Every year, countries all over the world select a team of six secondary school pupils to compete in the International Mathematical Olympiad (IMO). This year, the Swiss selection process has resulted in an extraordinary team, in which two out of six pupils are from IIL: Juraj Rosinsky and Tanish Patil. In July, they will represent Switzerland at the IMO in Cluj, Romania.
Is this pure coincidence, or is there a reason why two pupils from our school are on this team?
Juraj and Tanish: It is pure coincidence, although it does help to live in the Geneva area. With three big scientific institutions nearby: the University of Geneva, the EPFL in Lausanne, and Cern, there are quite a few mathematicians or mathematically minded people around. If we had lived in a more isolated area, it would have been less likely to reach our current level.
Does that mean that you were encouraged by others to do a lot of mathematics?
Juraj: My parents both have a mathematics background, so I think that mathematics played a more important role in my family than in many others. I have always done mathematics outside school. Already as a young child, I was doing Slovakian mathematical puzzles for my age group and participating in the Pikomat contests that you can do by correspondence.
Tanish: My parents aren’t mathematicians but my mother worked as an accountant before choosing to stay at home and look after her children. She has always asked me mathematical questions and coached me quite a bit in mathematics before I started school.
Is the Mathematical Olympiad related to school mathematics? Were you inspired by school mathematics?
Juraj: In my previous school we participated in the yearly French Kangaroo mathematics competitions, and it is through these competitions and thanks to one of my teachers that I joined a mathematics club in Lyon. I really like their approach, and it’s where I did most of my problem-solving training.
In general, I think Kangaroo questions are more interesting than the mathematics taught in the French Baccalaureat programme. In school, we learn theorems, often without really understanding why we should use them, and then you are expected to use the theorems to answer questions, in a way that does not require a lot of thinking. Often, the solutions are easily seen, or it is not clear why you would address a certain problem.
Kangaroo questions are different. They are multiple choice questions for example:
“Two consecutive numbers are such that the sums of the digits of each of them are multiples of 7. At least how many digits does the smaller number have?”
But they are not so simple to answer. And you won’t get instructions on how to approach the problem, so that the mathematical process is far more creative. Mathematical Olympiad questions are of a higher level, but the spirit is similar.
Tanish: I also got involved in puzzle-like mathematics through the Kangaroo contests, but as I follow the English programme I only knew about British competitions. As I really liked those, and was pretty good at them, I was interested in doing more. At some point my mother had read about the Euler mathematics programme at the EPFL, and encouraged me to take the entrance test. That test required a similar logical way of thinking. I passed and enrolled in the programme, and at some point the Mathematical Olympiad was presented. That is how I got involved in the Swiss selection process.
I partially agree with Juraj that the way mathematics is approached in school is less interesting, although the Y11 Additional Math’s course and the IB Higher Level Mathematics course allow for a deeper understanding of what we learn. For instance, I very much liked the way our teacher showed us how limits are used to obtain results in calculus, with simple examples that were very insightful because you can actually do the calculations by hand and see what are the crucial parts in the reasoning.
So would you advise to change the way mathematics is taught or done in school?
Juraj: Well, if my teacher would take the time to explain in depth what the background of certain theorems is, then probably half the class would be lost. It would be good though to spend some time every now and then on puzzle-like problems!
What is it that makes the Olympiad competition attractive?
Tanish: I particularly like the Olympiad questions because you always have enough time to think through the questions properly and to try different methods. In school exams, you immediately lose too much time if your first approach leads nowhere.
At the International Olympiad, you are given three problems per day for which you have six hours in total. On both days, there is one ‘easy’ problem, one intermediate, and one difficult one. If I cannot solve a problem within the two hours you have for it, I won’t be able to solve it in four or six hours either.
Juraj: Well, with all the training sessions we learnt a lot of mathematics, and it is not always clear which part of the maths we know is applicable. You can still be penalised if you spend too much time for an unfruitful approach.
Tanish: I prefer to work in an intuitive way if possible. It is true that mathematical proofs sometimes require pages of detailed reasoning. It is important to avoid that a theorem would not be true for some unexpected, strange cases. But I like to have handwaving arguments why something should be true or not. Many Olympiad problems require a good first intuition, before you then continue to fix the details.
Having said that the IMO questions are very hard to solve. If you manage to get full marks on only one of the six problems set, you already receive a certificate of honorable mention.
Juraj: I also like problems that are intuitive. Number theory and geometry really lend themselves well for this. I don’t really like to memorise things or to revise a lot for an exam. For the Olympiad, you can train by solving or attempting to solve a lot of problems, and by doing this you will remember the useful theorems.
What are your summer plans? What do your friends say when they hear you will be spending your holidays doing mathematics?
Tanish: I will not only go to the International Mathematics Olympiad, but also attend the PROMYS Europe Mathematics programme in Oxford. This means that almost my entire summer holidays will be filled with mathematics related activities. My friends don’t really talk about all the maths I do, but are more impressed to see where I have been travelling and which places and universities I have already visited thanks to maths. Some of them are jealous that at the end of Y12 I know perfectly well what I want to do and where I want to go after secondary school, while they themselves feel totally lost.
Juraj: After the IMO I will also spend another two weeks doing mathematics, at a mathematics and physics internship in the Czech Republic organised by the Karlova University of Prague. And then after the summer I hope to start studying Mathematics at the EPFL or the University of Geneva.
Thank you for the interview. We wish you every success in Romania!
Interview by Geertje Hek, teacher
Photo: IMO Suisse