>these competitions produce broad-spectrum excellence
If it was the case asian countries would not a shithole
From Niles Ritter
Here is my take on the situation: In every math competition I know of, the problems presented are already known to have solutions, and have been “reverse-engineered” by real mathematicians to not just have solutions, but likely very clever ones, often involving a symmetry or invariant (geometric or algebraic), about which the designer of the problem understands deeply. So to do well, contestants must be able to “see” a trick, that is already known to exist.
The job of a real mathematician is to extend mathematics into the unknown, where nobody has ever been, and it is not known if there is a solution, a symmetry, or other underlying structure about which anybody yet knows a thing. This involves a very different kind of thinking, closer to art perhaps, and a kind of bravery of journeying into an unknown world, using inductive reasoning, and pulling in tools and techniques from other mathematical fields or possibly even physics which nobody else had ever thought related.
The plight of the IMO Olympian is like that of a child at Easter Egg hunts, where they have grown used to finding pretty eggs laid out previously by adults, and then when they grow up and come to a large grassy field, they are frustrated, because no matter how hard they try they can’t find a single egg in the bushes —because in the real world of mathematics, there is no adult planting pretty eggs for them to find.