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For the criterion of the title, i.e., "where are they now?", from the article and more, sadly, it sounds like a Math Olympiad is not a very good way to do well

by graycat 12y ago

For the criterion of the title, i.e., "where are they now?", from the article and more, sadly, it sounds like a Math Olympiad is not a very good way to do well on the criterion. Why not very good? Because it looks like the students are given what, for the criterion, is poor direction and use of time and effort. E.g., when I look at my education in math and its use in applications, most of the best of the education had nothing to do with anything like a contest, especially a contest in the early and mid teens. Instead, the best education was well selected, well presented material into the best work in math, e.g., via the best authors -- Birkhoff, Halmos, Rudin, Royden, Neveu, Tukey, Kelley, Suppes, Simmons, etc. Or, my impression of encouraging kids in their early and mid teens to pursue math is to give them some enrichment material such as Pascal's triangle, some number theory, various puzzle problems, a lot of recreational math, etc. Why? Because mostly the people directing the efforts and selecting the materials are not very well educated in math. In simple terms, to have kids do well on the criterion in the title is just to have the kids proceed along the main line -- get through the standard high school material in algebra and geometry, with some applications to high school chemistry and physics, and then move on to a fairly standard college major in math -- calculus, modern algebra, linear algebra, advanced calculus, ordinary differential equations, advanced calculus for applications, partial differential equations, point set topology, measure theory, functional analysis, probability, statistics, stochastic processes, etc. Then that background promises to be good for a good answer 30 years later for the criterion "where are they now"?

psychometry 12y ago
What kind of odd browser do you use that results in all of your comments end up with manual line breaks after 30 characters?
- graycat 12y ago
  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.
  - psychometry 12y ago
    No, there is definitely something wrong with your config since no one else has this problem.
LiweiZ 12y ago
Don't know why you are downvoted by so many. But I think you provided a good comment here. Upvoted.
SamReidHughes 12y ago
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.
- graycat 12y ago
  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.
  - SamReidHughes 12y ago
    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.
kenjackson 12y ago
I think you wrote this post in good faith, but I have no idea what you are saying.
- graycat 12y ago
  > 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 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 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.

by graycat 12y ago

psychometry 12y ago

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

graycat 12y ago
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.
- psychometry 12y ago
  No, there is definitely something wrong with your config since no one else has this problem.

LiweiZ 12y ago

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

SamReidHughes 12y ago

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.

graycat 12y ago
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.
- SamReidHughes 12y ago
  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.

kenjackson 12y ago

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

graycat 12y ago
> 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 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 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.