The true nature of Mathematics and the British Mathematical Olympiad
“Maths is difficult because there is not freedom in it. There are lots of strict rules that force the procedure to solve a problem, and, being too many for- mulas, it is hard to guess the correct one.”
I have heard this from one of my private students, perhaps this is the thought of many others, but it is totally wrong. On the contrary, Maths’ world is fully democratic, since everything is permitted unless it is self-contradictory. Solving a problem or demonstrate a theorem is like traveling from one place to another place. Everyone can choose which path to follow and not always there is a best option: one way can be quicker, another way can be more comfortable, another more panoramic, it is also a matter of taste. Imagination and spirit of adventure are the keys to discover and enjoy new amazing routes and places. Sometimes, you can end up in a dead-end street, but it is not your fault, indeed this increase your knowledge and you will avoid that street in the future.
“He did not have enough imagination to be a mathematician, but he has become a poet and now he is fine.” said the famous mathematician David Hilbert, talking about an ex-student.
You might think: “Beatiful words, but what do they mean in practice?”. First of all, do not limit yourself to only apply the tricks that you are taught. Look at new ways, do not be afraid to be wrong, because if something seems logical, it is almost certainly right.
Secondly, do not accept to learn something without a full understanding of why it is so.
Thirdly, do not rush! If you try to learn too many formulas in a hurry, you will probably remember them just to pass an exam, after that, your study will be lost.
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Fourthly, do a lot of practice.
This approach has several advantages:
- it improves your ability to reason in order to solve never seen types of problems;
- it will enhance your experience, making you able to find very quickly an appropriate solution;
- you will remember what you have learned as well as the alphabet, even if you do not have a great memory;
- it boosts your self-confidence.
These directions are particularly rewarding in the context of the British Mathematical Olympiad, where a higher level of originality than at school is required, though they are generally valid anywhere: the concept is that you can produce more by having few instruments that you know how to manage rather than by having many instruments that you do not know properly. Finally, I want to emphasize that in a competition such as the British Math- ematical Olympiad, the psychological factor must not be underestimated: in my experience, it can make the difference between a very low score at the first round and a prestigious national award. In this respect, I suggest to:
• take care of your health in the days before the competition; • do not overstudy;
• think something to do not feel under pressure.
The last point is particularly important if you have great expectations, for example because you did well in a previous edition, so you pretend to confirm the result. In this case you should try to believe you were just lucky, or that your skill does not depend on this result.
In short, my recipe for being successful in Mathematics is: “No great mem- ory, no stress, but enjoyment and imagination.”
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