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During my Masters degree, I tried doing a proof with a pen and paper in my hand. This took me days to figure out. Today, I saw a proof and began to follow each step with a full comprehension of what was done without having to solve.

This made me remember how I started learning how to sight-read/sing. Symbols such as crochets, quavers, mimins, and semibreves were not easy to read. Things changed after some time.

My Question: Will there ever be a time when reading mathematics textbook will be like reading from the music sheet?

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    $\begingroup$ Well that depends on the textbook. $\endgroup$ – EuxhenH Mar 25 at 15:38
  • $\begingroup$ Depends on the mathematics too. Conventions, terminology, and notation all change so drastically between some disciplines. It can be like training as a classical pianist, then trying to read drum notation, by which I mean, much of it's familiar, but you couldn't really make head or tail of it without a bit of study. $\endgroup$ – user759562 Mar 25 at 15:41
  • $\begingroup$ @EuxhenH: I guess you have a point. In music, it also depends on the music sheet. $\endgroup$ – Omojola Micheal Mar 25 at 15:42
  • $\begingroup$ @user759562: True! True!! I observe that I do a series of practice to sing from the sheet successfully. Can we do that to maths, too? I'm finding joy relating Maths to Music while learning. $\endgroup$ – Omojola Micheal Mar 25 at 15:44
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This should probably be a comment, but it's too long. When I was in high school, I played the clarinet, so the sheet music I saw was usually the clarinet part of a piece written (or transcribed) for bands. I had no problem reading and playing that music.

But I've also seen the sheet music used by the conductor of the band, showing what every instrument is playing. That's obviously far more complicated to read.

On the one hand, I couldn't imagine sight-reading a conductor's score in the way I could sight-read a clarinet part (though I suppose experienced conductors develop that ability). On the other hand, studying the score would give the conductor a genuine understanding of the composer's ideas and how they fit together, an understanding that I could never get from the clarinet part alone, and that I only occasionally got after hearing the music several times in rehearsals.

What does this have to do with mathematics? When reading mathematics, one wants to get genuine understanding, analogous to what a conductor gets from the full score. The mathematical analog of the clarinet part would be a very superficial understanding, perhaps enough to do routine exercises but not much more. So it is reasonable to expect that learning mathematics would require work similar to studying a conductor's score. In particular, it's unrealistic to expect to learn mathematics by "sight-reading".

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  • $\begingroup$ +1. Wow! That was great! I have, indeed, learnt so much from your answer. $\endgroup$ – Omojola Micheal Mar 26 at 11:54

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