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This is very general question I am asking here. But I think it really needs to be addressed. Whenever I come across a new concept in mathematics, I try to understand it by searching on the internet. It is always the case for me that when I do find some stuff about those concepts, many times they are elaborated heavily with complex notations and highly formal language.I think a person with some/no mathematical background can never get it. Thankfully there are blogs/sites which explain it in more natural language help me not only understand those concepts but also show the beauty behind those mathematical concepts. Don't you think that extra formality and over usage of symbols really drives away people to go deep into those concepts and hinders the progress of mathematics as less people get involved. No branch of science has progressed with just few peoples getting involved. It is always seen that as more and more people get involved, more progress is done. We have seen that open source softwares evolve way better than proprietary softwares.

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closed as not constructive by Alexander Gruber, Will Jagy, Thomas, Zev Chonoles Feb 24 '13 at 22:08

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Try proving something without formally defining it, and you'll see why. –  Alex Becker Feb 24 '13 at 22:04
It does not have to be too formal. It has to be just formal enough. –  Trevor Wilson Feb 24 '13 at 22:07
1) Whenever I stumble upon a new Swahili word, I google it and am unhappy because it usually appears in pages full of Swahili words I don't understand. - 2) Mathematics is not proprietary as you see from finding explanations freely available online or in libraries. In fact, math lives from open collaboration. When was the last time you read through the linux kernel sources line by line? (Math is very userfriendly, it is just picky whom it considers a user) - 3) "We" mathematicians try to get as many people involved as possible, but must shrug off before mastering finitedimensional calculus –  Hagen von Eitzen Feb 24 '13 at 22:10
@MathGems: As written, the question is basically a rant. In fact, the FAQ specifically says not to ask questions of the form "I’m curious if other people feel like I do". If the post is rewritten in a calmer tone so that it asks a proper question, I would be happy to vote to reopen. –  Zev Chonoles Feb 24 '13 at 22:23
@ZevChonoles I don't care about "gaming the system" or whatever, but it does seem to me that one should either think a question worth answering or not, and only answer it in the former case and only close it in the latter. –  Ben Millwood Feb 25 '13 at 0:34

2 Answers 2

To steal a good alliteration from Gauss: the notions of mathematics require intuition; the notations of mathematics require precision. If someone isn't able to understand (much less formulate their own) precise logical statements and arguments, either in symbols or in "jargon", they aren't going to be contributing anything to mathematics research. There's no reason that just getting "more people" involved will help mathematics (or any other field for that matter).

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Would the downvoter like to explain their downvote? –  Zev Chonoles Feb 25 '13 at 18:49

It's true that we can talk about math informally in order to gain intuition and understanding. We can discuss examples. We can explain how we think about the math.

But when it comes down to it, everything still has to be stated precisely, and for this, formal language is necessary. That's the beauty of mathematics - everything is rigorously defined, to infinite precision. The exposition by itself is not enough. How can you prove that two lines intersect only at exactly one point if we don't define what a line is? We can say intuitively that it should be that way - but we can't prove it until we say what exactly a line is and what exactly it means for two of them to intersect.

You are probably frustrated because the internet is not, in general, a very good place for motivated mathematical discussion, especially in lower level disciplines. When people google about math, they're generally searching for homework solutions, so the solutions, without much explanation, tend to be what are most commonly available.

Books are much, much better for this. Many people who write math books try to motivate the subject and provide helpful exposition on how to understand the complicated ideas they present.

It takes more patience to read a math book than a short article, but that's just the name of the game. Math is hard, and it's silly to think that there should be some presentation which allows anyone to immediately understand it without careful thought. For that reason, math will probably never be as popular as watching TV or listening to music. But, that's just how it has to be. I still like it.

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+1 for your mention of homework solutions. It is there where an unnecessary abundance of formal language is found (quantifier bloating, rightarrows and therefore symbols for inference, ...), even when good mathematical writing would add a lot of prose (though keeping in the back of ones head that an undisputable formal translation is available) –  Hagen von Eitzen Feb 24 '13 at 22:15

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