*Sports serve society by providing vivid examples of excellence.* (George Will)

I greatly enjoyed my experiences with high school mathematics competitions (all the way back in the 1980s!). Like any other school sporting event, there is a certain level of excitement in participating with peers with similar interests and talents in a competitive activity. At the olympiad levels, there is also the opportunity to travel nationally and internationally, which is an experience I strongly recommend for all high-school students.

Mathematics competitions also demonstrate that mathematics is not just about grades and exams. But mathematical competitions are very different activities from mathematical learning or mathematical research; don’t expect the problems you get in, say, graduate study, to have the same cut-and-dried, neat flavour that an Olympiad problem does.(While individual steps in the solution might be able to be finished off quickly by someone with Olympiad training, the majority of the solution is likely to require instead the much more patient and lengthy process of reading the literature, applying known techniques, trying model problems or special cases, looking for counterexamples, and so forth.)

Also, the “classical” type of mathematics you learn while doing Olympiad problems (e.g. Euclidean geometry, elementary number theory, etc.) can seem dramatically different from the “modern” mathematics you learn in undergraduate and graduate school, though if you dig a little deeper you will see that the classical is still hidden within the foundation of the modern. For instance, classical theorems in Euclidean geometry provide excellent examples to inform modern algebraic or differential geometry, while classical number theory similarly informs modern algebra and number theory, and so forth. So be prepared for a significant change in mathematical perspective when one studies the modern aspects of the subject. (One exception to this is perhaps the field of combinatorics, which still has large areas which closely resemble its classical roots, though this is changing also.)

In summary: enjoy these competitions, but don’t neglect the more “boring” aspects of your mathematical education, as those turn out to be ultimately more useful.

For advice on how to solve mathematical problems, you can try my book on the subject.

Some collected quotes on mathematics competitions can be found here.

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11 June, 2007 at 3:13 am

AnonymousHi Terry,

Thanks for this kind of post. I am a college student from the Philippines (not a mathematics major though) and it is nice to hear from a highly-rated mathematician on things like these. Few top-rated mathematician will even try to post advices like these and they are invaluable to students like me in third world countries like us.

Carlos

16 June, 2008 at 12:31 pm

这等牛人也在wordpress上写blog！ « Just For Fun[...] also good to remember that professional mathematics is not a sport (in sharp contrast to mathematics competitions). The objective in mathematics is not to obtain the highest ranking, the highest “score”, or [...]

5 October, 2008 at 12:12 am

THDear Terry,

I know that mathematical competitions and mathematical research are very different, and that one who is good at the former may not be good at doing the latter. But what about the other way around. Do you think it is likely that (or have seen many examples where) one who is a good/creative researcher is not a particularly good problem solver (assuming that one has the knowledge to solve the problems and that time is not a constraint)?

TH

12 May, 2009 at 3:29 am

Duc HuyDear Prof Terrence Tao,

I’m a high school student in Vietnam. I decided to study Mathematics in higher level but I’m not sure if I’ve made a good choice or not. I’ve failed in my efforts to get into the Mathematics Gifted High School in my country, therefore I was unable to take part in any Mathematics competition. I found my passion in Mathematics very late but now I want to study Mathematics seriously. Do you think a “non-gifted” student like me should major in Mathematics?

5 June, 2009 at 4:53 am

Essential Career Lessons[...] 3. “Boring” things are important … enjoy these competitions, but don’t neglect the more “boring” aspects of your mathematical education, as those turn out to be ultimately more useful. (source) [...]

19 August, 2009 at 1:46 am

School Awardsi think maths competitions are a great outlet for students to showcase their skills, and i am in awe of anyone who takes part (my maths is horrendous)! and not everyone is into sports or drama or other supposedly ‘cool’ activities so maths comps are great for those who enjoy maths and stats. thanks for a great post

7 February, 2010 at 8:25 am

AMLAN CHAKRABORTYI AM A STUDENT INTERESTED IN MATHEMATICS AND THEORITICAL PHYSICS.HOW TO INCULCATE THE SCIENTIFIC TEMPERAMENT RIGHT FROM CHILDHOOD AND THEN INTO ADULTHOOD?

2 November, 2011 at 10:59 am

Thomas Lawrence (@TommyJLawrence)Hey there, I was wondering if you could advise me on an issue about my capabilities in mathematics. I consider myself to be quite a good mathematician with a good mathematical intuition owing to me being rather good in normal maths lessons. However, I am terrible in maths Olympiads mainly because I get flustered and confuse myself (I never have any fun doing them unlike normal classes). This really damages my confidence as I fare far worse than my piers,many of whom spend much less time reading and thinking about maths. Do you think that my consistently terrible performances on maths challenges show that I am not the type of person for a career in mathematics or physics? I am sorry for such a silly self-absorbed question.

2 November, 2011 at 1:35 pm

Terence TaoYou may find the quotes and discussion at http://lesswrong.com/lw/2v1/great_mathematicians_on_math_competitions_and/ to be helpful.

3 November, 2011 at 9:01 am

ronnie74Thanks Professor Tao, I plan on purchasing your book, as we have a gifted child that is taking interest in math competitions. I really don’t understand where she gets it from though, haha.

8 April, 2013 at 5:57 am

tomcircleAgree. China has been champion in International Math Olympiad (IMO) for over 15 years, but none of the Gold Medalists go on to be Fields medalist or great mathematician.

While France has not been doing well in IMO but produced 1/3 of Fields Medalists.

Math Olympiad is like “acrobaic t to the real Kongfu, although both look alike in kicks and punches, Kongfu (like Taij)i are real !

24 May, 2013 at 8:29 pm

tomcircleVery few mathematicians could recognize that classical math (Geometry, algebra, number theory) ‘inform’ modern math. Felix Klein spent his later part of his life promoting to ‘teaching Elementary Math from an Advanced Stand Point’.

As for Combinatorics, it appears in modern form in Hopf Algebra applied in Topology.

3 March, 2014 at 7:37 am

KaminiSir,

i don’t know what happen wit me..because when m goin study mathematics or science at that time i can able to undertand the difficulties or salution but when my teacher ask me that solutions the day of my study i cnt answer those questions..so please tell me sir how can i able to capture all those for all the time..

3 March, 2014 at 7:52 am

tomcircleUnderstand is not enough, Math needs a lot of practices. You must do Math exercises.

15 April, 2014 at 3:24 am

HabDear prof.Terrence Tao, thank you for your intellectual advice about “mathematical competitions”. I live in Ethiopia & I have got MSc. Degree in Combinatorics but still i don’t have a published scientific paper. Please can you advice me about researches in Combinatorial Mathematics.