>>12561981Competitions can be a good way of finding talented people, and we should invest in students who perform well in them. However, they also involve a very particular skill set, and actually learning and developing these skills is probably an inefficient usage of time for most students who are interested in pure math and other mathematically rigorous sciences. The best way to develop your mathematical abilities is either through proofs (if you are talking about developing abstract mathematical reasoning), or through creating really intricate, detailed mathematical models (if you are trying to develop your applied and computational skills).
>>12562125This is a somewhat simplistic and reductionist perspective. We don't live in a world where either cooperation is better or competition is better. It depends on the context and the task. Moreover, the concept of cooperation literally doesn't make sense without the concept of competition. These are basically dual concepts (in the mathematical sense of "dual"). The existence of one implies the other. For example, even if two agents are not competing against another agent, then they are competing against nature.
Pretty much everything in the realm of the biological and behavioral sciences is dependent on a balance between cooperation and competition. For example, scientific progress is based on a combination of both competition and cooperation. Evolution is based on a combination of cooperation and competition. The spread of memes, ideas, and culture is based on a combination of cooperation and competition.
Scientists have to cooperate by sharing epistemic standards, data, methods, research results, and funding. However they also have to compete by looking for data to falsify incorrect theories. They need to consider alternative hypotheses, and compare different scientists claims against each other. The whole point of the scientific method is to help us compare competing theories and correct mistakes.
