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In mathematics, the symbols represent things with clear and precise meanings. My question is regarding the experience of reading/doing mathematics.

When you are reading some piece of mathematics, is the symbols alone enough for you to understand it? Or do you read out the symbols in your head like when reading an ordinary article on the web? Or maybe represent them with some visuals inside the head?

I mean for example, $\frac{d}{dx}[f(x)]$, is it possible do understand this by just 'seeing' it? Like seeing a red light in traffic means stop. You dont have to go through an inner dialogue saying 'red means stop' therefor stop.

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In your derivative example, the expression is "taken in" as a whole. That's why it is in general important to use standard notation: any deviation will interfere with that process, just like an unconventional spelling would. There is even a small problem because of your use of square brackets. –  André Nicolas Sep 1 '12 at 13:25

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It is exactly the same as it happens with reading text. When reading, you perceive the letters and words immediately, while more complicated sentences may require some work before they become and idea in your head. People better trained at reading and thinking will be more efficient.

It's no different with math.

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