comparing learning math to learning the piano

[ranniks]

https://patrickjmt.com/about/

He says this:

I have been teaching mathematics for over 8 years at the college/university level and tutoring for over 15 years.  Currently I teach part time at Austin Community College, but have also taught at Vanderbilt University (a top 20 ranked university) and at the University of Louisville.

Often times, people are nervous about getting help in math: don’t be!  I tell my students all the time that math is challenging for all of us at one point or another.  My intent is to provide clear and thorough explanations, and to present them in an environment in which the student is comfortable.   mannequinAlthough I do not promise to make someone into an A+ student overnight, with regular help just about every student I have encountered makes significant improvements over time.  Think about learning math in the same way you would learn to play piano or learn another language: it takes time, patience, and LOTS of practice.

Is it true what he says? I believe so. After he said that, I became more confident about understanding math (I want to learn maths for future education and because it keeps the mind fresh and strong).

I believe he is right in what he says.

What is your input though?

I know a lot of people say 'you either get math or you don't', but how about this 'you're either musical or you aren't'. Usually the people who say they aren't musical are the same people who don't want to put in the hard work necessary to become a decent/great pianist.

In my young and perhaps naive opinion, I believe anyone could become as great as Lang Lang or Valentina Lisitsa with hard work and dedication. The amount of time is the only unknown value.

But doesn't the last part say something about learning math and learning piano? Doesn't that mean that someone who was once said to suck at math can achieve greatness in math if he or she puts in the hard work required?

[indianajo]

I can both do math up to the elementary levels of quantum mechanics, and play piano at a lower college level.  I don't see the two studies as being related, except that anatomists report that the same 1/2 of the brain is used in each. 
Some people are quite skilled at mathematics, yet are tone deaf.  A tone deaf person can mechanically learn to play piano, but unless the interactions of the tones do something emotional to him, it will be a very rote performance. 
Furthermore many skilled musicians never excelled at Algebra 1.  I had a little trouble with that one, the idea that letters and symbols meant something that should be studied.  Geometry was much more intuitive for me.   

[outin]

Furthermore many skilled musicians never excelled at Algebra 1.  I had a little trouble with that one, the idea that letters and symbols meant something that should be studied.  Geometry was much more intuitive for me.   

Since it was the opposite for me, does it mean I should have it easier with music? 

Maths and playing music both require concentrated high level use of brain functions, so I guess that's similar. And music theory is rather "mathematic" also. Apart from that just as any other skill they use a combination of different brain areas. In studies musicians' brain have shown specific changes in the acitivity of the different parts of their brain compared to average people. It's the same with high level scientists. There may be common parts, but probably also differences.

@ranniks
Discussion about whether one can become anything with enough work will just take us back to the issues discussed to death in the talent thread...

[chopin2015]

Piano=instinctive/repetition and structure>0.001(repetition and structure)

[maitea]

In abstraction I do clearly see the correlation, at least for me. But is tricky to put it into words.

If you accept the borrowing, both mathematics and music are 'language-systems', just either of them are languages! ok, ok.. I know this isn't making that much sense.. But I see them both as two different systems with their own 'rules' and 'codes'. I believe some people have more problems to get around non verbal systems, whilst other people are very comfortable in them. Practice and time (and a good teacher) make it possible to familiarise and get used to the levels of abstraction required.

On the other hand music is full of maths: half of a string produces it's octave, then fifth...

[dima_76557]

@ ranniks

You may want to read up on "Predictable and Unpredictable Occurrences" and "Random
Phenomena" and see that there is no way to predict the same kind of success for either, even if you exclude certain factors at random.

[bronnestam]

It is very hard to find a person who is genuinely tone deaf. If you really are tone deaf, your spoken language would sound very strange. Most persons I know can speak their mother tongue with a reasonably good intonation, rythm and expression, and that means they are not tone deaf. And this statement does not come from me originally, but from an acclaimed song teacher.

But there is another aspect, and that is interest. People say they are interested in learning maths and interested in learning to play the piano, but then they start and you can see that they are not focused enough. Maybe they try to convince both themselves and their surroundings that they are interested and willing to work hard, but the "hard work" mostly consists of ways to avoid the REAL work that must be done.

Don't get me wrong. This happens to all of us. We say we are interested in this and that, because we think we "should be", or because we think this interest will gain us other advantages (praise, admiration, money, a fancy job etcetera) but in long terms we all fail in this charade, because we have no genuine passion for the topic itself. And then we make up excuses like "I have not talent" or even "I suffer from this disability which obstructs me".

It is human not to be interested in everything. It is also human to make up these excuses, we all do that, but that does not mean they are true.

[dima_76557]

but the "hard work" mostly consists of ways to avoid the REAL work that must be done.

These are wise words. It is not always easy, though, to analyze your own intuition and the intuition of others. It's that feature that made Einstein so great.
1) Many who attempt to play the piano had better follow a thorough Alexander or Feldenkrais course first before they even start touching the first key on a piano.
2) Many who want to learn mathematics really well had better start with a course on mathematical philosophy, because the "solve-the-equation" exercises at school have not as much to do with mathematics as one may think.

A little rant in this context. Just like the "just relax" command that doesn't work when a person is really tense, the trap with the "it's all hard work - my way or the highway" lie is that the ones who sell their "How-to" courses will always fall back on the "it's you who didn't work hard enough, it's not the method" excuse if the results don't come within the expected 10.000 magic hours. Instead, they should have the courage to sell the guinea pigs the most important CD-course of all: "How to deal with disappointment", at a bargain of only $29.95, free shipping included. That can also be learned "if you work hard".

[ranniks]

Instead, they should have the courage to sell the guinea pigs the most important CD-course of all: "How to deal with disappointment", at a bargain of only $29.95, free shipping included. That can also be learned "if you work hard".

I find these words somewhat offending. You are denoting the hard work principle.

I'm sorry, but I strongly disagree.

About 4 years ago people laughed at me when I said that I wanted to become a physician, because I didn't have the foundation for the science subjects. Today I'm ready to apply for medical school and all those people who never expected anything from me are like 'wow dude'. This is a country in Europe FYI and not USA medical schools.

How did I come so far? I worked hard and persevered. If there was any talent/intelligence in me, then no one found it in me 8 years ago, otherwise I would have been ready to apply for medical school back then.

Today I'm smarter, more accurate, increased vocabulary, I write, I play two instruments, I exercise and other things that I really should 'by normal standards' have no time for. Yet I do.

I have hard work to thank for that. Intelligence to me doesn't mean 'look at me I have a high IQ', to me it's 'I've worked hard, and the fruits of my endeavours have paid off, now I can think and read faster, understand things faster and much more'.

And it's definitely true. If it's a genuinely good method (step by step explanation, not going too fast, caring for the student's progress), then it's the student's faulth for not working hard enough.

Someone's definition of hard work might be '2 hours a day', but someone else's might be '6 hours a day'. Note: hard work shouldn't be defined by a number of hours, but if each hour is spent wisely, then yes.

No one has to accept their fate, you can change at any time that you wish. Just because there are people who have failed themselves (this applies to most people who say that you can't do something), doesn't mean that you have to listen to them and follow their experiences.

If someone says 'I work hard' I want to hear 'I have things on my mind until I go to sleep', not 'oh you know, I study like an hour a day or something'.

I want to believe that this applies to math and the piano to. I have a somewhat strong foundation in math now, but I want to go even higher for purposes that will benefit me later in life, but I lack confidence so I want to hear what others think about it. Of course you can critique the 'hard work' principle, but there are ways to do that without offending/being crude.

Another question would be: can hard work create another Bach? I sigh at this question that is my own, because it is a difficult one, because I have yet to see someone do it in the 21st century. My aspirations lay elsewhere, so it's not me who should try, not that I actually assume that I could do it.

If someone devotes his/her ENTIRE life to music, and not only learning musical pieces by various composers, but composing day by day, then I believe that person may very well become the next Bach.

Think about it:

Name: Unknown
Age: 20
Level: classical pianist
Experience: 10 years of music lessons, each day practise 2 hours on avarage.

If this person devotes the next 10*365=3650 days to composing (most of the time in a day, genuinely enjoying himself/herself). It might look like this:

Day 1-100: this sounds absolutely horrible
Day 100-1000: Why can't I get it to sound like difficult classical musical pieces?
Day 1000-2000: It's sounding like Yiruma/Yann Tiersen, is this my 'limit'?
Day 2000-3500: Look at the amount of pieces that I've composed.
Day 3500-3650: Wait, can I even play what I've just written down? Bach is this what you did?

Maybe I'm an optimist, but one who looks at contents of one's hard work too.

[dima_76557]

I find these words somewhat offending. You are denoting the hard work principle.

I am sorry, but that was not my intention. The only golden rule is that if some of a person's needed "talents" are BLOCKED, they should be UNBLOCKED first, otherwise "hard work" will only lead to ever greater disappointment. This process of unblocking may take much, much more time than people realize. I really hope that with time, you will appreciate the deeper wisdom in those words.

[ted]

For me they are different in the sense that mathematics concerns itself with universal, external truth. Art, and particularly music, which is completely abstract, describes internal experience, personal landscapes of the mind. A piece of mathematics has a clear meaning invariant over all human brains, but a piece of music has different meanings for different minds.

Inner experience and imagination probably play a big part in the workings of the actual discovery process of the best mathematical minds, but the purpose of the end product is very different. Algorithmic composition may yet enact the converse and imitate the products of inner human experience, although exactly what "experience", if any, is being imitated, is a rather tricky question. I once wrote, easily enough, a simple heuristic program to compose and play fugues, about one in fifty or so of which I enjoyed more than fugues produced by humans; although that probably says more about the shallowness of my own musical perception than anything else.

[outin]

I find these words somewhat offending. You are denoting the hard work principle.

I'm sorry, but I strongly disagree.

About 4 years ago people laughed at me when I said that I wanted to become a physician, because I didn't have the foundation for the science subjects. Today I'm ready to apply for medical school and all those people who never expected anything from me are like 'wow dude'. This is a country in Europe FYI and not USA medical schools.

How did I come so far? I worked hard and persevered. If there was any talent/intelligence in me, then no one found it in me 8 years ago, otherwise I would have been ready to apply for medical school back then.

Today I'm smarter, more accurate, increased vocabulary, I write, I play two instruments, I exercise and other things that I really should 'by normal standards' have no time for. Yet I do.

I have hard work to thank for that. Intelligence to me doesn't mean 'look at me I have a high IQ', to me it's 'I've worked hard, and the fruits of my endeavours have paid off, now I can think and read faster, understand things faster and much more'.

And it's definitely true. If it's a genuinely good method (step by step explanation, not going too fast, caring for the student's progress), then it's the student's faulth for not working hard enough.

I am not questioning that you have worked hard, but consider the possibility that you always had the tools (talents) in you to be what you are now, you just needed to grow up a bit to really find the motivation to use them to benefit such goals.

Your last statement may be considered equally offending to those who do not have those tools...

[dima_76557]

Your last statement may be considered equally offending to those who do not have those tools...

This and the other topic are so "religious" that there simply can't be agreement. You know why? From what the OP writes, one can conclude that he simply assumes that anyone who does not agree:
1) does not work hard;
2) does what (s)he does incorrectly;
3) cannot claim success.

@ ranniks

About 2 years ago, I was at 12 hours of hard work a day. The result: failure.
After that, and with special help to address underlying causes of my problems, I went to 6 hours of hard work a day. The result: success. Go figure. I have now 6 hours left to do something else, like reading good books, going to a museum or to a concert, etc., things that are also very valuable for my all-round development. Clearly, it was the unblocking that did the trick, not the amount of hard work.

[dima_76557]

Thought I'd just have a look what professional mathematicians say themselves about the problem. One example of colleagues talking. There are plenty of other examples online: How Much Work Does it Take to be a Successful Mathematician?

Summary: Hard work alone is not sufficient is the consensus. Dedication is the keyword. To become really good at it ("achieve greatness in math" as the OP phrased it), it has to fill your mind, even while you play tennis, or while you are asleep.

[ranniks]

@dima_ogorodnikov   

You are making it sound like I think like this: ‘it’s either my way or the highway’, which is not true. It’s not very nice to formulate things about someone and making it seem like he said that.

You are putting words like ‘religious’ out there, not me. I’m simply presenting the formula that I think will most definitely bring you success. There are of course other roads to success. Success can be many things, ranging from being an excellent painter to a great scientist to a great composer to endless possibilities (some small and some larger). 

What I want to achieve with this topic is see if people can tell me any similarities between these two fields and if the mathematician’s quote was true, but in asking that question I knew that it is true what he wrote.

You know, 100 professional mathematicians can tell me hard work will not be the key factor to becoming a great mathematician, but that won’t mean that I’ll take their word for it. The professional mathematician in the opening post certainly seems to think otherwise.

Leonhard Euler was a genius, but you can’t tell me that without hard work he would still be famous.

Johann Sebastian Bach was a genius above geniuses, but you can’t tell me that without hard work he would still be famous.

@ted

Hmmm, you’re getting philosophic, which I like.

@outin

You have the tools. The thing that stands in your way is that you don’t want to look at those tools because you think they are not there. Open your tool eyes and you’ll see them.

For example: if you could play 10 hours piano each day, how would you fill those hours up? Slowly you'll put two and two together and you'll undertand how to most efficientiantly spend your time.

These are all the tools that you have but only need to grasp from within: motivation, hard work, dedication and belief.

[ranniks]

I am sorry, but that was not my intention. The only golden rule is that if some of a person's needed "talents" are BLOCKED, they should be UNBLOCKED first, otherwise "hard work" will only lead to ever greater disappointment. This process of unblocking may take much, much more time than people realize. I really hope that with time, you will appreciate the deeper wisdom in those words.

All is well:).

Talents blocked? But in that sense most people's talents are blocked because they either have doubts/fears/etc.

[dima_76557]

@ ranniks

Do you understand what the underlying problem is with something like piano playing?
There is no scientific concensus about how to move a key. You as a student are supposed to figure it all out for yourself because the best most teachers are capable of is simply repeating what they have learned. If you have specific problems, they often don't know how to solve them, so they just give you yet another etude to chew. You condition your wrong movements and at a certain point, the body just refuses to carry it all out. The teacher's reaction: you either are "untalented" or you "don't work hard enough". If you don't improve by [time frame], they will just expel you from the institute as a lazy a$$.

I was lucky to have found a specialist who can even teach an ape from the zoo how to play the piano, post the results on YouTube and get very rich. He made me do all kinds of things traditional piano methodology frowns upon, but it worked for me. I am free. Do you know that feeling of being completely free to do ANYTHING on the instrument? I can now finally function as expected from me.

About mathematics and working hard: The famous mathematician Grothendieck simply burned out from all his hard work, 12 hours a day, and went into seclusion.

You also have to learn how to enjoy other sides of life, otherwise succes just won't come. And if you have a partner, (s)he will have to accept that (s)he will never be number one in your life. Such is the price you and everybody around you have to pay for your wish to become "good enough".

[outin]

@outin

You have the tools. The thing that stands in your way is that you don’t want to look at those tools because you think they are not there. Open your tool eyes and you’ll see them.

Oh but I was not talking about myself. I have a lot of tools, even if not everything I would like to, but I'll probably have enough to compensate for what's missing eventually.

There are many people who are not that fortunate. There are people who could do all the work possible with all the best tutoring and still it's not possible for them to become a piano virtuoso, a math genious or get into a medical school. Just be glad you are not one of them.

I hope you'll get in BTW!

[indianajo]

It is very hard to find a person who is genuinely tone deaf. If you really are tone deaf, your spoken language would sound very strange. Most persons I know can speak their mother tongue with a reasonably good intonation, rythm and expression, and that means they are not tone deaf. And this statement does not come from me originally, but from an acclaimed song teacher.

Having worked with a junior choir and sat in an adult choir, I disagree.  About 40% of the kids attending junior choir could make their pitch go up and down, but what came out had no relation to the actual tone or chord I was playing. 
And two members of our 20 member church choir emitted similar random tones.  I made it my goal to ensure the one sitting in my section (bass) did not sing with the women or hang over when we were cut off.  I could do nothing for his random tones.  He condition did not seem to diminish his pleasure at "making music", either.  After 12 years of this, I gave up.  He is still singing up there in front. I start listening when the choir goes off and the minister goes on. 
Having had my college physics career ruined by the professional mathmetician's introductory course that all you needed was the right axioms and the ability to prove theorems, I am no respector of that teaching curriculum.  Seeing physical modeling equations worked out by example would have been a much better course of instruction for me.  The fact that the professor found it all so obvious as to not need words to explain it, was not a method of instruction IMHO.  What really ****** me about this course, was that I paid cash for it out of my hard earned lawn mower and truck driving salaries.  I would really have gotten a much better education at the local state school, which was staffed in the evenings by employed engineers and scientists, instead of mathmeticians. 

[bronnestam]

Having worked with a junior choir and sat in an adult choir, I disagree.  About 40% of the kids attending junior choir could make their pitch go up and down, but what came out had no relation to the actual tone or chord I was playing. 
And two members of our 20 member church choir emitted similar random tones.  I made it my goal to ensure the one sitting in my section (bass) did not sing with the women or hang over when we were cut off.  I could do nothing for his random tones.  He condition did not seem to diminish his pleasure at "making music", either.  After 12 years of this, I gave up.  He is still singing up there in front. I start listening when the choir goes off and the minister goes on. 
Having had my college physics career ruined by the professional mathmetician's introductory course that all you needed was the right axioms and the ability to prove theorems, I am no respector of that teaching curriculum.  Seeing physical modeling equations worked out by example would have been a much better course of instruction for me.  The fact that the professor found it all so obvious as to not need words to explain it, was not a method of instruction IMHO.  What really ****** me about this course, was that I paid cash for it out of my hard earned lawn mower and truck driving salaries.  I would really have gotten a much better education at the local state school, which was staffed in the evenings by employed engineers and scientists, instead of mathmeticians. 

Well, I cannot sing either. My pitch also goes up and down, because I don't have the technique. I don't doubt, however, that I CAN learn to sing properly if I just get a teacher. Right now I am not interested in that, though. And I am not tone deaf. My piano playing technique is not that excellent, but at least people use to praise me for "understanding the music".
The kids who "cannot sing" probably are not interested enough in singing. Adults in a church choir who "cannot sing" and still hang there, may be enjoying the company and the activity, but singing correctly is perhaps not their first priority? So forgive me for being stubborn, but I still believe in my theory here.

I took a master of science degree in applied physics and electrical engineering and I did not like maths very much, especially not after having heard the lecturer scornfully reply "but that is elementary!" to the shy questions he got ... I took my exam - after hard and painful work. If I had enjoyed maths thoroughly, I don't think I'd have to struggle that hard. Learning something you love is not painful, it is a pleasure.

[dima_76557]

Learning something you love is not painful, it is a pleasure.

I think that depends on what our end goals are. If you want to "achieve greatness" like the OP says in the indicated subjects, then it is much like being pregnant with an idea you want to give birth to: you cannot be a little pregnant, so you have to accept EVERYTHING, pleasant or unpleasant, painful even, and you have to live with it night and day. For many, the game is just not worth the candle, and it is best to realize that in advance. Not all is pleasant, something may go wrong in the process (miscarriage), nobody can predict whether the "baby" will be healthy, or whether it will win a beauty contest. And even if everything goes well, the burden and the responsibility never end; you have to keep going because the competition never sleeps. This is more than hard work and skills. It's a Choice for Life.

[indianajo]

The kids who "cannot sing" probably are not interested enough in singing. Adults in a church choir who "cannot sing" and still hang there, may be enjoying the company and the activity, but singing correctly is perhaps not their first priority?

the kids that "weren't interested" enough to learn to synchronize pitch on songs, were interested enough to learn all the words.  I see the chorus singing with the New York Philharmonic on television, with folders of scores in their hands.  Are those select singers not interested enough to memorize the words? I was a great boy soprano in the fifth grade choir. Nobody showed me now to match pitch, it just happened.  It just doesn't happen to other people.   Whereas for me, learning to throw and catch a baseball is something that just didn't happen.  It is so intuitive, years of gym class showed me nothing. I was in my fifties before I saw the dynamics of the windup explained on NOVA with how it imparts speed to the ball. I still can't do it.  
About mathematics- those strings of words that make up the axioms and the theorems didn't do anything for me.  The bad grades I got in elementary quantum mechanics because I had no idea you were supposed to transform equations by infinite series were the school's fault, not mine.  Once I transferred to the state college and they would actually show you the mechanics of "math" transforms, I started making A's again.  By contrast, nobody in the physics curriculum mentioned that Einstein thought of relativity by thinking about lights shining from trolley cars going opposite directions. And he thought of general relativity by thinking about what would happen on earth if Jupiter disappeared.  Those kinds of models affect my mechanical brain intuitively, I can follow that sort of reasoning without much help.  I learned this bits of history off of NOVA television, again.
As far a competition, I don't view piano or music in gereral as a competition.  It is a kind of art that gives inherent pleasure, and even more so when shared among like minded people.  The competition comes when people try to prove they are important so they will be paid for their skill.  Rare is the person whose musical skill is worth paying for, IMHO.  Most musicians in modern culture that get paid don't play the piano.  

[swagmaster420x]

i definitely agree with the comment that "working hard" is often an excuse for not "working right" - there are a bunch of times when i'm practicing that I mindlessly play something over and over again because i don't feel like expending the mental effort to focus and actually practice with intent, which requires more exertion, but would take less time. That way, i'm "working hard" because what i'm doing takes more time, so i justify it like that and it sits well in my mind.

[ranniks]

i definitely agree with the comment that "working hard" is often an excuse for not "working right" - there are a bunch of times when i'm practicing that I mindlessly play something over and over again because i don't feel like expending the mental effort to focus and actually practice with intent, which requires more exertion, but would take less time. That way, i'm "working hard" because what i'm doing takes more time, so i justify it like that and it sits well in my mind.

I do not agree with this at all. It assumes that you know what people think when they're working hard.

[kakeithewolf]

I started early in math. I picked up an algebra book, read it, and understood it. I picked up a geometry book, read it, and understood it. I picked up a trigonometry book, read it, and understood it. Then I picked up an calculus book, read it, and understood it.

By third grade, I had a basic calculus understanding. By sixth, I could do triple integrals.

That's how I learned math.

I started late in piano. Started at 19, with a keyboard. Played it, and got to the point where I could improvise decently. Sometimes I make improvisations better than my actual composing, which is sad, because a piano alone compared to a vast array of instruments shouldn't be a competition at all.

Probably been doing this for about a year. I can't read sheet music, I can't play even a single piece (not ever something like Mozart's first piece). The extent of what I know is the ostinato of Bach's Passacaglia and Fugue in C-Moll, probably the first ten seconds of the Goldberg Variations, a bass line from a generic video game piece, six notes of a random electronica song (and those are vocal notes), and about 20 seconds from yet another video game piece.

That's how I learned piano.

I put the same amount of effort into each, invested the same kind of time commitment, and read plenty on both. I know math, I don't know piano.

So do I think the two can be compared? No.

[ranniks]

I started early in math. I picked up an algebra book, read it, and understood it. I picked up a geometry book, read it, and understood it. I picked up a trigonometry book, read it, and understood it. Then I picked up an calculus book, read it, and understood it.

By third grade, I had a basic calculus understanding. By sixth, I could do triple integrals.

That's how I learned math.

I started late in piano. Started at 19, with a keyboard. Played it, and got to the point where I could improvise decently. Sometimes I make improvisations better than my actual composing, which is sad, because a piano alone compared to a vast array of instruments shouldn't be a competition at all.

Probably been doing this for about a year. I can't read sheet music, I can't play even a single piece (not ever something like Mozart's first piece). The extent of what I know is the ostinato of Bach's Passacaglia and Fugue in C-Moll, probably the first ten seconds of the Goldberg Variations, a bass line from a generic video game piece, six notes of a random electronica song (and those are vocal notes), and about 20 seconds from yet another video game piece.

That's how I learned piano.

I put the same amount of effort into each, invested the same kind of time commitment, and read plenty on both. I know math, I don't know piano.

So do I think the two can be compared? No.

I beg your pardon, but one case does not conclude any study. You would need more results to conclude the last part of your post. But I think you meant yourself in this case.

[j_menz]

All work and no play makes Jack a dull boy.

And dull boys do not make great pianists, nor great mathematicians.

[kakeithewolf]

I beg your pardon, but one case does not conclude any study. You would need more results to conclude the last part of your post. But I think you meant yourself in this case.

My point was not that everyone applied to my case. Quite the opposite. I implied my case does not apply to everyone else, and vice versa.

Can the two be compared? In some cases. My point was this: Can the two be ubiquitously compared? In a word, no.

[thesixthsensemusic]

https://patrickjmt.com/about/

He says this:

Is it true what he says? I believe so. After he said that, I became more confident about understanding math (I want to learn maths for future education and because it keeps the mind fresh and strong).

I believe he is right in what he says.

What is your input though?

I agree it has a lot in common. Especially with algebra: take a very complicated equation with a number x in which you have to identify x, which appears 10 times.

In math class you will be taught how to break down the equation in smaller bits and bring it down to a simplified form in which the x appears only once, so you will be able to identify it.

Piano playing is similar in having a huge complicated task ahead of you, like learning a Chopin Ballade or a Beethoven sonata. You go and break it down and eliminate many hurdles on the way to being left with only one task: playing through the piece you learned in order to polish it.

But just as in math, before you can solve a problem, you need to analyse it and actually turn any problem into an equation in the first place.

I compare it with sight-reading through a piece, analysing the spots that require, the most work, and doing the same with all chunks of these passages that need special attention. Breaking them down into bits small enough to handle in one go after a few repetitions.

Also, music is written according to structures and based on motifs of any kind, wether in rhythm, harmony or melody or both. It is a set of more or less complex algorithms. Your brain processes them unconsciously, which explains why it;s easier to play a part of a piece in one key, perhaps a major one, whereas a highly similar passage occurred in another completely different key earlier on.

And as with math, only methodical practice in which you actually decipher stuff and comprehend what is going on, will be able to get you further in the end.

But I don't think one has to be good at math in order to play the piano well;

Plenty of good music school students I knew when I still had lessons there, followed curricula at their regular school that emphasised social sciences and languages.

Both math, and language skills are based on deduction and logic, but they are expressed in numbers, or in linguistical terms, and one could IMHO compare music to language skills (text analysis and dialectics) in a similar way as done with math.

Throw in the notion of cultural studies, history, and the social skills connected with playing music with others (like solving disagreements and interacting with one another in making it sound better), the physiological side of ergonomic body movement when learning a particular instrument, be it with the fingers or your breathing as with singing and wind instruments, and music is basically combining all branches of science.

That's what is so fascinating about it to me, I guess.