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I'd argue that any attempt at understanding mathematical notation universally will fail. Different fields and different sub-topics and different authors have va
by gspr 6y ago
I'd argue that any attempt at understanding mathematical notation universally will fail. Different fields and different sub-topics and different authors have vastly different conventions, for good reason.
Sure, one can perhaps expect that something that uses an integral sign shares some properties with ordinary integration of real functions, but to really understand what the notation entails, one really has to study the underlying material.
I feel that what you're asking for is kind of akin to wanting to read a novel in a foreign language using only a dictionary of the 10% most commonly used words of said language, with each entry resolving only to one meaning of the word.
- maxmcd 6y agoSurely the optimist would take this question to assume that someone is interested in expanding their math knowledge and might not have an issue getting exposed to more math. I think your answer is akin to telling a french tourist that they shouldn't try and learn basic conversational french because they could never hope to understand the complexity of the complete language.
- gspr 6y agoI understand your point. I just suspect, perhaps wrongly, that people asking the question on HN may be inclined to base serious stuff on their tourist's understanding of French. There's a place for tourist math, but it can be dangerous when misused.
- binarymax 6y agoSee the book recommended by @kasbah above - one of the best parts of that book is that this ambiguity is addressed front and center, and the reference is broken up by domain...it’s the best attempt I’ve seen and works very well.
- downshun 6y agoI've been working on some of these ideas. Even if you had mathematica-grade program implementations of all mathematical objects and properties, you can't get over things like "you can't solve the quintic this way, dummy!" Or "no, you can't have a good visual of R^n in a 2D screen!" Etc. That doesn't mean all hope is lost. For now, I won't say more.