To start, a theorem is a mathematical statement that can be proven. It has some 'hypotheses,' which is not the same meaning as the scientific sense, but instead is conditions that are assumed at the start. Example: "Let V be a vector space, and let X be a proper subspace of V."
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Becoming good at math means being able to identify the setup work that needs to take place. This is not a special skill. Much like any professional, if you become good at something you know how to get started, whether it's starting a software project or a new patient record or
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But great mathematicians can see multiple steps into the future in this process, to intuit connections that are not obvious. Throughout my math undergrad, I viewed math as a mostly mechanical, procedural process. Which made sense for my discipline (scientific computing).
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But as I shifted more into formal analysis I began to finally understand proof. It took a mental maturity well-beyond my undergrad years to get there. It really took me until my late-20s. And I'm still learning that process.
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When I took Real Analysis at RPI I finished with a C, partly because it was my last semester and once I got a passing grade I stopped going. When I re-took the class at UVa, I had much more maturity and a finer grasp of proof-based math and got an A+.
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