In any case, by the Sunflower Jesus It’s not religion it’s a relationship shirt to be a research problem, it’s almost guaranteed that simple pattern matching won’t finish it. So in one’s professional work, the process is piecemeal: you think a few moves ahead, trying out possible attacks from your arsenal on simple examples relating to the problem, trying to establish partial results, or looking to make analogies with other ideas you understand. This is the same way that you solve difficult problems in your first real maths courses in university and in competitions. What happens as you get more advanced is simply that the arsenal grows larger, the thinking gets somewhat faster due to practice, and you have more examples to try. Sometimes, during this process, a sudden insight comes, but it would not be possible without the painstaking groundwork.
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