wasn’t smart enough to compete with the smart people I’d choose to work on stuff the smart people didn’t like to work on.

      • Moreno Klaus says:

        +1 … I had the same feeling while going through an econometrics programme: I am not economics/econometrics/statistician material!!! , I also feel kind of disapointed sometimes, but being in another (relatively easier or with relatively less competition) field in academia I do not think I lost that much…

        • Rahul says:

          Real smart people make interesting career choices. If we could magically reallocate some of the geniuses working on Siegel modular forms to better battery design my opinion is we’d be living in a better world.

          Some might say that genius in pure math does not translate to usefulness in applied research. Maybe. But many of the very people I’ve known I suspect would have sufficiently good aptitude for both. It was only a question of generating interest or motivation from another perspective (“greater human good”?)

          I’m not advocating Soviet style allocation of human capital but just saying that we sometimes have lost sight of what makes for an optimum allocation of talent to various areas. e.g. I feel there’s too many smart guys working on Quantum Computing & too many mediocre ones on, say, efficient ship engines.

    • pavetack says:

      For lesser mortals like me that realization came at Freshman Orientation – “oh, everyone else here was Valedictorian of their high school also”. The first big exam in a weedout was a similar dose of reality. Kids with 99th percentile SAT scores getting 50 out of 200 points begin to question their assumed superiority.

    • Martha says:

      Gosh, I realized in high school that there were others better at math than I was. Might have had something to do with being a girl in the 1950’s. Might also have had something to do with going to an unusually good high school. In some cases, might have had something to do with assuming others were better than they really were (probably connected to possible reason 1). But I naively kept doing what seemed like the next step that others were doing (not having an ultimate goal in mind) and found myself with a Ph.D. in math, and proved theorems in pure math for several years — till I stopped finding that satisfying (partly because increasingly the theorems I was interested in proving were really hard), so gradually turned to more socially worthwhile things like teaching teachers and statistics.

      • Rahul says:

        +1 for the ” assuming others were better than they really were” bit. Fighting this “impostor syndrome” can be a hard battle. I think it gets worse the smarter you are.

        The smartest people often seem to view their own abilities very harshly and negatively.

    • santaraxita says:

      Pretty much the same happened to me within the first few months of grad school. However, I decided to stick on (still few years from completion). Paradoxically, one of things that helped me was realizing that there were other things that I could do well.

      There was a very specific event that made me realize this. I have always had a side interest in cognitive science, so a friend referred me to a paper by one George Lakoff (who is evidently a big deal) called ‘The contemporary theory of metaphor’. It has over 4000 citation in google scholar (for comparison, Serre’s GAGA has ~800 and this is a landmark of modern mathematics). My first thoughts on reading that paper was it had to be some sort of an elaborate joke because I simply couldn’t believe the reasonably obvious things that it contained could constitute research – let alone a much cited one. But, there it was: not all things academia finds worthwhile need be difficult (a realization thats so obvious in hindsight). The experience had a profoundly therapeutic effect on me.

  7. Andrew, was this a joke (I can never tell with you, especially on the blog)? “Obviously the most talented math kid in the group (and thus, by implication, in the country).” That’s obviously nonsense!

    There are two huge flaws in this reasoning.

    1. Assuming math ability is something that has a total (rather than partial) ordering. To use an anology, it would be like concluding the person who’s best at basketball is the best athlete. Michael Jordan was really awesome at basketball, and while he was way better than most at baseball, he wasn’t good enough to play in the majors. How would he have done at football or hockey or gymnastics? Or long-distance running or swimming? Math ability’s like sports and comes in all sorts of flavors, with all sorts of advantages for training. I’d wager that sports “ability” has a non-diagonal covariance matrix over sports (and positions in that sport) and that many of the entries are negative (sumo wrestling and gymnastics, for instance). Math’s the same way.

    2. Assuming that someone who’s good at taking a test is good at the real thing. These competitive tests are all very specific tests of problem solving ability of a very narrow kind (I’ve never heard of the Math Olympiad, but assume it’s like the Putnam Competition given Andrew’s comment on Noam’s paper). Like grades in school and grades on standardized tests, the main thing they show is your ability to get good grades or score well on tests. The real world also forces you to choose good problems, focus, work with others, communicate, and get things done in the long run, not in a short closed-book test. I’d wager Andrew’s near the top of this latter business.

    For some background and personal anecdotes, here’s a link to the Putnam test for the first full year I was an undergrad:

    http://www.math.hawaii.edu/~dale/putnam/1982.pdf

    On the personal side, Michigan State had an awesome team, with my classmate Eric Carlson scoring in the top 5. Frank Sottille, another classmate (there weren’t many of us doing pure math at MSU), was also on the team, and MSU as a whole got an honorable mention. Frank’s a math professor at Texas A&M and Eric’s a physics prof at Wake Forest.

    I stood no more of a chance of getting on the Putnam team than I did getting on the football or basketball or hockey teams. I don’t think I could solve more than 1 problem per test given all week (but then I’m not claiming to be great at math of any kind — I’ve seen great at math and it ain’t me).

    On the personal side of varying ability across areas, on a pure problem-solving in a math undergrad degree basis, I was way better at discrete than continuous math. I aced algebra, combinatorics, set theory, logic, topology, computation theory, etc., but nearly got kicked out of my undergrad program I was so bad at 3D calc (and here I am, doing continuous stats — sort of a reverse Gelman, I suppose). The also tried to kick me out of high school honors math because I nearly failed geometry in 10th grade, only to go on to be at the top of my class in algebra and honors calc. But then of the 750 or so class size, not many had very good training either from parents (mainly in the auto industry) or teachers (could barely do calc themselves).

    • Andrew says:

      Bob:

      Intonation is notoriously difficult to convey in typed speech.

      In this case, I was not quite serious and not quite joking. My statement about talent was an expression of what I think most of us believed at the time.

      • Popeye says:

        +1. This post was an interesting trip down memory lane for me — I was in another iteration of MOSP, at a similar rank to Professor Gelman, and it is funny to recall the super-precise rankings that we all had in our heads back then. I think the career outcomes indicate that these rankings were not a perfect predictor of professional mathematical productivity, although obviously Noam Elkies is a super genius by any measure.

  8. Anonymous says:

    I used to think the intelligence of the upper end of the stats community made no difference. They were about as smart as smart people in any other subject. But over the years I’ve come to the opposite conclusion. The best statisticians just aren’t as anywhere near as capable as Bernoulli, Laplace, Maxwell, and Gibbs. Neyman for example comes across as a failed mathematician who found he could make a name for himself with some easy irrelevant proofs in statistics. If statistics had remained the plaything of first rate mathematical physicists of the old style rather than failed mathematicians and floundering biologists, it would be in vastly greater shape today.

    • In my opinion, the best statisticians were Laplace, Gauss, and Kolmogorov. I don’t think any of them were physicists, per se.

      I think it makes sense to separate probability theory (a mathematical subject) from statistics (an applied field). The application of probability theory to statistics problems in physics today is hardly something to brag about.

      Some physicists added some computation to stats in the 20th century (Metropolis and Ulam are credited with the fundamental breakthroughs of Monte Carlo methods, for example), but I don’t think they’ve added much to probability theory (though arguably differential geometry is going in the right direction, theory-wise). Maybe I missed something? Maybe all the work on stochastic processes, of which I know very little? Also, the non-parametric Bayes revolution’s pretty nifty—I don’t really know who to credit for that or what their backgrounds were.

      • Andrew says:

        Bob:

        I always thought Laplace was a physicist. Ulam considered himself a mathematician.

        • I never knew Laplace was a physicist, but then I haven’t done much physics! I should’ve looked at Wikipedia first. As to Ulam, he designed weapons of mass destruction; so whatever he considered himself, he’s most notably a weaponsmith.

          I think the history of science is peppered with mutual discovery and rediscovery. Attribution’s a very tricky business. It often goes to the best popularizer or best communicator (both of which I think of as laudable goals, by the way). I would highly recommend James Gleick’s book Genius, which is ostensibly a biography of Richard Feynman, but at a deeper level is a great case study in the the sociology of science and who gets credit for what. I think pretty much anything that’s ever been discovered that’s of import would’ve been discovered by someone else, usually sooner rather than later. So much of science is being in the right place at the right time, such as having the right math built up to do physics or vice versa.

          My own experience at the start of grad school was that I’d come up with a proof of a computational complexity or computability result that I didn’t know about, then someone would point out it had already been done. My undergrad pure math program was much tougher than grad school in computational linguistics. I imagine the world might be a better place if the Peter Principle weren’t such a strong force in human behavior. I constantly feel in over my head in stats, whereas I felt completely in control in computational linguistics. Of course, maybe that’s just the Dunning-Kruger effect, because I now know much better what I didn’t know then.

          • Martha says:

            +1 for “So much of science is being in the right place at the right time” — but it applies to a lot more than science.

          • Anonymous says:

            Don’t forget Maxwell and Gibbs in all this. While Laplace and Gauss were major original mathematicians outside of their work in physics, Maxwell and Gibbs were much more of what we’d think of as full time Physicists. So how much mileage did they get out of using probabilities?

            Well, Maxwell derived a probability distribution from pure thought, with no fitting to data, which gave a highly unintuitive prediction about viscosity. Everyone thought it must be wrong, but when they did the experiment it turned out Maxwell’s prediction was right.

            For Gibbs, virtually every successful physical prediction made in statistical mechanics, of which there are very many, used Gibb’s methods.

            How many big time statisticians alive today have had anything even approaching that level of bottom line success in science using probabilities?

      • Anonymous says:

        Gauss and Laplace were definitely considered mathematical physicists in the style of Newton and made huge monumental contributions to physics. You’d be hard pressed to find any major result attached to kolmogorov that wasn’t actually done by physicist much earlier.

        • So who should I be attributing the model theory of probabilty to? That’s not a sarcastic question, I’m geniuinely curious about the history.

          Kolmogorov complexity, by the way, which I think of Kolmogorov’s greatest contribution, was independently discovered by three different people (Ray Solomonoff and Gregory Chaitin being the other two). And Solomonoff was a physicist, at least insofar as he did an M.S. studying with Fermi (he didn’t even have a Ph.D., for all those degree snobs out there). The Wikipedia’s dead wrong, though, in attributing probabilistic languages to Solomonoff; Shannon beat him by a decade if the Wikipedia’s right about when Solomonoff (perhaps independently) developed them.

          • Anonymous says:

            Mathematical statistician’s learned many things through Kolmogorov so they call it “Kolmogorov whatever”. It’s like we call call our numbers Arabic numerals because we learned them from the Arabs even though they originated in India. That’s not a knock on Kolmogorov any more than it’s a knock on Fibonocci for introducing the Hindu system to Europe in the 1200’s. Here’s three working hypothesis about the origins of statistics:

            (1) Everything with “Kolmogorov” in the name was done much earlier by some physicist.
            (2) Every pedestrian statistical idea in the social sciences was done by some psychologist at least half a century ago.
            (3) Your best stat related idea appears in one of I. J. Good’s 1000+ papers somewhere.

            Advances in computing power hide just how remarkably stagnant Statistics is in truth.

            • Keith O'Rourke says:

              > how remarkably stagnant Statistics
              Certainly the impression I got when I looked into the history of meta-analysis (originally known as combination of observations)…

            • hjk says:

              I think there is a reasonable argument that Kolmogorov was a mathematical physicist in a sense.

              V.I. Arnold was a student of Kolmogorov (and strongly influenced by his views). He said:

              “Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.”

              Arnold also said:

              “Kolmogorov – Poincaré – Gauss – Euler – Newton, are only five lives separating us from the source of our science.”

              As mentioned above, Kolmogorov did work on turbulence for example. Some of the best work to follow on this topic is also by people either supervised or directly influenced by him. My impression is that there is a rich tradition of Russian mathematics intimately tied to physics.

              • hjk says:

                Also relevant to the Olympiad thing and Kolmogorov. Arnold said (see: http://www.ams.org/notices/201203/rtx120300378p.pdf)

                “When 90-year-old Hadamard was telling A. N. Kolmogorov about his participation in Concours Général (roughly corresponding to our Olympiads), he was still very excited: Hadamard won only the second prize, while the student who had won the first prize also became a mathematician, but a much weaker one! Some Olympiad winners later achieve nothing, and many outstanding mathematicians had no success in Olympiads at all.

                Mathematicians differ dramatically by their time scale: some are very good tackling 15-minute problems, some are good with the problems that require an hour, a day, a week, the problems that take a month, a year, decades of thinking. A. N. Kolmogorov considered his “ceiling” to be two weeks of concentrated thinking.

                Success in an Olympiad largely depends on one’s sprinter qualities, whereas serious mathematical research requires long distance endurance (B.N. Delaunay used to say,“A good theorem takes not 5 hours, as in an Olympiad, but 5,000 hours”). There are contraindications to becoming a research mathematician. The main one is lack of love of mathematics.

                But mathematical talents can be very diverse: geometrical and intuitive, algebraic and computational, logical and deductive, natural scientific and inductive. And all kinds are useful. It seems to me that one’s difficulties with the multiplication table or a formal definition of half-plane should not obstruct one’s way to mathematics. An extremely important condition for serious mathematical research is good health.”

              • Martha says:

                Nice quote from Arnold.

                Reminds me of once when a colleague sent me a paper with my name on it as co-author. I protested, saying all I had done was answer a couple of questions she had asked me. She replied that those were two things she didn’t think she would ever have been able to get herself, but there were also two steps that she was pretty sure I would never have been able to get, and the rest was just standard stuff that either of us could easily have done.

      • Anonymous says:

        Also metropolis was a physicist but his contribution to Monte Carlo was small and would have (and was) done by many others.

    • Chris G says:

      > If statistics had remained the plaything of first rate mathematical physicists of the old style rather than failed mathematicians and floundering biologists, it would be in vastly greater shape today.

      Damn, that’s cold.

  9. anonymous says:

    Leonid Fridman https://www.linkedin.com/in/fridman “Entrepreneur, mad scientist.”

  10. Jack Brennen says:

    Hi, Andrew!

    Yeah, I went to Carnegie-Mellon, studied Electrical & Computer Engineering. Been a full-time embedded software guy since 1988. Lived in San Diego since 2005.

    I’ve been in touch with Noam Elkies and Ken Zeger in recent history. Ken’s daughter and my daughter both attended the San Diego Math Circle for a while, and Ken and I would see each other quite often, but it’s been a few years. I took Noam out for dinner a few years ago when he was in San Diego, and interact with him online quite a bit.

    I saw Brian Hunt about 12 years or so, when I visited the Montgomery County math team’s practice at Blair HS.

    My best man at my wedding worked with Gregg and Jeremy on Wall Street for a very short time in the ’90s.

    I’m connected with Leonid Fridman on LinkedIn. He was my roommate in ’80, but other than connecting with him there, no interaction.

    • Andrew says:

      Hi, Jack! I’m impressed that you are in touch with all these people. Tell them all hi from me!

    • Jim Ferry says:

      Hi Jack. I came across these reminiscences of the 1980 MOP, thinking there would be little overlap with the one year I was there: 1984. That year I had a roommate who showed up late because of car trouble, then left shortly thereafter because he broke his arm, if I remember right. Anyway, I hope the car and arm didn’t cause you too much grief. It sounds like I missed out on the opportunity to hear the insider’s history of the MOP though.

      BTW, a college friend’s older brother lived in the same dorm with Miller Puckette at MIT. I’m told he had a habit of riding on top of elevators and opening the hatch to annoy the passengers in various ways.

      • Jack Brennen says:

        Jim:

        Just saw this reply.

        I honestly don’t remember much about the 1984 MOP, apart from a few names and some vague recollections of playing Diplomacy. I showed up late and missed the Team Selection test, so I was basically out of contention to make the IMO team. It seems like it was about 3 or 4 days after I arrived that I lost my footing running down the stairs to the mess hall one day and landed awkwardly on the side of my left foot. Fractured the outside bone in my foot. If it had been my arm, I’d have stuck around — but getting around the Naval Academy on crutches was rather difficult and with no chance to make the team, I talked with Dr. Klamkin and told him I would be heading home to recuperate. As I recall, I made the decision to leave very quickly — my mother had come to Annapolis to take me to see the orthopedist (she only lived about 1.5 hours away by car) and I ended up just leaving that day and going home with her.

  11. Jack Brennen says:

    Also, the other assistant (other than Mike Larsen) was Miller Puckette.

    He has his own Wikipedia page, you can get his information there.

    Another 1980 participant was Nadine Kowalsky; she died of leukemia in 1996.

  12. Dougin Walker says:

    Hey Guys!

    I do exist as well and my name still does make me easy to find. In fact back in the early years of searches (when Alta Vista was the search engine) one of the guys at my office said one of his favorite things is that you could just put Dougin into a search and all your hits were me.

    I certainly was not at the top end of the group in terms of anything mathematical (and I think Noam was the top by pretty much any standard you choose), but I suppose I may have ended up being the best triathlete of the group. I also did stick with the math competitions through college, I took the Putnam and was on the team that tied for first one year at Wash U (I think I was 15th overall).

    And your guess is right, Watermark is a hedge fund, or rather the manager of a hedge fund. I don’t feel like getting into a long discussion about Wall Street, but I don’t see any reason why someone who applies his skills in whatever field he chooses is better or worse than someone who does something like pure math, ASSUMING HE BEHAVES ETHICALLY AND DOES NOT MAKE MONEY BY FRAUD OR FORCE. Making money by taking a spread in the process of matching up lenders and borrowers (which is effectively what anyone in fixed income does) is no better or worse than making money by making bread and selling it for more than it cost to make it. Which is not to say there is not a lot of unethical behavior on wall street (there definitely is), or even specifically at Goldman Sachs (no comment). But I don’t see criticizing someone’s choice of career because they aren’t in some theoretical field. There may be beauty in those things for the few that understand them, but as far as contributing to society, I am happy with what the business owner is doing (with my ethical caveats). Now it may be that there is effectively no unethical behavior in higher theoretical math, so it is perhaps comforting to think that the top brains are doing things where their brains are not being used to steal money from anyone.

    Sorry about that.

    Anyway, I think there were two girls from the Boston area in our year, but I have no memory of names. I also think they wrote a poem about the summer there called The MOPossey, but I would guess I lost my copy long ago – it was written on paper. I think it ended with Greitzer saying to turn the lights out. And somewhere in there Klamkin offered a fribble to anyone who solved some impossible problem.

    • Andrew says:

      Hi, Dougin. Indeed, I have a copy of that poem. I was thinking of scanning and posting it, but when I reread it, it didn’t seem so interesting!

      • Andrew says:

        P.S. As I wrote in an earlier comment, no need to take that hedge fund comment so seriously. It was just my impression. Somebody else might well express disappointment that I became a statistician (indeed, my boss at Bell Labs had that reaction when I told him I was switching from physics to statistics). Goldman Sachs has a bit of a reputation. I think that’s fair enough: they get the big bucks, they can live with the rep.

        • Anonymous says:

          You should use that supposedly brilliant but clearly closed minded bigoted brain of yours to actually understand what the finance industry does.

          • Dougin Walker says:

            What kind of pathetic comment is that? And Anonymous, no less. There is plenty of bad behavior to go around on Wall Street. Sorry I continued this discussion, Andrew.

            • Andrew says:

              Dougin:

              Yes, the point of the post was just to reflect upon the olympiad program, 35 years later. It’s a bit disappointing that the discussion got distracted by comments along the lines of “liberal douche butthurt.” Such is the internet, I suppose. Most of our threads work out much better than this!

  13. Benji Fisher says:

    Are you recalling the 1980 or 1981 MOP? In 1981, the team was Gregg, Noam, Richard Stong, Jeremy, Brian, David, Jim Roche, and me. I do not recall David being there in 1980. Probably this page is more trustworthy than my recollection: https://www.imo-official.org/country_individual_r.aspx?code=USA

    Nadine Kowalski was a high-school freshman in 1980-81. I think I would have remembered if she had been at the MOP with me in 1981 or if she had been on the team in 1984, so if she did attend the MOP I think it would have been in 1982 and/or 1983. She was valedictorian at Bronx Science, smashing the record for GPA, and had a position at the IAS until her untimely death.

    David Yuen’s claim to fame was solving the Rubik’s Cube in 3 hours. That and getting a Ph. D. from Princeton in 3 years.

    David Wolland, not Wollen, was there, but I do not recall which year(s).

    As for myself: ponytail, yes; big, no. I was a little under 5′ 9″, but with short legs and a long torso you might guess 6′ if you see me sitting down. Sorry not to follow up in ’96.

    • Andrew says:

      Hi, Benji. It was definitely 1980. There was no international olympiad that year, so they were able to include in the program some promising younger kids such as me (of course, I didn’t live up to that promise, but that wasn’t Greitzer’s fault!). The kids I remember from 1980 were definitely there that year; I know because I didn’t do it any other years!

      It took me about 3 weeks to solve the Rubik’s cube on my first try, a few days on my second try, . . . then I could get it down to about 2 minutes. But a few years ago I tried and I couldn’t remember how to do it at all! I had a vague memory of my edge-flipping and corner-twisting operators but I couldn’t remember the details.

  14. Rahul says:

    Isn’t this sort of argument futile about who was a physicist versus statistician and who exactly to credit with a certain, now well established idea?

    • Anonymous says:

      Yes, if Statistics has a solid foundation and is resulting in good science. Or better yet, good science in proportion to the money, IQ points, and man-hours put into it. Does that sound even remotely like Statistics currently to you?

      If not, then rather than listen to yet more evidence-free self serving wishful thinking claims about what good science looks like, maybe it’s worth looking at how it was done the last time people were doing good science.

      The fact is people like Maxwell and Gibbs got far superior results with probability distributions than anything I see today, and did so in ways that pretty well completely contradict what everyone today says is good scientific modeling methodology**. That despite the fact that they were modeling aggregate macro-systems just like a political scientist, economist, medical doctor, or ecologist. It’s enough to make me at least lament that physicists of the caliber of Bernoulli, Laplace, Maxwell, and Gibbs left the field to failed mathematicians and floundering biologists.

      **they didn’t collect a bunch of data and fit a model. Indeed, the distributions they did use aren’t practically “verifiable” in a frequentist sense over human time scales, or even geological time scales.

      • Rahul says:

        How do you feel about the Physics of today versus the Physics of 150 years ago? Or Chemistry or Math?

        Are you saying Stat is particularly bad today or are you nostalgic about most areas in general?

        • Anonymous says:

          Just to keep it related to statistics, Physics is pretty bad today. There are some physicists in Astronomy doing good statistics (as far as that goes) and other one-offs doing something in stats, but for the most part if you grab a physicist and tell them to start doing statistics (usually in a social science setting of some kind) the results are occasionally adequate by todays low standards, but mostly horrendous.

          All they’d do is quickly try to get spun up on what Statisticians are doing, which is a confusing muddle of insanity at best, and then try to apply it without the long experience which tempers some of the more egregious stupidity in statistics.

          Most physicists by the way have no exposure to statics and aren’t going to understand vocabulary like “p-value”. At a deeper level, the founders of quantum mechanics from Einstein onwards seem to have never encountered Bayesian Statistics.

          Physicists changed from a 150 years ago in at least two ways. First they stopped trying to be natural philosophers in the mold of Newton, Euler, Gauss, Cauchy, Maxwell, Planck, Poincare and all the rest. Today top physicists want to be the next Einstein (i.e. a colorful rebel who overthrows established theories with unintuitive neo-mysticism). And second, they aren’t involved with statistics the way key physicists in the 19th century often were.

          I believe that lack of involvement was a major disaster for both fields, neither of which has really earned their paychecks in a long long time.

          • Rahul says:

            So, if I’m reading you correctly, academic research in general, field agnostically has gone downhill over the last 150 years? Any area you think is better off today than 150 years ago? Math? Chemistry?

            • Anonymous says:

              I don’t know about chemistry. Chemists have told me some fields have become stale such as organic chemistry.

              Progress in math is fundamentally different from the sciences. Although some sub-fields have become stale (at least temporarily) there are others doing great and, unlike the social sciences, most things published in math journals are true and permanent contributions. In the long run math is getting along just fine.

              • Keith O'Rourke says:

                That’s not really fair, in the math replication of results is almost costless (anyone with requisite skills gets all the data and only needs pencil a paper and some time to replicate the result). Most authors don’t think of publishing results without themselves or colleagues making a few replication attempts. So errors seldom get to print or they are almost always caught immediately and corrected (like Andrew’s proof error he talks about).

                Make it impossible for mathematicians to check their work, force delay of years before anyone can attempt to replicate it (even in their imagination) but force tentative acceptance of it in others’ work until then. You probably would end up with a similar literature.

              • Anonymous says:

                I admit that it’s right but unfair.

    • hjk says:

      While aspects of the debates can be quite tiresome I think the history and perspectives of those involved is actually pretty interesting. Especially those like Kolmogorov, and yes the ‘natural philosophers’ of the past (I can think of at least one modern academic who stil holds that title formally), who weren’t so constrained by disciplinary boundaries. While polemical (and pretty much just repeating Jaynes) there is a fair point that many disciplines actually shield people from valuable ideas and methods relevant to their problems instead of sharpening their skills.

      It’s also a very sociological point. Perhaps we should look to that literature, anon?

      • Anonymous says:

        I don’t need to read the sociology literature. No one needs to read the sociology literature; not even sociologists. I got something better to read. Max Planck. Planck is interesting for a number of reasons. Although not mentioned by Jaynes much, he marked the transition from the older the newer era we’ve been talking about. And in the black body radiation problem he did hugely successful science using probability distributions.

        He’s also of interest because he tells us what probability distributions meant to him. He had too because what he was doing was radical. Most people think statistical mechanics was closely tied conceptually to mechanics. For the black body radiation problem, Planck wanted to apply it to the Electromagnetic fields which conceptually, physically, and mathematically are very different from gases of particles. So he had to make clear just how universal the “statistical” part of statistical mechanics really was.

        So what does he say his probability distributions mean? Well he does not claim they represent the frequency of given states in any sense whatsoever. Not even approximately, or in the long run, ergodically or anything. Rather he says what he’s doing will work if the one physical state that actually exists is one of the “common” states described by the high probability region of the distribution. The high probability region is determined according to him by other “partial” measurements of the physical state. “Partial” in the sense that the state isn’t determined uniquely by the measurement.

        I would word it by saying the (partial) measurements give a bubble of uncertainty around the true state which is modeled by an (objective) Bayesian probability distribution, not a frequency distribution. He even does an clean maximum entropy construction to get a needed probability distribution. It took at least another 50 years for statisticians to realize that every major common distribution they had been using can be derived the same way.

        Although Planck spells this out so clearly and intuitively its hard to imagine anyone not understanding it, the fact is that 100 years later, these ideas are still so radical it’s well nigh impossible to get a statistician to understand them, let alone their implications. Planck’s 100+ year old text on black body radiation is an improvement over any book on the foundations of statistics that I’ve seen written by a statistician.

        Which all ties back to my original thesis: statistics paid a huge price when first rate mathematical physicists left the subject to failed mathematicians and floundering biologists.

      • Anonymous says:

        P.s. Jaynes thought Physicists leaving the field to Biologists was a problem because they worked on different kinds of statistical problems, which caused biology oriented researchers to think their type of problems were more universal than they are and hence gave them a warped view of the subject. Keeping the physicists around would thus have given a fuller understanding of the big picture in statistics.

        I’ve come to the conclusion a bigger problem is that the failed mathematicians and biologists just didn’t have the talent needed, and by the time that talent did come along Frequentism was dug in so deep they wasted all their potential on irrelevant proofs about irrelevant limits of irrelevant estimators.

        • Also Anonymous says:

          Is it possible that the main paradigms of statistical inference only work in problems like those in physics, where one really understands mechanistically the general context of the data being analyzed?

          • Anonymous says:

            In the short run there is some truth to that, in the long run there’s no reason statistics is inherently less effective in the social sciences than in physics.

            The situation is a bit like two different people looking at the same algebraic equation, but each with different knowns and each solving for different unknowns. Each is going to see that identical equation differently. Something like that is happening here.

            Specifically, when a physicist looks a given state of a gas, they know how the macrovariables Energy and Volume are related to the microstate. They have an explicit functional form for the relations and an explicit representation for the state.

            In contrast, in most of the social sciences the relationship between the macro variables of the system being studied and the microstate are unknown. To get around this social scientists do the following trick. Basically they try to “learn” that unknown structure by observing lots and lots of different values for the macrovariables.

            An example might be a economist looking at the macrovariables Unemployment (U) and Interest rates (I). They watch the system (economy) evolve through different microstates and observe various pairs (U_i, I_i). Based on that historical data they want to “learn” the structure of how they’re connected to each other through the microstate. That’s what an econometrician is doing when they use (U_i, I_i) to create a statistical model.

            Note physicists don’t have to do this because they know how they’re connect from the beginning.

            What the economist is doing can in principle work, but theres a hidden assumption in all this. The assumption is that the economy will evolve in just the right way that the so that it passes through a “representative” set of microstates. That is basically never true, certainty not over human lifetimes, and without it holding the structure you “learn” through the model created from (U_i, I_i) isn’t going to work predictively and isn’t going to replicate.

            If that were the only way statistics can be applied to the social sciences then I guess they’re permanently screwed. Fortunately, it’s not the only way to apply statistics to the social sciences. So there’s long term hope.

        • santaraxita says:

          Okay. Maybe I should know better than to ask this, but, what do you think of Gromov’s ideas on probability? He gave a talk at IHES last year. (for non-mathematicians: Gromov belongs to that rather small list of mathematicians which includes Poincare and Hilbert)

      • Rahul says:

        Some aspects of this debate have the flavor of “Is my favorite comic superhero stronger than your favorite.”

        • Nick Cox says:

          Rahul: I never knew that was ever a question.

          The debates for this start with a confident assertion “My favorite comic superhero is stronger because {he|she|it} really understands {Bayesian statistics|quantum mechanics|string theory|postmodernwhateverism} properly.”

          But come to think of it, all my experience here is based on watching _Big Bang Theory_.

        • Anonymous says:

          Rahul, I gave specific examples of actual reasoning used by real physicists that produced probability based science demonstratively far more successful than anything you’ll see today, even though it was done 100-200 years ago.

          I stand by my claims that (1) the reality of highly successful uses of prob and stat is very different from statistician’s current rhetoric, and (2) the 100 year lead in the scientific uses of probability opened up by physicists from Laplace to Planck was pissed away in the 20th century by failed mathematicians like Neyman.

          The result of (2) is that in the year 2015 “statistics based science” is very nearly a synonym for “pseudoscience”.

          • Anonymous says:

            Nor incidentally do I think it’s controversial that Neyman was a big fish in a small pond. He described what motivated his career choices and much like Nash moving from math to econ, he deliberately moved to a smaller pond when he switched from math to stats.

            I’m sure he was a genius. All math professors are geniuses. But if he had to compete directly with Hilbert and Feynman he would have been one of the many tens of thousands of run-of-the-mill math professors no one has ever heard of.

            He didn’t want that. That’s great for him, but was it great for statistics? I don’t see how.

            • Popeye says:

              Why is it smart to look for a “great man” explanation of why “statistics based science” is terrible? I can’t think of an issue that’s so clearly a systemic problem instead of a function of the career choices of one particular individual.

              • Anonymous says:

                If the foundations of statistics were squared away, then Neyman would have been more than sufficient. But they weren’t and they aren’t and it needs more than failed math profs to set it straight.

              • Popeye says:

                So what? Did Neyman somehow prevent supergenius physicists from doing statistics correctly?

                I mean, it’s great that you have this worldview of Wonderful Supergeniuses versus Moronic Third-Rate Failures, I can totally see how it provides you with both moral drama and moral clarity in what might otherwise be a completely humdrum life, but I’m honestly not getting any value out of it.

              • Anonymous says:

                Popeye,

                As stated, physicists voluntarily abandoned the field long before Neyman for reasons I don’t know.

                The reasons Andrew gave in the post for moving from math/phys to stat are similar to the reasons Neyman gave for moving from math to stat. There are many others who made the same progression for similar reasons. Back before circa 1900 or so, that was NOT what brought people to statistics.

                That year 1900 also seems to be about the turning point where statics lost it’s way. Given how screwed up statistics is currently, I find it helpful to think back to when statistics took that “wrong turn at Albuquerque”. If you don’t then ignore it.

              • Andrew says:

                Popeye:

                This discussion is interesting because Anonymous is demonstrating the sort of unidimensional attitude that plagued the math competition world the idea that there is one dimension of mathematical ability and that’s all that matters. Anonymous’s view of mathematical ability is more sophisticated than that of the olympiad world—he is interested in solving real scientific problems, not artificial problem sets—but I think he’s still mired in the idea that the ability that matters is unidimensional. But I don’t think that’s so. Just to take a few examples: Galton, Fisher, Box, Efron, and Rubin have all made important contributions to statistics, even though none of them would qualify as a top-tier mathematician or physicist. Yes, Gauss and Laplace were world-class physicists who also made huge contributions to statistics, but that doesn’t mean that physics intuition can necessarily be translated into statistical intuition. Gauss and Laplace happened to have ideas in both areas.

                By saying all this, I’m not saying that math = physics = statistics. Some subjects are more technically challenging than others. But researchers don’t work on their own, and the statisticians listed above have made important contributions that I haven’t seen coming from various physicists who do statistics. I do think there are concepts that are inherently statistical, not just spinoffs of math.

                To put it another way, there’s a reason I write these papers about philosophy and there’s a reason I go into a lot of detail about methods in my applied papers. It’s not just turning the crank, and by facing our difficulties squarely I believe we can make progress. It is through anomalies that we learn.

              • Martha says:

                An addendum to Andrew’s comment: Gauss was first and foremost a mathematician — many mathematicians consider him the best mathematician ever. But he was so incredibly intelligent that he was able to make strong contributions to physics and statistics as well. People like him don’t come along very often.

              • Rahul says:

                @anon:

                Is it possible that “( Planck like) physicists abandoned the field” simply because there weren’t as many interesting problems in the field any more? You can only discover stat mech so many times.

                In a larger sense, I’m wondering why diminishing marginal returns cannot be a more reasonable explaination for statistical stagnation (if any) than incompetant practitioners?

              • Anonymous says:

                Actually Andrew I started out strongly favoring the hypothesis the top in every field were about equal intelligence. The view that there are real differences and that those differences had a big impact on statistics grew grudgingly as the evidence to that affect built up.

                Secondly, whether these kinds of things make a difference depends on the nature of the subject. Some subjects don’t have hard conceptual difficulties to get over, so it all matters less. Statistics is not one of those fortunate subjects.

                Third, the dimension statistics seems to lack more than anything isn’t raw intelligence or quickness of the math Olympian kind. If I had to put a word to it, I would call it “wisdom”. The greats, it seems to me, didn’t excel because they could get clever solutions easier. Maybe sometimes that happened, but mostly they excelled because they could get clever solutions at least as well as anyone else and because they had to the wisdom to work on more fruitful lines of inquiry.

                Larry Wasserman (or Feller) for example strikes me as someone with all the requisite cleverness and none of the wisdom. Maybe he would perform just as well on a math Olympiad as Laplace, but the fact is Wasserman spends most of his theoretical time proving irrelevant theorems and Laplace spent most of his time proving relevant ones. I don’t think that’s accidental and I do believe it reflects a significant change in the kind of person who concerns themselves with statistics from the 19th to the 20th century.

                Forth, being a big contributer to modern statistics like Fisher, Box, Efron, Rubin, is only an honor if modern statics is doing well. But modern statistics is not doing do well on any metric other than (A) ability to scam grant money and (B) number of papers written. To everyone not wedded to statistics professionally, it’s a disaster of epic proportions. There’s always a best researcher, but that doesn’t mean the best physicists in 840 AD are on par with the best physicists in 1940 AD.

              • Andrew says:

                Anon:

                Fisher, Box, Efron, and Rubin did a lot more than “scam grant money” and write papers. If you really think that, that’s your privilege, but then reading this blog might not be the best use of your time!

              • Anonymous says:

                Andrew,

                When the Titanic sank the ship’s band supposedly performed on deck. No doubt there was one musician more talented than the rest who contributed more to the performance than anyone else. No one can take that glory away from him. But the ship still sank.

                Statistics hit an iceburg. Efron and Rubin and all the rest turned in a virtuoso performance with their research careers. No one can take that glory away from them, but the only thing anyone will remember is that Statistics sank. I take that back: they might remember that unlike the Titanic’s band, Efron and all the rest could have given statistics a different fate.

                Statistics really did sink. In the face of clear evidence most statistics based research is false, and that any field which relies on classical statics as it’s main tool has stagnated since before most of us were born, our most popular response is “preregistration”. Preregistration rests on the idea that the import of a statistical calculation hinges crucially on what day the question was asked. That’s where we are in 2015. Arguably it’s a step backwards from 1815.

                Scientists 200 years from now are going to look back on us and think we’re as crazy as “doctors” who tried to the cure the plague with incense, witch burnings, and blood letting. I’m not exaggerating.

  15. Rahul says:

    If you look at the initial decades of say aviation or computer algorithms or organic chemistry I think the rate of super important ideas was far higer than the most recent decades of these field.

    Might that explain away many of the pessimistic observations made by @Anon?

    i.e. You cannot attribute the relative decline in the dynamism / excitement / vibracy of a field in 1900 vs now to quality of practitioners alone.

    • hjk says:

      Chicken or egg? Talent supply in different areas seems very complicated. Both within academia and between academia and the rest of the world. I mean look at the wall street vs academia issues in this thread.

      And, accurate or not, it’s widely observed (if only in ‘private’ or off the record conversation) that it’s often harder to convince e.g. the ‘best’ mathematics students to take up applied instead of pure math, or to convince the ‘best’ students of physics/math to pursue engineering or statistics rather than physics or mathematics.

      Similarly for getting ‘good’ grad students in those areas or outside of the top whatever ranked universities.

      While I dislike it, academics – from students to professors – are constantly rating and ranking everyone else (again, accurately or not) and bemoaning the relative lack of talent in this or that area or university. It’s actually pretty tiring to be around.

      So I’m not saying that the problems in one area are actually any less difficult or important than those in another. Or that one can’t be better at stats than someone who is better at maths or any other ‘multidimensional’ qualifications of intelligence (I mean look at Ed Witten’s history!).

      But the people involved sure seem to act like there is an undersupply of the truly talented and that the areas deemed currently most exciting or whatever tend to get a bigger share of the ‘best’ talent.

      So if an area is deemed to be less fertile for big exciting new discoveries, doesn’t it follow that they may have a lower supply of talent flowing into it?

      I mean, new discoveries and aptitude for specific problems aren’t so predictable so it may be advantageous to not follow the crowd etc, but still.

      PS
      It’s a different conversation but I also feel like the current university system massively squanders the talent allocation even within these constraints. I’m thinking of the paper/citation/funding incentives, length/style of contracts, exploitation of phds/postdocs by senior faculty, lack of development or support structures, even without mentioning all of the many more ‘self-inflicted’ problems ranging from discrimination to favouritism etc etc.

      It’s not just people like anon saying it – all the time I hear senior academics (including those who made fundamental discoveries or founded new areas) saying academia is a mess and that they probably wouldn’t pursue it if they were to start now. I mean, most of them rarely actually take any concrete steps to improve the situation, and are typically much more complicit than they realise, but like good middle class folk they certainly feel ‘sympathy’ for those in less fortunate positions.

  16. Mark Bowron says:

    Came across this page searching for an email address for Zachary Franco. Not sure “medical researcher” suffices to describe someone who gets a math Ph.D. at Berkeley then later goes on to get an M.D. at Pittsburgh. Who does that?! Sort of reminds me of the main character in Michael Lewis’s “The Big Short.”

    Several in your list are famous enough that I immediately recognized their name, but the only one I’ve ever met is Murray Klamkin: I visited him and his wife Irene at their home in Edmonton in October 2002. He was in his 80s then and passed away a few years later.

    Zachary Franco is currently listed as a collaborating editor of the American Mathematical Monthly’s Problems and Solutions section. I’ll soon be emailing all of them (that I can get addresses for) to announce the recent upload of my free pdf of MathPro Press’s “Index to Mathematical Problems 1975-1979” and give an update on the current state of math problem indexing.

    While I’m here, I might as well pass along links to the 75-79 pdf. It is freely available at the following four URLs, the first two of which require (free) site subscriptions to download the pdf:

    https://www.researchgate.net/publication/267164498_Index_to_Mathematical_Problems_1975-1979
    https://www.academia.edu/37249387/Index_to_Mathematical_Problems_1975-1979
    http://www.mathematrucker.com/problems_1975-1979.pdf
    http://www.stanleyrabinowitz.com/bibliography/problems_1975-1979.pdf

    If I may say, it’s a really nice pdf. Includes lots of internal hyperlinks.

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