It seems to me like plain regression effect. Also your argument makes no sense because most or virtually all of those people had all that standard math curriculum too. You'll find that "is a professor" is very well correlated with "wants to be a professor" among that set.

Edit: Pascal's triangle??? Sorry but if you give some mopper Pascal's triangle they'll have already heard about it or invented it themself.

The question was where are the people now who did well in Math Olympiad in middle and high school.

Good grief: Lots of people in middle and high school get pushed into math competitions such as the Math Olympiad but don't go on to be math majors in college and grad school.

My point is that the middle and high school Math Olympiad directions basically don't help people be good at math later in life or good at anything later in life. So, bingo, presto, people who were good at Math Olympiad show little or no good effect later in life.

But if want to study some math that has a chance of having a positive effect later in life, then follow what I outlined.

Net, sadly, Math Olympiad and other middle and high school math competitions are unpromising for doing any good later in life. Such middle and high school efforts would, could, and should be helpful but not by pursuing recreational math, etc.

Seems totally obvious to me -- sorry you don't agree.

Difference of opinion is what makes horse races.

You proposed enrichment materials such as number theory puzzles and other recreational mathematics. That's already what the math olympiad contests consist of.

> Good grief: Lots of people in middle and high school get pushed into math competitions such as the Math Olympiad but don't go on to be math majors in college and grad school.

This isn't true at all. Most people in high end math contests are just smart and do no preparation. They just accidentally scored high on the AMC. A lot do some practice for fun, because the contests are fun. Possible exceptions are a handful of people at Philips Exeter++ and maybe Thomas Jefferson High School, I'm not familiar with that dynamic. Contests like the ARML are oriented around making local friends more than anything. At the most local levels it's like, some high school teachers will corral their students into doing a contest at the nearby college one afternoon.

For example some friends of mine in the Philadelphia area thought it would be neat to enter the Harvard/MIT math contest (which is way more fun and difficult than the Temple School of Actuarial Sciences contest or Drexel's). It was the kids telling their parents they were doing this, and deciding to practice for it. I think the same happened with a group of students in Albany.

++and they were recruited after performing well on middle and elementary school math contests that parents are completely unaware of.

> You proposed enrichment materials such as number theory puzzles and other recreational mathematics. That's already what the math olympiad contests consist of.

No, I did just the opposite: I said that others proposed such materials; I did not propose them but criticized such proposals. Again, for a high school student to be pushed into seeing lots of tricky things in Pascal's triangle, attacking number theory exercises, doing recreational math won't do the students much good in later life -- so as in the title of this thread, we won't expect to see many such students successful in math later in life. Instead, the efforts there in middle and high school will rarely come to anything.

Helping middle and high school students do better in math than what is in just the usual courses would, could, and should be doable and done, but the path is not recreational math, etc. but, instead, as I outlined, just proceeding with the main line of math education -- rush through the high school math of algebra and geometry, likely also trig, and then get a college calculus book and dig in.

E.g., the high school math teachers I had were eager to say that we "were not ready for calculus". Nonsense. It was the teachers who didn't know calculus.

I very much would have rushed ahead had I had some good guidance. Eventually I knew enough to rush ahead when I was a college freshman: I'd had four years of math, grades 9-12, at a relatively good high school but for my college freshman year went to a state school that was cheap and close enough for me to walk there and back. They wouldn't let me take calculus but pushed me into a course beneath what I'd already done in high school. So a girlfriend told me when the tests were, and I showed up for those. The teacher said I was the best math student he'd ever had -- in no very real sense was I his student!

I asked to be permitted to start calculus but was turned down. So I got a good book and dug in. I did well (in high school mostly I'd been teaching myself from the books and sleeping in class anyway). For my sophomore year I went to a good college with an excellent college math department, started on their sophomore calculus, from the same text used at Harvard, and did well.

I'm hot on this stuff about what middle and high schools do to good math students: My eighth grade arithmetic teacher gave me a D and took me aside one on one and fervently urged me never to take anymore math. In some significant ways, my father was good at education and just laughed.

That eighth grade teacher didn't have a clue about what math was: For the actual math, I'd done well in her class. What I did poorly on was multiplying two four digit numbers, and the reasons were (1) my handwriting was sloppy (common for boys), so sloppy I didn't get the columns lined up and then added wrong for the final answers, (2) my clerical ability was just awful (common for boys), (3) I understood the ideas right away but never worked on the clerical skills to get correct answers, (4) my parents never urged me to work to get right answers (my father had some high-end views of education and just wanted me to learn, especially out of interest, and didn't care at all about grades, and I did learn).

But in the ninth grade, the teacher saw right away that I was his best student, and he sent me to the state math tournament. In the summer after the 11th grade I was sent to an NSF math and physics program.

So, net, I was a good math student, was very interested in math, was eager to race ahead, but the school did a poor job helping me.

There is a little more to the story: When the SATs came back, I was called out of study hall to get my scores, from the same teacher I'd had in the sixth grade. Nice woman. Sweet. Ignorant! She, along with most of the rest of the teachers, thought I was a dunce. So, she read me the Verbal SAT score -- 538. She said "Very good". BS! It sucked! But she was sweet. She may have thought that I would get 250 or some such!

Then she looked at my Math SAT and hesitated. She looked worried. Confused. She said "There must be something wrong." Then she said the score was 752 and "That's uh, uh, very good.". Darned right it was good. But she was correct that there "was something wrong" and had been for 4, 6, 12 long, wasteful, painful years.

I had had no idea what the SATs were about and had made no effort to prepare. But I finished the Math SAT early, checked my answers, and still had 15 minutes. I'd very much like to know what the CEEB thought I'd missed. Maybe they scaled the scores and didn't give anything much higher.

My Math SAT was second out of a grad class of about 180, which is about right from the statistics, 2.5 sigma above the mean of 500. The #1 guy beat me by a few points. The best student in the grad class was a little behind me -- he went to MIT and burned out his fuses in his freshman year.

I was a good math student, had been eager to rush ahead in math, physics, and chemistry, but I'd had poor guidance. So, I'm hot on grades 6-12 continuing to give good math students bad advice. So, here I say, mostly, for the actual Math Olympiad competitions, waste of time. To do well with math, just go down the main road to a ugrad math major as I outlined. Simple. And to heck with, say, learning to play Nim in Courant and Robbins, What is Mathematics, about Pascal's triangle, etc.

Yes, I'd learned about Pascal's triangle. So when I was in grad school and had been pushed into a silly ugrad class in probability, the prof went all arrogant and emphasized that due to the factorials it can take some really long precision arithmetic to calculate even relatively ordinary binomial coefficients. BS: Just work in from one side of Pascal's triangle and never see a factorial. Indeed, I raised my hand and stated so in the lecture. I'd long since written software do to just that.

Next he did a sloppy job explaining the glory of the central limit theorem, and I dropped the course. But I was taking and grading in the Neveu measure theory level course at the same time, my first official course in probability, and did well. E.g., I was the only student who showed that there are no countably infinite sigma algebras.

The schools who want to send their good math students to Math Olympiads are likely also doing a poor job helping their students. Then, as in the title of this thread, in later life we mostly won't see much effect from such high school efforts.

Net, my hot button is that the schools in grades 6-12 don't know enough math to do well helping their students eager to race ahead in math.

> > Good grief: Lots of people in middle and high school get pushed into math competitions such as the Math Olympiad but don't go on to be math majors in college and grad school.

> This isn't true at all.

Of course it's true: E.g., you gave some examples of how high school teachers try to get some of their students into such competitions, i.e., "push" the students. That's lots of students, and in college math is not a very popular major. So, lots of middle and high school students in math competitions don't major in math in college, just as I claimed.

For more, you mentioned some activities at the college level; I was addressing the high school level. Sure, college students who do well on the Putnam are likely college math majors who are taking math very seriously. Again, I was addressing high school.

Why are you acting as if these contests do a poor job training kids? The OP never suggested that -- in fact, it seems nearly all of them grew up to be very successful. Your stance seems to be in direct contradiction of the evidence offered in the original article.

The article implied that the Math Olympiad work didn't much result in significant results 30 years later from the work in math for the contest.

You are correct that the OP didn't directly say that the "training" of the "kids" was poor.

My view of such high school math competitions is that they waste the time and effort of the students and, otherwise, with good guidance, there would be significant results from the efforts 30 years later. In this sense, then the training was a "poor job".

But the OP did not say that directly -- that's my interpretation, heavily from what I saw used as efforts to have some high school students do better in math -- the efforts were a waste of time for all concerned and because the people directing the efforts didn't know enough math.

I'm still not following. In what way are there not significant results from the kids in the contest? They almost all seemed to have had significant success.

> For more, you mentioned some activities at the college level

I didn't mention any activities at the college level. It's clear you have no idea what you're taking about.

> I didn't mention any activities at the college level.

Instead, you wrote:

> Harvard/MIT math contest (which is way more fun and difficult than the Temple School of Actuarial Sciences contest or Drexel's)

Sounds like college.

> It's clear you have no idea what you're taking about.

What's now fully clear is just that you are angry about something and want to attack me personally, not my writing or thinking but just me, personally. Not good.

Nope, not college. You don't know anything about high school math contests or the motivations of students that do them, or anything about that world at all, and amid irrelevant stories about your life you're just pretending that you do.

To clarify: I think you don't know what kinds of problems they ask, what their contest format is like, what students learn and practice when preparing for them, how it affects students' interest in research mathematics and how it develops their abilities there. Why do I think that? Because instead of talking about the USAMO or ARML or the NSA's mail-in contest or anything specific about whether these contests actually harm or distract students' attention from what you think they should be doing, instead of rebutting the well-known "calculus trap" opinion or showing that you have any awareness of it, instead of showing knowledge of what students do to prepare for these contests, you've talked in abstractions, and there is no glue tying the words you are saying to objective reality.

I think you wrote this post in good faith, but I have no idea what you are saying.

> I have no idea what you are saying.

Sorry not to be clear.

My view of efforts in grades 8-12 or so to have students do well in math competitions, e.g., the Math Olympiad, is that those efforts are not promising for helping those students do well with math or anything else later in life. Instead, mostly the efforts are just wasteful for all concerned.

The main reason for the waste is that the people, usually the high school math teachers, running the programs don't know enough math to give good direction to the students that might want to do especially well in math, well enough that 30 years later we would commonly see significant positive effects from that direction and the resulting efforts of the students.

So, the direction that is commonly given is to have the students study relatively useless material, say, recreational math, some puzzle problems, every tricky thing they can see in Pascal's triangle (the binomial coefficients, that is, the coefficients of (x + y)^n with one row for each value of positive integer n), and there are a lot of such tricky things.

But, right, the binomial coefficients have some nice properties, some of which are good to know, and an early volume of D. Knuth's The Art of Computer Programming has some good coverage. But, net, mostly to heck with the triangle and, if insist, then read the relevant sections of Knuth -- but even there Knuth has a good reason for presenting that material, and what's important is the applications Knuth makes, so, really, just read on in Knuth.

So, instead, students who do want to do better in math, and I did, should just proceed along the usual topics, texts, etc. for a ugrad math major. In particular, as a first goal, ASAP get a good college calculus text, get the basic prerequisites, and dig in.

By the way, the time I looked at the AP calculus materials I didn't like them and concluded that the people who wrote the materials didn't understand calculus very well. Instead, just get a good college calculus text.

For the rest I mentioned, about have to have a relatively applied ugrad math major to understand: So, would need to know some linear programming, network flows, optimization, integer programming, something about the question of P versus NP, and more.

For Lagrangian relaxation, that's a bit tricky and specialized and not commonly well known even among college math profs. I did give an outline in

https://news.ycombinator.com/item?id=8919311

but it's not really easy reading. But it's a cute topic with some a good intuitive views, a bit amazing in some ways, and at times shockingly powerful.

E.g., the guy who first did the many worlds interpretation of quantum mechanics, a Ph.D. physics student of J. Wheeler at Princeton, an expert in relativity theory, was H. Everett, and at one time he had a nice applied math shop near DC doing resource allocation for the US DoD using a first, simple version of Lagrangian relaxation. What I outlined in

https://news.ycombinator.com/item?id=8919311

is more general and powerful and makes some cute use of some convexity -- that there is convexity there is also surprising but true and powerful and, with the right setup, easy to prove.

OK, thanks. Much clearer.

Don't know why you are downvoted by so many. But I think you provided a good comment here. Upvoted.

What kind of odd browser do you use that results in all of your comments end up with manual line breaks after 30 characters?

Browser? Firefox 35.0.1 with some updates.

When I view my posts at HN, my browser flows the lines ignoring my end of line indications except does honor blank lines.

I thought that such text flowing was arranged by some internal HN server logic.

No, there is definitely something wrong with your config since no one else has this problem.