1. Zugzwang
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    13 Jul '18 22:201 edit
    The 2018 International Mathematical Olympiad was held in Romania
    (site of the first IMO) and has just finished. The results were rather surprising:

    In the team competition:
    1) USA
    2) Russia
    3) China
    4) Ukraine
    5) Thailand
    6) Taiwan
    7) Republic of Korea
    8) Singapore
    9) Poland
    10) Indonesia
    11) Australia
    12) UK
    13) Japan
    13) Serbia
    15) Hungary
    16) Canada
    17) Italy
    18) Kazahkstan
    19) Iran
    20) Vietnam

    Many east European teams have strong mathematical traditions, but in
    recent years they usually have finished behind east Asian teams while
    still finishing ahead of west European teams. In 2018 (did the location help?),
    several east European teams (Russia, Ukraine, Poland, etc.) did unusually well.

    India did unusually well in 28th (having finished 52nd in 2017).
    Major Western countries such as Germany and France finished in
    31st and 33rd respectively.

    Nearly all of the top Western teams were dominated by students of
    Asian heritage. Each team has six members.
    1) USA (4 Chinese, 2 Indians)
    11) Australia (5 Chinese, 1 white)
    16) Canada (5 Chinese, 1 apparent East Asian of unclear ethnicity)

    The UK team apparently had 4 whites, 1 Indian, and 1 Chinese.
    The Indian and the Chinese were the two highest scoring members.

    In the Debates forum, there has been much racist trolling, with a (white) troll
    implying that mathematics tests are racist (because blacks score lower on average)
    and that the only reason that Asians score higher on average is having
    unfair advantages (for which all Asians presumably should be penalized).

    Among the top individual results, two students had perfect scores
    1) Agnijo Banerjee (UK)
    1) James Lin (USA)
    3) Mihir Anand Singhal (USA)
    4) Marat Abdrakhmanov (Russia) (He seems to be from a Muslim minority.)

    The results show that mathematics is open to everyone and that students from many
    diverse cultures can excel, though students from some cultures seem more likely to excel.
    People who know mathematics know that what I write is right.
  2. Subscribersonhouse
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    14 Jul '18 06:371 edit
    Originally posted by @duchess64
    The 2018 International Mathematical Olympiad was held in Romania
    (site of the first IMO) and has just finished. The results were rather surprising:

    In the team competition:
    1) USA
    2) Russia
    3) China
    4) Ukraine
    5) Thailand
    6) Taiwan
    7) Republic of Korea
    8) Singapore
    9) Poland
    10) Indonesia
    11) Australia
    12) UK
    13) Japan
    13) Serbia
    1 ...[text shortened]... ultures seem more likely to excel.
    People who know mathematics know that what I write is right.
    And no aspersions on you but I see Iran only one up from last place Vietnam. Why didn't Vietnam do better since they are clearly Asian?
    I guess it's a good thing you managed to get out of Iran.
    What educational level do you consider the math questions? Would they be on a Masters level? I would think the problems would be above BA levels but how much higher? Or am I totally wrong about that?

    How many math categories were represented by the questions?
    How well would the average maths Phd have done on those questions? would you expect those Phd's to also ace the problems?
  3. SubscriberWOLFE63
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    14 Jul '18 08:22
    Awesome!!!

    Looks like the smartest Chinese and Indians came to America. I wonder why?

    Strange though, India didn't make this list. I guess they couldn't get away from work at the Call Centers.
  4. Germany
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    14 Jul '18 08:381 edit
    Originally posted by @duchess64

    The results show that mathematics is open to everyone and that students from many
    diverse cultures can excel, though students from some cultures seem more likely to excel.
    People who know mathematics know that what I write is right.
    You neglect an important cultural aspect, relating to how likely people are to be interested in competing in the Olympiad. For example, I went to a MIT-level university that had more open places than applicants; my application was a formality. I was never under pressure to compete with other students or engage in extracurricular activities (such as these sort of competitions) in order to distinguish myself from other students. Hence, in Dutch culture these kind of competitions simply aren't as popular. So these results should not (only) be interpreted as a gauge of the level of mathematics education or the likelihood that someone from a certain "culture" is interested in mathematics.
  5. SubscriberWOLFE63
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    14 Jul '18 12:23
    Originally posted by @kazetnagorra
    You neglect an important cultural aspect, relating to how likely people are to be interested in competing in the Olympiad. For example, I went to a MIT-level university that had more open places than applicants; my application was a formality. I was never under pressure to compete with other students or engage in extracurricular activities (such as the ...[text shortened]... education or the likelihood that someone from a certain "culture" is interested in mathematics.
    True, self-respecting "MIT-level grads" would never be seen wading in the shallows of these insignificant forums.

    Before boasting of alleged grad-school math prowess, please provide specific qualifying credentials. Otherwise, your opinion will be given the consideration and seriousness normally reserved for a profit-driven trade school.
  6. Germany
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    14 Jul '18 12:38
    Originally posted by @wolfe63
    True, self-respecting "MIT-level grads" would never be seen wading in the shallows of these insignificant forums.

    Before boasting of alleged grad-school math prowess, please provide specific qualifying credentials. Otherwise, your opinion will be given the consideration and seriousness normally reserved for a profit-driven trade school.
    My bad - I must've taken a wrong turn at the intersection between insignificant and significant forums.

    I could tell you that I am an academic with a PhD in theoretical quantum physics. Or that could be made up in order to impress some senile Americans. One can never be sure these days.
  7. SubscriberWOLFE63
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    14 Jul '18 13:20
    Originally posted by @kazetnagorra
    My bad - I must've taken a wrong turn at the intersection between insignificant and significant forums.

    I could tell you that I am an academic with a PhD in theoretical quantum physics. Or that could be made up in order to impress some senile Americans. One can never be sure these days.
    Touche' on both counts!
    I'm American and I'm impressed. πŸ™‚
  8. Zugzwang
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    14 Jul '18 18:463 edits
    Originally posted by @sonhouse
    And no aspersions on you but I see Iran only one up from last place Vietnam.
    Why didn't Vietnam do better since they are clearly Asian?
    I guess it's a good thing you managed to get out of Iran.
    What educational level do you consider the math questions? Would they be on a Masters level? I would think the problems would be above BA levels but how much ...[text shortened]... e maths Phd have done on those questions? would you expect those Phd's to also ace the problems?
    "I see Iran only one up from *last place* Vietnam ..."
    --Sonhouse

    In fact, Tanzania finished in last place of the 107 teams participating.
    Given that the IMO results were NOT completely available yesterday in a readily
    accessible form, I did not feel like digging up and posting a list of 107 countries.

    In 2018, Iran finished 19th and Vietnam finished 20th.
    In 2017, Iran finished 5th and Vietnam finished 3rd.
    Both Iran and Vietnam have strong traditions in mathematics.
    An Iranian (woman) and a Vietnamese have won Fields Medals.

    "Why didn't Vietnam do better since they are clearly Asian?"
    --Sonhouse

    Iran's also Asian. Israel (another Asian country) finished 26th (better than 32nd in 2017).
    Asia's a continent with extremely diverse societies who have diverse traditions in mathematics.
    In 2017, Vietnam finished 3rd, ahead of the USA (with only one non-Asian member).

    "I guess it's a good thing you managed to get out of Iran."
    --Sonhouse

    Maryam Mirzakhani, the first woman and only Iranian to win a Fields Medal, died one year ago (14 July 2017).
    She presumably would be dismayed, though not surprised, by the ignorant trolling here.
    In Tehran, she attended (before university) schools for exceptionally gifted girls.

    "She obtained her BSc in mathematics in 1999 from the Sharif University of Technology.
    She then went to the United States for graduate work, earning her Ph.D. in 2004 from Harvard University."
    --Wikipedia

    Iran does NOT attempt to stop people from leaving to study, to work, or to live.

    By the way, the top student on Ukraine's team (which surprisingly finished 4th) is named
    Nhok Tkhai Shon Nho (of east Asian heritage).

    "Or am I totally wrong about that? "
    --Sonhouse

    Yes. IMO problems are NOT comparable to normal problems in academic examinations.
    All IMO participants are secondary (high) school students. No knowledge of calculus is required.

    "How well would the average maths Phd have done on those questions?"
    --Sonhouse

    Who's an 'average maths PhD' ? IMO problems are NOT comparable to normal academic problems.
    The IMO always has at least one problem designed to be easy in order to give almost
    everyone a realistic hope of avoiding a zero score. Apart from that, the 'average maths
    Phd' would struggle on most IMO problems.

    Doing well on the IMO is NOT a linear thing of accumulating mathematical knowledge.
    It's supposed to emphasize insight and ingenuity over memorizing advanced mathematics.

    Sonhouse may download the 2018 IMO problems in English (or many other languages)
    and try them for himself. (I am not available to answer any questions about them.)
  9. Zugzwang
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    14 Jul '18 19:132 edits
    Originally posted by @wolfe63
    Awesome!!!

    Looks like the smartest Chinese and Indians came to America. I wonder why?

    Strange though, India didn't make this list. I guess they couldn't get away from work at the Call Centers.
    In its last 30 times (China boycotted in 1998) at the IMOs, China has won 19 gold medals,
    8 silver medals, and 2 bronze medals, clearly the best team performance of all countries.
    In contrast, India never has done very well, with its best finish (twice) in 7th place.

    There's not a big correlation between a country's population size and success at the IMO.
    Singapore (which has a much admired school system) routinely far surpasses India at the IMOs.

    "Looks like the smartest Chinese and Indians came to America."
    --Wolfe63

    FALSE. The top ethnic Chinese students represent several countries.
    Out of the top 25 individuals, 11 (44 % ) apparently were ethnic Chinese.
    Only 3 of these 11 students represented the USA.
    China (3), Taiwan (3), USA (3), Singapore (1), Australia (1)

    Individual Rank (often with tied scores), Name (in Western order), Country
    1) James Lin (USA)
    4) Shih-Yu Wang (Taiwan)
    6) Jung-Tao Cheng (Taiwan)
    9) Yiyi Chen (China)
    10) Zexuan Ouyang (China)
    10) Vincent Huang (USA)
    12) Guowen Zhang (Australia)
    12) Yixiao Li (China)
    19) Yu Peng Ng (Singapore)
    19) Andrew Gu (USA)
    24) Wei-Ping Huang (Taiwan)

    Only 2 (8% ) of the top 25 individuals apparently were of Indian heritage, yet
    Agnijo Banerjee (UK) finished 1st (tied) and Mihir Anand Singhal (USA) finished 3rd.

    "I wonder why?"
    --Wolfe63

    Ignorance (at best) quickly leads Wolfe63 to jump to wrong conclusions.
  10. Zugzwang
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    14 Jul '18 19:302 edits
    Originally posted by @kazetnagorra
    You neglect an important cultural aspect, relating to how likely people are to be interested in competing in the Olympiad. For example, I went to a MIT-level university that had more open places than applicants; my application was a formality. I was never under pressure to compete with other students or engage in extracurricular activities (such as the ...[text shortened]... education or the likelihood that someone from a certain "culture" is interested in mathematics.
    "The results show that mathematics is open to everyone and that students from many
    diverse cultures can excel, though students from some cultures seem more likely to excel."
    --Duchess64

    I wrote that "students from some cultures seem more likely to excel."
    KazetNagorra agrees that Dutch students seem less likely to excel.

    I did NOT write anything about WHY "students from some cultures seem more likely to excel".
    KazetNagorra apparently criticizes me by making unwarranted assumptions about what I think about why.

    Historically speaking, the IMOs began in Communist eastern Europe and were more promoted there.
    I believe that's one reason why poorer eastern European countries tend to do better
    than richer western European countries at the IMOs. Some western European teams
    have disproportionately many immigrants from east Asia or east Europe.
    At the 2018 IMO, the Dutch team had Thomas Chen (Chinese) and Szabi Buzogány (Hungarian).

    "I went to a MIT-level university ..."
    --KazetNagorra

    One of my uncles attended MIT (the real thing), where he was about one year away from
    earning a PhD in electrical engineering when he accepted a job offer from Hewlett-Packard.
    So he moved to California and forgot about finishing his PhD. He never had any interest
    in Olympiad-type problems. He's competent but not particularly good in mathematics.
    He's also very 'Americanized', rather anti-intellectual, valuing money over brains.

    "...likelihood that someone from a certain "culture" is interested in mathematics..."
    --KazetNagorra

    KazetNagorra misunderstands what I wrote.
    I refer to the likelihood of people being interested in the mathematical problem-solving
    of Olympiad-type problems. Believe it or not, there are people (such as those too old
    to be eligible for IMOs) who are interested in recreational mathematical problem-solving
    even when they know that they never can get rewarded with gold, silver, or bronze medals.

    My general point is that the Olympiads and mathematics in general are inclusive and
    welcome people from every cultural background. It's true that people who grow up in
    some places may be disadvantaged (as I was, learning chiefly on my own) compared
    to people in other places. But mathematics, as a whole, tends to be refreshingly free
    (albeit perhaps not completely) of hateful biases that thrive in so many other fields.
  11. Subscribersonhouse
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    14 Jul '18 19:451 edit
    Originally posted by @duchess64
    "I see Iran only one up from *last place* Vietnam ..."
    --Sonhouse

    In fact, Tanzania finished in last place of the 107 teams participating.
    Given that the IMO results were NOT completely available yesterday in a readily
    accessible form, I did not feel like digging up and posting a list of 107 countries.

    In 2018, Iran finished 19th and Vietnam fi ...[text shortened]... languages)
    and try them for himself. (I am not available to answer any questions about them.)
    Thanks for answering that, I know I would MAYBE solve the very first one, but that would be itπŸ™‚
    So who are the people making up the problems? Are they fields metal winners or some such?
  12. Zugzwang
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    14 Jul '18 19:502 edits
    Originally posted by @sonhouse
    Thanks for answering that, I know I would MAYBE solve the very first one, but that would be itπŸ™‚
    So who are the people making up the problems? Are they fields metal winners or some such?
    Here's the first problem from the first IMO (in 1959 Romania).
    It's extremely easy, easier than every other IMO problem of which I know.
    (I could solve it at first sight, within a few seconds.)
    I can post a solution (not rewriting Principia Mathematica as DeepThought may expect) later.

    1959 IMO Problem 1:
    Prove that the fraction (21n+4) / (14n+3) is irreducible for every natural number n:
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    14 Jul '18 20:12
    Originally posted by @duchess64
    Here's the first problem from the first IMO (in 1959 Romania).
    It's extremely easy, easier than every other IMO problem of which I know.
    (I could solve it at first sight, within a few seconds.)
    I can post a solution (not rewriting Principia Mathematica as DeepThought may expect) later.

    1959 IMO Problem 1:
    Prove that the fraction (21n+4) / (14n+3) is irreducible for every natural number n:
    I would guess it's something to do with common factors. 21n/14n where n is a natural number will always have common factors 7 and n. However, 4 and 3 have no common factors other than 1, which doesn't count for the purposes of simplification. I think that adding 4 and 3 to the numerator and denominator respectively of a fraction that is already simplifiable means that it can no longer be simplified, as 4 and 3 have no common factor.
  14. Zugzwang
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    14 Jul '18 20:27
    Originally posted by @ashiitaka
    I would guess it's something to do with common factors. 21n/14n where n is a natural number will always have common factors 7 and n. However, 4 and 3 have no common factors other than 1, which doesn't count for the purposes of simplification. I think that adding 4 and 3 to the numerator and denominator respectively of a fractio ...[text shortened]... lready simplifiable means that it can no longer be simplified, as 4 and 3 have no common factor.
    1959 IMO Problem 1:
    Prove that the fraction (21n+4) / (14n+3) is irreducible for every natural number n:

    3(14n + 3) - 2 (21n + 4) = 1
    So the greatest common divisor of (21n + 4) and (14n + 3) is 1.
    Therefore, the fraction (21n+4) / (14n+3) is irreducible.

    Note to DeepThought:
    The IMO judges don't expect a proof from scratch of every basic theorem in number theory.

    With that trivial problem (charity) out of the way, I would proceed to the real test.
  15. Zugzwang
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    14 Jul '18 20:32
    Originally posted by @ashiitaka
    I would guess it's something to do with common factors. 21n/14n where n is a natural number will always have common factors 7 and n. However, 4 and 3 have no common factors other than 1, which doesn't count for the purposes of simplification. I think that adding 4 and 3 to the numerator and denominator respectively of a fractio ...[text shortened]... lready simplifiable means that it can no longer be simplified, as 4 and 3 have no common factor.
    In 2018, South Africa finished 62nd (60th in 2017) out of 107 teams.

    Here are the names of its members:
    Ralph McDougall, Tariq Mowzer, Timothy Schlesinger, Emile Tredoux, Emil van der Walt, Adri Wessels.

    Emile Tredoux won an individual bronze medal.
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