let’s say I’m trying to solve a mathematical problem that has not yet been solved or that I have not encountered yet. One where I don’t yet have the mathematical toolset to solve the problem. Assuming I make no mistakes, should I end up doing things that don’t work? Or in other words, should there sometimes be instances where you can’t know weather or not you can solve a problem a certain way until you try it? Kind of like going through a maze, you have to try things knowing that they might not work and you’ll have to try something else? When math is being taught, the teachers usually say something like, to solve this problem you do this, then this, then this, then this. When I’m solving particularly complex problems that I don’t have much experience it seems like there is a lot of fiddeling involved. Should that be the case, or is that indicative that I’m making mistakes while solving these problems?