Means of Promoting Mathematics in Young Countries! We all know mathematics is life, this question is for Mankind. It's mathoverflow here when some parts of the world we have mathunderflow! I think we can do something through ideas.  A  similar question "Good ways to engage in mathematics outreach" has been featured but this is a different question all together.
In this question, am interested in understanding what the so called super countries in mathematics  done right utilizing the little resources they have in the promotion(development) of mathematics. How can very young  country (mathematics development is wanting, the research output is low, some fundamental courses are not even taught at the first place due to lack of resource persons) move on? What are some of the ideas which have helped countries with a small economy grow? Are there mathematicians who have been involved in development of mathematics in developing/ less developed countries which are experiencing an upward trend? How did you do it?
 A: As it was said in an other answer it seems like a good idea to send students abroad to study at strong places and have them come back, or if they don't, keep contact, have them give courses in their home country etc.
A scientifically excellent place helping with precisely such a policy is the ICTP in Trieste, see the "Education and Training" and the "Research "sections of their website (they are called institute of theoretical physics, but they have a strong mathematics section). Concretely they provide training programmes for undergrads to prepare them for a PhD - see here - and they also offer short and longer term stays for working scientists from developing countries, as well as institution partnerships, see here.
A: I wasn't there to see the birth of Brazilian mathematics out of essentially nothing in the 50's and 60's, but it is clear to me that its beginning was due to a handful of idealistic individual mathematicians with great talent and strong personalities. Sure, there were universities and engineering degrees where the budding mathematicians could start to learn but if these pioneers hadn't the fortitude to go abroad to get their PhD's and then come back to build it, it wouldn't have happened. 
Once they came back, if they stayed at the universities of the time they would have been stifled and left (in fact the early ones kind of commuted to the US and back for a bit). It was only with the creation of IMPA (and a benevolent government that gave some money for its maintenance) that things started to pick up. There was an ambient of research and graduate studies that tried (and eventually succeeded) to emulate the institutions of the developed world. Always uncompromising with regards to quality, IMPA had open doors, a good library, courses in the summer for bright undergraduates, conferences and the Brazilian Mathematical Colloquium which besides a conference had mini-courses at various levels to spread the word.
A: Dear Ongaro Nyang' 
Although Israel is no longer so young, it was young, (even 
younger than most other countries,) not so long ago, and
it is a small and rather isolated place, with some difficulties.
So some lessons from Israeli mathematics, especially in its early days 
may be relevant.  

A) Immigration

1. Immigration
Israeli mathematics was initially based on and had benefited all the 
times from immigration of mathematicians to Israel. The ability to 
absorb immigration, in general, and to attract and absorb immigrating scientists, in particular, 
is crucial.(Keeping the relations with mathematicians who immigrated from 
Israel is also an important issue.)

B) Financial matters.

Investing resources is, of course, crucial. There was a large public investment 
in universities in Israel's first years even when the country itself 
was in rather bad economic shape. Overall, theoretical academic 
subjects like mathematics are "cheaper." Keeping the right balances 
regarding policies for spending the money is very important. 
Let me mention two items.
2. Sabbatical/Travel money
1.1 Good Sabbatical opportunities: Israeli mathematicians (and scientists
in general) had relatively good sabbatical terms which make it possible
for them to get (from the Israeli institution) a reasonable European/US
salary while in sabbatical abroad. This was especially effective when the
Israeli salaries were very low compared to salaries abroad. The academic 
system is built on 15% or so of the faculty being on sabbatical at 
any time. (Often people spend additional time abroad on leave.)
2.2 In addition, Israeli scientist (with academic university positions) and graduate students (who works as T.A.'s)  have funds for short-term
travels: (Fixed amounts depending on the academic rank per year) This
enable participation in conferences and joint research.
Both the sabbatical and travel money apply to all people with academic
positions (Sabbatical only to lecturer/asst professor position and above)
and are essentially automatic. (Minimal amount of bureaucracy, no
committees to judge qualification and to decide on amounts, no requirement
to be an invited speaker in a conference, etc. etc..)
3. Salaries 
Keeping the right balances when it comes to salaries is also important. 
Low salary gives incentives to leave but very high salaries (compared to 
average salaries in the country) are morally problematic and may 
give incentive for corrupting the hiring and promoting system. 
The salary system in Israel is based on essentially equal salary for equal
academic rank and (overall) there are no substantial salary awards for
academic excellence beside the academic rank. (There is some (modest)
awards for people getting external grants and larger but still rather small
for people serving in administrative positions.)
I think that not having overly differential salaries and not 
being "in the game" of offers and counteroffers is actually beneficial.

C) Activities

4. Activities for national math society
There are, since early times, 
regular annual meeting of the Israeli Mathematics Union and some
other local activities. 
5. National mathematical journal
There was a substantial effort, again from early times,
to create and maintain an Israeli journal of 
mathematics. (In the 40th there was even a professional research level 
journal in Hebrew for a few years.) 
6. Conferences and visitors.
There was, again from early times, some resources devoted to conferences 
and visitors. Carefully administered and with attention to
the added value for the local people this can be very fruitful. 
Arranging visits of top people in mathematics for lecture series and visits 
can also be useful. It seems that it is a good policy (when the country is not
rich)  not to over-pay for such visitors (among other reasons, because this set standards which push the cost of visitors in general too high.)  
Of course, warm hospitality is priceless.

D) Content

7. Maintaining a sense of tradition.
Basing activities on areas with long tradition of success which are
identified with the country's mathematical strength can be a successful
and well excepted by the whole mathematical community.
8. Self-breeding can work
The success of Israeli mathematical departments was largely based on 
successful self-breeding, namely absorbing as faculty member people who
graduated at the department. 
9. Self-confidence, Tolerance for "sporadic"(or non-main stream) areas 
(and tolerance in general)
This seems to me a strength of Israeli mathematics and looks (to me) a
good attitude especially for a peripheral and somewhat isolated place. 
Tolerance is important especially since mathematical quality is rather 
high dimensional (some dimensions being 
importance/depth/visibility/applicability/usefulness.) 
(There is also
complete tolerance and essentially indifference in the context of
mathematical life towards matters of politics, attitude towards religion,
etc, issues that Israel is very torn apart about.)
10. Patience, realistic goals, unrealistic dreams
Building a good mathematical activity takes time, and there are 
ups and downs as well.

E) Outreach

11. Issues concerning high school mathematics
There is some efforts to promote interest in mathematics among gifted high
school students: special mathematical journal (in Hebrew), some "clubs"
and "summer camps" math Olympiads etc. I think this had some factor in
promoting math among young people.  Usually, what it takes is some
mathematician in academics which is devoted to this issue and some (not
large) budget. Giving an incentive for such an activity and such a
mathematician may be a good idea. Popular Math books and text books in
Hebrew had substantial influence. A. Frankel (the set theorist) 
wrote  wonderful five-volume Hebrew books introducing 
mathematics (It was called "An Introduction to Mathematics") in the 40s/50s. 
(More recently, the Hebrew edition of Singh's
book on Wiles proof of FLT increased popularity of mathematics.)

F) Relations with other areas

12. Relation with CS, physics and other disciplines
In Israel CS department were largely built out of math departments (not
electrical engineering) and there are still strong academic ties between
these communities. Connection with CS seems valuable. Of course, relations with physics are very important (not so strong in Israel).  Relations between math and economics seems strong in Israel. 
(In Jerusalem there is an interdisciplinary "center for
rationality" which involves people from math/economics and some from
statistics/psychology/philosophy/law/biology.)
In summary, when it comes to mathematical life in a small somewhat isolated and
at times a bit troubled place, it seems that it is valuable to make the
right balances in the local mathematical community between competition and
solidarity, to practice a lot of patience and tolerance, to be open to new people and new directions, and to be careful about incentives. 
Like in Brazil the efforts of few pivotals mathematicians was very crucial. 
As usual, luck is useful too. Good luck.
A: One organization that is actively pursuing the growth of math research in country 
without a strong math history is CIMPA (http://www.cimpa-icpam.org/) which every year
organizes several "research school" in country like Nepal, Mali, Pakistan etc 
whose participants are graduate students from the hosting and nearby countries. 
For more informations refer to the above link.
A: (Disclaimer:  I'm relatively young and so may not be in the best position to speak on this matter;  I hope other Filipinos who are more qualified will edit this answer.)
I would say the Philippines is a "young country" when it comes to mathematical maturity and that things started moving when the Mathematical Society of the Philippines was created in 1973.  More details can be found at http://www.mathsocietyphil.org/MSPHistory.html, but I would summarize it this way:


*

*If your country has relatively few PhD's in mathematics, send candidates abroad on scholarships and have them return with PhD's.

*Create a national mathematics society and involve as many universities as possible in annual workshops and conferences.  Invite foreign speakers to present the latest developments.

*Start a national refereed mathematics journal (with foreign referees if necessary).

*Create a strong mathematical doctoral program by establishing a consortium among the local universities that are strong in math and having them share qualified faculty members.  (This was done in the Philippines starting in 1977 between Ateneo de Manila, De La Salle University, and the University of the Philippines.)


I think the first three of these items are "obvious," but the last item should be particularly helpful.
A: Not sure this helps, but...
I heard a talk on development of mathematics in Africa by Aderemi Kuku, student of Hyman Bass, who was at msri approximately 2003,
http://www.math.buffalo.edu/mad/PEEPS/kuku_aderemi.html 
He is past president of the African Mathematical Union (AMU) so you might look into their activities, if you are not already involved. Quotes from CV: 

As President of the African
  Mathematical Union (AMU) for nine
  years, (1986-1995), I was responsible
  for organizing and coordinating
  various mathematical activities all
  over the continent of Africa. During
  my tenure, I created four Commissions-
  AMU Commission on Mathematics
  Education, AMU Commission on
  Pan-African Mathematics Olympiad, AMU
  Commission on History of Mathematics
  in Africa, and AMU Commission on Women
  in Mathematical in Africa. I also
  created a Pan-African Mathematical
  Sciences Network involving sixteen
  selected Universities/Research Centres
  in Africa with the aim of enhancing
  graduate training and research as well
  as co-operation North – South and
  -South. I was a Vice-Chairman of the First Congress of African Scientists,
  which, in 1987, created the
  Pan-African Union for Science and
  Technology and I have since made
  several contributions to the
  development of Science and Technology
  all over Africa. As a member of the
  International Mathematical Union
  Commission on Development and Exchange
  for eight years (1986-1994), I made
  contributions on the South development
  and exchanges in mathematical research
  in the developing countries, and other
  parts of the world.
CURRENT POSITION: Professor of
  Mathematics, Grambling State
  University, Grambling, LA, USA.

The other mathematician listed as helping with the AMU website is Paulus Gerdes in Mozambique:
http://www.math.buffalo.edu/mad/special/gerdes_paul.html 
Finally, AMU
http://www.math.buffalo.edu/mad/AMU/index.html 
is hosted at Buffalo because of Scott W. Williams,
http://www.math.buffalo.edu/people/faculty_instructors.shtml
