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Check out graph theory and discrete mathematics. If you like coloring in circles and drawing lines to solve problems, I would highly recommend looking into that and computer science. When I am “doing Awesome Easily Distracted By Beer And Guitar Shirt. I have a cup of coffee and a pen and paper, maybe a collaborator,. Maybe a chalkboard if I am lucky, then I am doing nothing like what you described. I am saying things like “well we can make this blob behave like that thingy, so we can assume that all thingies are essentially blobs plus a constant amount of noise” or whatever. This is because I have developed, over years, intuition for the things I study (combinatorial objects, computational problems) and, over months, quite deep intuition for my current focus.

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However, when I come to write it down, I can’t just write down my intuitions. This is partly because intuition can be wrong (and good problems fight back), but also it’s a bit like reproducibility. I have proof in mind that I am convinced works, and I need another. Mathematician Awesome Easily Distracted By Beer And Guitar Shirt the proof in their own minds. So I need to write it down in an unambiguous way. It’s sometimes a bit tedious but it’s also useful for more intuition building. The stage where you have to prove completely trivial theorems, which. You already learned at school, is only a short temporary stage. Beginning of learning rigorous proof-based mathematics. And this early stage of where you write out proofs for trivial theorems in full detail is just there to teach you what full proofs really look like. It doesn´t last more than a few weeks.

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