Competition Mathematics
This involves mathematical problems of a very different nature than the problems given as part of academic learning, as they focus more heavily on creative thinking and pattern recognition than just testing whether one knows how to apply academic theory.
I was very interested in such competition type mathematics when I was in high-school and also now:
I created and am in charge of the Problem of the Week programme in KU Leuven
I was team leader for KU Leuven in the International Mathematics Competition 2023 in Bulgaria, where we came 8th place and got 3 Gold Medals.
With some teammates from Sweden and Stanford University EPGY, we grabbed 3rd place in the Purple Comet! Math Meet! competition. This is an international competition in mathematics for high-school students, relying heavily on time pressure
With teammates from my highschool Malmo Borgarskola, we won 3rd place and 2nd place (2011, 2012 respectively) in a regional competition Matematikpilen hosted by Lund University
I ranked 4th place in the Swedish national high-school maths competition Kangarootavling. This competition is created by the NCM in Sweden
In February 2019 I created the Queen Mary Olympiad in London. The problems can be found here
I have also co-created the Cantor Contest mathematics competition in the University of Edinburgh in February 2015
In February 2014 I co-created the University of Edinburgh Mathematical Olympiad
There are a lot of problems of this nature online. For example one can look at the mathematical olympiad qualifiers for specific countries, or the questions that have been sent for selection (the BMO has a long list of these for example). The MMA website has a lot of good problems.
A great book I can recommend, which contains problems but also the thought behind solving them (and helps improve one's creative abilities) is Paul Zeitz's The Art and Craft of Problem Solving. There are of course many more.
