Twitter: I want to get better at maths, to make up for lost time in college. Who/what should I read?
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Replying to @tommycollison
This book was important to me: https://www.amazon.com/Problem-Solving-Through-Problems-Problem-Mathematics/dp/0387961712 … Problem-solving was how I got better at math. _Stopping_ reading proofs, and instead trying to figure them out was also incredibly important (& incredibly time consuming). YMMVG.
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Replying to @michael_nielsen @tommycollison
But trying the proof directly can work for relatively "easy" results, based on a few manipulations and one, as much two clever ideas. But many results have been the product of lots of brilliant ideas, work, etc. If you're a beginner in the field, you can hardly distinguish.
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Replying to @davidsuculum @tommycollison
Yes. There were many results where I failed, or where it took repeated attempts over months or years. There are a few results where I succeeded after more than two decades.
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It also, I might add, makes "reading" incredibly slow. I'd often be stuck for a few hours trying to prove some lemma or another. Eventually I'd give up and move on (surprisingly often, though, I'd later see the proof very quickly).
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The result was that 1 page per day was reasonable progress through a book that I really wanted to understand.
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Sorry to write so much here! One last tweet: I wrote more here: http://cognitivemedium.com/srs-mathematics , here: http://augmentingcognition.com/ltm.html , and here: https://news.ycombinator.com/item?id=666615 But those strategies all need to be secondary. Being stuck & trying stuff is by far the high order bit.
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Replying to @michael_nielsen @tommycollison
Really appreciate your sincerity, Michael. I should certainly remember your comments when I'm stuck with something for a lot of time. BTW, I like how you explain stuff, your notes on gauge theories were illuminating.
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