
USA tops International Math Olympiad for first time in 21 years - tokenadult
https://www.washingtonpost.com/news/morning-mix/wp/2015/07/17/winning-formula-usa-tops-international-math-olympiad-for-first-time-in-21-years/
======
kafkaesque
This is definitely off-topic, but have people taken a look at Po-Shen Loh's
company expii.com? He's the coach for the US team.

It says:

 _Expii is a collection of free, interactive, explanations written by people
from around the world_

Interesting!

~~~
expii
Thanks for noticing! :) Indeed, I've been working with a certain segment of
the population through my roles as the national coach of the USA IMO team and
as a math professor at Carnegie Mellon University.

However, after being appointed to the national coach position, I realized that
the USA would not be able to consistently deliver top results unless we lifted
our mathematical level across a broad base. It seemed that technology could
provide the solution to that problem, in the sense that it's possible to
crowd-source the scripting of automatic virtual tutors, which can then be
replayed (for free) on mobile devices throughout all regions, rich or poor.
Thus, expii.com was born.

[https://www.youtube.com/watch?v=11SdySDDrMk](https://www.youtube.com/watch?v=11SdySDDrMk)
[https://www.youtube.com/watch?v=t6WVbFIz43M](https://www.youtube.com/watch?v=t6WVbFIz43M)

\-- Po-Shen Loh

~~~
pervycreeper
That's really interesting. Deserving of a top-level submission, too, I think.

May I ask what your plan is for defending lessons against cranks, crusading
ideologues, and the less-than-knowledgeable once it gets more adoption? Other
collaborative projects such as Wikipedia have suffered as a result of this,
but I noticed in your talk that your aim is to maintain "higher" quality than
Wikipedia or even Stack Exchange and Quora. I'm curious how this can be
accomplished once the user base expands beyond its initial network.

Congrats on this year's IMO result!

~~~
expii
Expii uses voting (like Reddit, Quora, Stack Overflow, etc) to identify the
best content. After that, since we have the luxury of focusing only on the
"heavy-hitter" topics which at least 100 million people need to know, there
really aren't that many topics. When we do reach the size at which quality is
an issue, we can simply moderate the topics in-house.

Wikipedia cannot do this because their objective is to cover 100 million
topics (breadth), and so in-house moderation doesn't scale. Our objective is
depth: we ultimately want to provide the absolute best free interactive
lessons on every heavy-hitter topic in the world. :)

Thanks for your well-wishes!

------
datamingle
A Canadian got a perfect score. Only one I found while checking around. No
American nor Chinese got a perfect score.

[https://www.imo-official.org/participant_r.aspx?id=19624](https://www.imo-
official.org/participant_r.aspx?id=19624)

Also, only 1 person got 3 perfect scores in the history of the event: Ciprian
Manolescu (3 for 3 perfect) [https://www.imo-
official.org/participant_r.aspx?id=3789](https://www.imo-
official.org/participant_r.aspx?id=3789)

------
vixen99
Astonishing performance (3rd place) by North Korea with pop. around 25m. Not
sure what incentives were in place for the contestants.

~~~
nopinsight
Singapore at the 10th with fewer than 6 million people is also quite
noteworthy. I wonder how much it has to do with importing talents or talented
families from abroad, and how much from training starting at a young age.

(I know that Thailand does have a series of math competition for kids starting
at grade 3. This was started less than 20 years ago, which helps explain its
much improved IMO performance over the last decade.)

Any Singaporeans care to explain?

~~~
archlight
Singapore set up NUS high school a couple of years ago to nurture development
of students talented in maths and science. I remember a ex IMO coach from was
hired from China to prepare for the competition. it is not surprising it
stands at tenth place if you have long term plan for it. btw 6 mio people are
total population out of which only 3mio are singaporean. but if you are really
talented and wealthy, you can quickly become singaporean

~~~
netvarun
Thanks for posting this. I've always wondered how come we "suddenly" started
performing really well in the IMOs.

Considering the fact that until 2011, we had only won ONE gold medal and
rarely featured in the top 30.

But from 2011 onwards, have won 10 gold medals and have started to
consistently appear in the top 10.

Background: Singaporean who once aspired into getting into the IMO team [this
was circa <=2004]. But ended up with a crappy silver medal in the informatics
olympiad. Now a washed up, recovering Perl hacker.

------
tokenadult
I think the reporting from _The Guardian_ a few days earlier,[1] mentioned in
this article, provides some good perspective on the International Mathematics
Olympiad (IMO) from across the Atlantic Ocean from this _Washington Post_
report.

[1] [http://www.theguardian.com/science/2015/jul/15/us-wins-
harde...](http://www.theguardian.com/science/2015/jul/15/us-wins-hardest-ever-
international-maths-olympiad)

------
lacker
Congrats to the team! I'm curious if any of the six team members are reading
HN.

~~~
ryanalweiss
Hi. :)

------
giech
Not related to this year's competition, but you may also be interested in the
hall of fame [1], which contains many well-known names.

[1] [https://www.imo-official.org/hall.aspx](https://www.imo-
official.org/hall.aspx)

------
Grue3
Russia nowhere to be seen. We used to be a powerhouse too, but it seems the
education here is in absolute shambles now.

~~~
lacker
To be fair, this contest measures the performance of six people. The education
that is most directly tied to IMO performance is specific "math for the top
few students in the country" stuff which is usually some specialist math camp
thing. So I don't think it necessarily means that much about a whole country's
math education, if their IMO team doesn't do well.

~~~
vph
Don't know about other countries. But in the USA, the six people who make the
team are selected among high schoolers after rounds of competition. It does
reflect very much a country's math education. But math education is just part
of a much larger equation.

------
graycat
For Problem 6 given in the OP, the claim is false:

Notation: We borrow subscript and superscript notation from D. Knuth's TeX.
So, a with a subscript j is written a_j.

Consider the simple graph, based just on typing, below. The graph shows the
first four values of a specific sequence a_j. This sequence is a contradiction
to claim of Problem 6.

In this graph, the values of j = 1, 2, ... are plotted on the horizontal axis
with 1, 2, ..., and the values of the a_j are plotted on the vertical axis
from 1 to 2015\. We plot a value of a_j as just 'a'. Due to constraint (ii),
we indicate by 'x' points that, due to prior values of a_j, cannot have an
'a'. So, the graph is:

    
    
           2015
              .
              .
              .
         a_j  .
              5
              4
              3 a a
              2  x x    ...
              1  axax
    
                123456789
                    j
    

Then the first two terms of the sequence a_j are:

    
    
         a_1 = 3
    
         a_2 = 1
    

and generally for j = 1, 2, ..., a_j is:

    
    
                 /
                 | 3 if j is odd
                 |
         a_j =  <
                 |
                 | 1 if j is even
                 \
    

Then for any positive integer b and j = 1, 2, ...

    
    
         (a_j - b) + (a_{j + 1} - b) >= 2
    

More generally for positive integers m and k,

    
    
         sum_{j = m + 1}^{m + 2k} (a_j - b) >= 2 k
    

Then for any positive integer N, we can set m = N and n = m + 2(1007^2) and
get

    
    
         | sum_{j=m+1}^n (a_j - b) |
    
         = sum_{j=m+1}^n (a_j - b)
    
         = 2 (1007^2) > 1007^2
    

showing that the claim is false.

~~~
paulfr
There are no absolute values in the summands, so in your example pairs of
consecutive terms sum to 0 when you choose b = 2.

The theorem seems entirely correct to me. You can prove it with these sub-
steps:

(1) the set of all j + a_j is the set of nonnegative integers minus a finite
number of gaps

(2) thus for large enough n you can express \sum_{j=1}^n (j + a_j) as a
quadratic function of n, plus a residual term e(n) of magnitude at most
1007^2/2

(3) more precisely, \sum_{j=m+1}^n a_j = g (n-m) + e(n) - e(m) where g is the
number of gaps in (1)

Then choosing b = g solves the problem.

Hope that helps.

------
archlight
it is a good news. because American become more confident in educating their
kids in maths and abandon the idea that you can be lawyer if you are not good
at math. on the other hand, Chinese can stop believing that math is highest
form of intelligence and pursue career as lawyer etc.

~~~
bilbo0s
???

Wouldn't it be better for mankind ... if as many people like these kids as
possible pursued math and science more vigorously ??? Especially kids like
these, who have what I would term "creative" intelligence.

Why would we want those people in law ??? That gives us far less than having
them in math and science. And we will get the MOST by having them in art AND
math and science. Then we'd really get their creativity going as they look for
solutions to problems.

~~~
Retric
IMO, high level Math and Science is generally a waste of a lot of really smart
peoples time. The LHC for example is studying particle energy's so far outside
of 'reasonable' that we are not going to get useful technology from there. The
same is true of a lot of esoteric Math which mostly ends up divorced from
anything actually useful.

That's not to say funding such things is necessarily a waste, just the focus
on STEM education may be excessive. Russia for example ended up with a lot of
highly educated security guards.

~~~
gus_massa
The standard example of unexpected esoteric physic application is the Special
and General Relativity corrections of the GPS. 100 years ago nobody thought
that we would ever use that small correction or that everybody would have a
special-and-general-aware device in the pocket.

Another cool application is the superconductors in the NMR devices. They can
see what is inside your head and even do something equivalent to a chemical
analysis (with NRM spectroscopy) without opening it. The first superconductors
experiments used Helium at 4K, so they were only a laboratory curiosity.

For everyday use, I like the giant magnetoresistance. This is my favorite case
to explain that strange quantum effects have real world direct applications.
Just start talking about the spin in electrons. Then explain that some
magnetic conductors have a different value of the current with spin up and the
currents with spin down. Then add the sandwich with non-magnetic conductors.
At this moment it looks like a weird laboratory experiment. Then suddenly
explain how it is used in hard disks heads:
[http://en.wikipedia.org/wiki/Giant_magnetoresistance](http://en.wikipedia.org/wiki/Giant_magnetoresistance)

~~~
Retric
<Playing the devils advocate.>

Don't get me wrong, QM for example was ridiculously useful. But, pointing to
past and saying these tiny particle accelerators where useful let's make a
multi billion dollar one feels like cargo cult science for the lack of a
better phrase. We just keep piling higher and deeper without a clear reason to
do so other than we can afford to do so.

String theory is another example where lot's of effort from seemingly smart
people with no practical basis.

Dumping all of LHC's money into say a large ITER style fusion project would
have also been cutting edge, but there would have at least had the possibility
of useful results. Hell, even ISS would qualify as vaguely useful.

How about a self sustaining bio-dome in Antarctica. Now that's probably harder
and possibly more expensive, but would have real useful applications if we
ever want to try and colonize Mars.

PS: Not that the 13+Billion for the LHC was all that expensive, but there are
a lot of similar projects out there.

~~~
pervycreeper
GH Hardy famously predicted that elementary number theory would have no
practical applications. Lo and behold, today it is an indispensable part of
web cryptography used by hundreds of millions every day. Waiting on the order
of decades for a ROI on fundamental research is simply part of the game. I
suspect the point where we experience diminishing returns from this is much to
far in the future to even consider the question.

~~~
Retric
Elementary number theory is the opposite of what I am talking about. RSA is
from the kiddie pool of that field.

Consider, we know the first five digits of the gravitational constant. So,
while it might seem like the diminishing returns are a long way off. Yet, each
extra digit becomes exponentially more expensive and less useful. So, actually
learning g out just 9 digits is probably a huge waste of resources.

Or in the words of a physicist, in 1920 second rate physicists where doing
first rate research. Now, first rate physicistare doing second rate research.

~~~
pervycreeper
>Elementary number theory is the opposite of what I am talking about.

In number theory, what's considered 'elementary' now was cutting edge in the
times of Diophantus, all the way to Fermat, to Euler, to Gauss (etc). The fact
that children are now routinely conversant in it, I think, is another point in
favor of the importance of making such discoveries in the first place.

My point is that applications that were never envisioned for these (at the
time) centuries-old-facts, are now commonplace and indispensable.

I think that there is a bit of survivorship bias that warps our understanding
of old science. We remember only the great discoveries because those are the
most likely to be republished and read.

Also, in the case of math, it is my impression that an amazing amount of very
significant progress is being made in the present era.

~~~
Retric
It was old hat 1500 years ago, and rediscovered repeatedly. I am suggesting
there is a legitimate separation from what people find out in the first few
years of research on a topic and what's built after that. So, you really need
to pick a deeper topic if you want to defend your argument.

As to survivorship bias, that's huge but it's not just based on good ideas.
Copernicus was ~4,500 years late to proposing the sun was the center of the
solar system. But, the pop story looks better when Darwin is breaking new
ground instead of simply collecting more evidence in support of an old theory.

As to Amazing progress, I would hope the ~1,000,000 active mathematicians are
not all wasting their time. But again, the point is we don't need to
maximizing the number of Mathematicians, we are well into diminishing returns.

------
bjwbell
What's happened to Germany? They used to be one of the best in mathematics.
But the recent IMO results are very poor (27th this year).

Has their education system declined or something else perhaps? I know they
have a low birthrate....

------
kelukelugames
This makes me want to chant USA a lot more than the soccer game.

~~~
ams6110
Something about this comment really annoys me. It's like you are disparaging
high achievement by others just because it's not in a field you are personally
interested in?

~~~
kelukelugames
No I like sports. It's just boring when team USA wins again because they are
always so dominant. Winning once in 21 years makes us the underdog.

Getting really annoyed is silly. I try not to be easily offended by hackernews
comments.

------
helmett
congratulation...I see a hedge fund career for many

~~~
overpaidgoogler
I hope not. When I did math Olympiads (including the IMO) I was presented with
a false dichotomy of pure math or finance. This is really unfortunate because
finance in general does not use very deep math. A tiny number of people might
use SDEs but by now the techniques are standard and boring anyway.
Furthermore, even mainstream economists doubt that this sort of finance has
positive externalities. The amount of resources that go into finance is just
way out of proportion to what seems necessary for price discovery.

In contrast, all of the science and engineering disciplines can make use of
very interesting math. Not deep compared to research math, but used in a much
more interesting way than in finance. E.g when you study the statistics of
markets, you are just playing a game, and don't care that much about external
reality per se. On the other hand if you study the statistics of DNA or gene
expression, you are doing real science.

I think the best advice to a young person studying math is what was given to
me at the age when I was doing the IMO (and interestingly, after I graduated
by someone else): Don't neglect statistics.

~~~
rtpg
As someone who neglected statistics as a student ( topology was a lot funner)
, would you have any recommendations for self-learning tools for statistics?

~~~
chestervonwinch
Casella & Berger's "Statistical Inference" is a nice introduction to basic
probability theory and statistics. I found it pretty readable, and it's used
for many 1st year graduate stat programs.

Duda & Hart's "Pattern Classification" is one of the best introductions to
machine learning IMO. It assumes very little in the way prerequisites, which
is nice for first time exposure.

Hastie & Tibshirani's "Elements of Statistical Learning" can be a little
intimidating without having been exposed to the ideas of the previous two
texts. Afterwards, however, it is a gem.

------
enimodas
I looked a bit at the gender distribution for the gold and silver medalists, I
would guess only 1 in 10-20 is a girl, most seemed to be from the eastern bloc
countries.

~~~
booop
I can't believe the audacity of Po-Shen Loh to send a team exclusively of boys
to the IMO. When you have to select 6 team members how can you NOT select at
least 1 female? This flies in the face of all the outreach work people have
been doing to get more girls into STEM, and this victory will only discourage
them. It appears the top 3 teams are all 100% boys.

I'm delighted that this is currently the top comment here. It shows we are
clearly concerned with the right issues. I hope from now on all national teams
participating in international competitions will be gender balanced. In order
to remedy this situation we need:

    
    
       1) A Twitter mob
       2) An email campaign addressed Po-Shen to not repeat this and discredit his work and efforts. 
       3) A post of the team's picture to the popular twitter/tumblr account which shames all male conferences and gatherings 
       4) An email campaign addressed to IMO to implement rules that all teams should be gender balanced.
       5) A solution to Poe's law.

~~~
Tinyyy
This guy is being sarcastic, I don’t really understand the down votes. Maybe
that’s just the way it is over here.

~~~
DanBC
It's a pointlessly baity answer and deserves downvoting.

~~~
jazzyk
Respectfully disagree. He ridicules the simplistic solutions proposed to
certain issues (lack of women in a math competition in this case). In my
opinion, it adds a valid (and funny) point - you may agree or disagree with
him, but it is not a reason to downvote. Sarcastic - yes, ad hominem - no.

