by: Hojoo Lee, Tom Lovering, Cosmin Pohoat
The book's foreword:
The International Mathematical Olympiad is the largest and most prestigious mathematics competition in the world. It is held each July, and the host city changes from year to year. It has existed since 1959.Originally it was a competition between students from a small group of communist countries, but by the late 1960s, social-democratic nations were starting to send teams. Over the years the enthusiasm for this competition has built up so much
that very soon (I write in 2008) there will be an IMO with students participating from over 100 countries. In recent years, the format has become stable. Each nation can send a team of up to six students. The students compete as individuals, and must try to solve 6 problems in 9 hours of examination time, spread over two days.
The nations which do consistently well at this competition must have at least one (and probably at least two) of the following attributes:
(a) A large population.
(b) A significant proportion of its population in receipt of a good education.
(c) A well-organized training infrastructure to support mathematics competitions.
(d) A culture which values intellectual achievement.
Alternatively, you need a cloning facility and a relaxed regulatory framework. Mathematics competitions began in the Austro-Hungarian Empire in the 19th century, and the IMO has stimulated people into organizing many other related regional and world competitions. Thus there are quite a few opportunities to take
part in international mathematics competitions other than the IMO. The issue arises as to where talented students can get help while they prepare themselves for these competitions. In some countries the students are lucky, and
there is a well-developed training regime. Leaving aside the coaching, one of the most important features of these regimes is that they put talented young mathematicians together. This is very important, not just because of the resulting exchanges of ideas, but also for mutual encouragment in a world where interest in mathematics is not always widely understood. There are some very good books available, and a wealth of resources on the internet, including this excellent book Infinity.
The principal author of Infinity is Hojoo Lee of Korea. He is the creator of many beautiful problems, and IMO juries have found his style most alluring. Since 2001 they have chosen 8 of his problems for IMO papers. He has some way to go to catch up with the sage of Scotland, David Monk, who has had 14 problems on IMO papers.
These two gentlemen are reciprocal Nemeses, dragging themselves out of bed every morning to face the possibility that the other has just had a good idea. What they each need is a framed picture of the other, hung in their respective studies. I will organize this.
The other authors of Infinity are the young mathematicians Tom Lovering of the
United Kingdom and Cosmin Pohoat¸˘a of Romania. Tom is an alumnus of the UK
IMO team, and is now starting to read mathematics at Newton’s outfit, Trinity
College Cambridge. Cosmin has a formidable internet presence, and is a PEN activist
(Problems in Elementary Number theory). One might wonder why anyone would spend their time doing mathematics, when there are so many other options, many of which are superficially more attractive.
There are a whole range of opportunities for an enthusiastic Sybarite, ranging from
full scale debauchery down to gentle dissipation. While not wishing to belittle these
interesting hobbies, mathematics can be more intoxicating. There is danger here. Many brilliant young minds are accelerated through education, sometimes graduating from university while still under 20. I can think
of people for whom this has worked out well, but usually it does not. It is not sensible to deprive teenagers of the company of their own kind. Being a teenager is very stressful; you have to cope with hormonal poisoning, meagre income, social incompetance and the tyranny of adults. If you find yourself with an excellent
mathematical mind, it just gets worse, because you have to endure the approval of
teachers. Olympiad mathematics is the sensible alternative to accelerated education. Why
do lots of easy courses designed for older people, when instead you can do mathematics
which is off the contemporary mathematics syllabus because it is too interesting
and too hard? Euclidean and projective geometry and the theory of inequalities (laced with some number theory and combinatorics) will keep a bright young mathematician intellectually engaged, off the streets, and able to go school
discos with other people in the same unfortunate teenaged state. The authors of Infinity are very enthusiastic about MathLinks, a remarkable internet site. While this is a fantastic resource, in my opinion the atmosphere of
the Olympiad areas is such that newcomers might feel a little overwhelmed by the extraordinary knowledge and abilities of many of the people posting. There is a kinder, gentler alternative in the form of the nRich site based at the University of Cambridge. In particular the Onwards and Upwards section of their Ask a Mathematician
service is MathLinks for herbivores. While still on the theme of material for students at the beginning of their maths competition careers, my accountant would not forgive me if I did not mention A Mathematical Olympiad Primer available on the internet from the United Kingdom Mathematics Trust, and also through the
Australian Mathematics Trust. Returning to this excellent weblished document, Infinity is an wonderful training
resource, and is brim full of charming problems and exercises. The mathematics competition community owes the authors a great debt of gratitude.
Dr. Geoff Smith
http://ifile.it/3hq4x9k/infinity.pdf
http://rapidshare.com/files/234686217/Infinity.rar
