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I used to struggle a lot when I first started studying mathematics seriously as part of my Computer Science degree. I could never understood how people ever cam
by chrisandchips 6y ago
I used to struggle a lot when I first started studying mathematics seriously as part of my Computer Science degree. I could never understood how people ever came up with proofs for problems that seemed completely abstract and foreign to me. Even the very notion of proving a theorum or time complexity itself seemed alien.
It was a painful journey, but in the end I found that it comes through the following:
Practice, a lot. I don't believe that anyone pulls solutions out of thin air. When tackling an abstract problem, people draw on the similar things that they do understand and then leap to the solution they're chasing.
Study the field you're trying to understand. Read over as many examples of solutions to abstract problems, and really analyze why they work. Try to solve your own problems, using what you've observed in those ones. Hop between these two until you start to close the gap more.
In reality, you're always going to make lots of mistakes and the practicing is never going to end. Its all part of the learning, and that's a journey that shouldn't stop.
If you're interested in this field of Mathematical Logic, I suggest you listen and read about it as much as possible, that you try to pursue problems you are interested in, and that you collaborate and discuss things with others. This constant doing, in small quantities but without getting up, will eventually help you see the abstract problems for something that is much more relateable.