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My teacher has same opinion as you do, scales and arpegios for warm-up and Hanon exercises for well, exercise. And I believe he'd also include playing simple pieces like the Minuet as a warm-up.

I dont think i said anything contrary to that. Cold stretching, and light stretching as a complement to a warm up or after the practice are 2 different things.

For your second question, most of the technique exercises prepare you for basic but not advanced music. As you grow as a pianist you might not find the most rudimentary exercises to be as useful anymore.
For scales, pieces in the repertoire rarely are simple runs that begin and end on the tonic. Something I do occasionally is to play scales starting and ending on each note of a key--sometimes it requires fingering you're not used to. As you get to 20th century repertoire, you should be familiar with pentatonic, whole tone, and octatonic scales. There are lots of more advanced kinds of scale techniques (Busoni's first book of his 10 Book Klavier-Ubung documents a great number of these).
I think basic arpeggios don't really prepare you for a lot of advanced repertoire. In advanced repertoire, you see arpeggios that require wide spans (Chopin Op. 10 No. 1), four fingers or five fingers per hand position, double notes (like thirds and fourths in Liszt's "Jeux D'Eaux" or seconds in Ravel's "Ondine" or even arpeggios that are alterations of chords and single notes which crop up in Busoni's Elegies), counterpoint in one hand with an upper or lower voice, and also thumb-centric arpeggios that you split between hands while the other fingers play melody and bass that you might see in Mendelssohn, Schumann, and Faure, among others.

I think as you advance the type of exercises or technique-focused practice you do will depend what you're learning and what you would like to learn. I generally take a day a week to include a little practice on configurations from pieces I would like to one day play--not trying to do them at tempo but to play them in a relaxed way, getting used to their challenges. I'm learning Scriabin's Op. 11, so one day a week I visit the pieces I know will be challenging for me (octave technique, chords, leaps, melody and accompaniment in one hand, double notes in both hands, etc.), practicing what I know I have to work on in order to perform the piece.

Yes and the statement that i was in disagreement with is that there is no need to do a "thorough" warm up before doing some light stretching or extensions of the fingers and hands. I did not say that one has to execute some form of heavy stretching right when starting to play. Even though i think that some well chosen exercices can actually replace to some extent the warmup. And to be honnest for most beginners or intermediate students, who play 1 hour or so, i dont even see the need for a "thorough" warm up. Some low level playing and for me some flexibility extensions are quite sufficiant. There is no need to overengineer the subject.

Every physical activity has it own set of requirements. Warming up for a short race is not the same as when warming up for a 20k. Warming up for climbing is different than for biking. Piano playing is nothing like running or other various comparisons i have seen everywhere. Except for advanced pianists who play at high intensity, piano is a low key activity. Cardiovascular level is a little higher but playing a couple of hours is not like running 10k. It does not mobilize muscles at the same level and therefore in my view a lot of the studies made for high intensity sports are barely applicable, if any. Most frequent injuries when they occurr are related to repetitive stress or poor technique when practising. So the type of stretching we are talking about and its effect here is completely different from the stretching a runner would do.

That said, i think we all are giving advices and copying various studies sometimes contradictory, me included, when most of us are not experts in the area (except of course some who are experts in nearly everything). I think it is a modern deviation, based on the so many data now available on the net. So that part i will amend and just say that my point of view is the result of my personal experience, injury free (at least major long term injury) and that what i say has worked well for me. Others can do, of course, as they wish.

My warm-up routine is brief and is for mental purposes only. By the time I sit down to practice, I will already have been doing many activities as part of my normal, daily routine that serve to get not just my hands, but my entire body 'warmed up.'

My warm-up routine at the piano is a (one) major scale, its relative minor (nat, harmonic, melodic) and the associated arpeggios with the major and minor scales. Sometimes I add I, IV, V7, I in all three inversions. I do an abbreviated warmup when I go to my lesson, where I'm playing a different piano and need a minute or so to adjust my ear and touch to that piano.

the result is: there are many different warm-ups and many talk about a mental warm-up.
The question: what is a mental warm-up? This is something I really find interesting.

I really like minuets. Not many people dance it anymore but I think people should.
What I disslike about certain kinds of warm-up is that it doesn't really ask you to feel the bodily movements involved. You might play with too much force or the opposite. The western tradition as I understand it is: exercices first and then pieces.
Question: are people who teach piano often assuming that the student find it easy to relate exercices to the pieces.
I am refering to this: https://youaut-aknow.com/generalization-of-skills/

Apropos of warming up prior to playing, I remember watching Garrick Ohlsson being interviewed about Chopin interpretation. There was a grand nearby, and he decided to demonstrate something from a nocturne, and went to the piano. Immediately afterwards, he apologized that his fingers weren't warmed up, and he couldn't play it properly.

No - he didn't play any wrong notes, nor were there unwanted accents or rhythmic vagaries. I think it was just that he didn't voice it quite the way he wanted, because his fingers were too 'stiff', though hardly anyone would have noticed anything amiss.

Which is to say, depending on your level and what you (are trying to) play, how - or whether - you warm up is different from one student to the next.

For instance, I'd make a hash of Chopin's Etude Op.10/12 or Mendelssohn's Rondo capriccioso if I tried to play either without having warmed up with other stuff for at least ten minutes (which is why, in my recitals, I always program them last, or nearly last). On the other hand, I could play something like Liebestraum No.3 within a couple of minutes of warming up, say with the Goldberg Aria.

And experienced pianists like Ohlsson can perceive 'problems' with their playing when they haven't sufficiently warmed up, even if it's largely unnoticeable by others.

No, I don't think so. Exercises are not meant to be applied to pieces directly. When you encounter a difficult passage in a piece, you work right on that passage, maybe with some rhythmical and articulation variations, using some technique, and in fact no more general exercises are needed for this.

Exercises, on the other hand, are meant to work on more fundamental level of technique, developing and polishing many micro-motions that would later be unconsciously utilized in how you play. But an exercise must be truly mastered in order for that to happen. Only polished and deeply internalized micro-motions get transferred into general playing. That's why it's important to work on exercises of appropriate difficulty and work till final victory (at your stage).

why should you not relate fundamental technique to the pieces you are playing? I find it very stupid not to relate fundamental technique to the pieces you are playing. If you can just learn technique by playing pieces then technical exercices are unimportant and a waste of time. You are confusing me!
Or are you saying that people should be able to unconscously relate the technichal exercices to the pieces? I'm sorry to say that it does not work for many of us!
I have issues with generalization and many professionals talk about it. Why do you say that they are wrong? Why are we wrong?
WHy should all people be "Normal" people without this problem? Perhaps you are "normal" and think everyone is like you, right?

Piano lessons are only for people who can relate exercices to pieces unconsciously and who can learn music without using the ears, ie onlyt using finger memory. Most lessons suck! Many teachers need to wake up and see reality! Most music teachers refuse or cannot see reality!
No wonder many quit piano lessons!

Tip: Using the word STUPID when disagreeing with someone's opinion is not a good way of building forum relationships.

I have the right to think it sound stupid. It is my opinion. You have your opinion and I have mine!

Dude chill, take a pill or something :))

I've had no intention to insult you in any way. Nor to say that fundamental technique is unrelated to pieces, nor to say that you are not "normal" because you have difficulties. It's absolutely normal to have difficulties, I have them, too.

My thought was that the reason behind the poor transfer of exercise's skills to pieces is unfinished state of the exercise. The more polished an exercise is, the more skills (I call them micro-motions) get transferred. By the way, the same concerns repertoire pieces. This transfer happens unconsciously, it's based on how our brain chooses the optimal path to motor neuron through neural networks. If I understand that process correctly (I've written some things about it here), only the unconscious transfer leads to optimal neural connections, if you start to interfere in that process consciously you most likely over-write the networks instead of letting optimal connections to appear naturally.
Although I may be wrong, it's my hypothesis. But practically I see that it's true. You just need to work on polishing your stuff and wait patiently until your brain does its job.

You are right: you are far too clever to need lessons.

You should teach yourself to become a concert pianist, like Víkingur Ólafsson (though he had good teachers).

Here, pour yourself a large measure of the finest vodka on the planet, and chill with this:

What I have been tought is: just do the exercices!
This has been problematic as I was never tought how I should do the exercices, ie what to listen for and how I should move arms, wrists and fingers. This I think is what you are talking about as well.
Also, why do I bring up "relating pieces to exercices"? In pieces you don't always play the same thing as in the exercices. Some people think that if you do the exercices then you will automatically know ho to play the pieces. It is not always true. You need to learn how to play something that is not the same as in the exercices. Some people think the technique in the exercices is exactly the same as in the pieces. It's not always true. To me it is different situations even if they are simmilar. People need to work a little extra with me on this. People are often better at generalization and can apply what they learned to a different situation.

Yes, it's an important thing. Many people play exercises in a drumming manner, and it's useless. Exercises must be played with full focus on sound quality, just as pieces. It's crucial to maintain nice tone when playing an exercise and to listen to and to avoid the subtlest rhythmical and dynamical disturbances, only in this case an exercise brings its full benefit.

Most exercises can be played in several ways technically. I think it's greatly helpful to try to play the same exercise using different techniques, sometimes it's an eye opening experience. But certainly more time should be spent on techniques that you feel less comfortable with.

For example, in the beginning you may play the 1st Hanon's exercise using finger technique, not helping yourself with the wrist and arm weight much, trying to keep working finger parallel to the key. Then play this exercise doing circular motions with your wrist. Then play it with your fingers like walking on the keys using arm weight. Then play it using some ultra-finger technique with hand in slightly adducted fixed position. Then play it in ultra-arm weight manner, not moving your fingers much and pushing keys mostly with your shoulder. Finally play it in some Taubman-like manner, using forearm rotation for every keystroke.
I promise that if you will be patient enough to go through that cycle every day for one month you will understand much better what piano technique is all about. And it will probably change how you play generally.

Exactly.
I think most teachers don't talk much about listening. This is true for many singing teachers as well.
Many, I guess, take listening for granted ie. you will automatically know what to listen to. This is why just singing or playing scales never really helped me. I mean, I love scales a lot but only if it's done by using the ears. Now, many teachers are really good at this so not all of them are bad at this.

One of the biggest issues in piano playing has been this: I just have to understand the music.
I always search for patterns in the music. If I have knowledge of theory I use it but it's not a must. I am not talking about a theoretical understanding even if that could be a part of it.
Let's take the first movement of Für Eise as an example. Most people who learn this don't focus on how it i beginns with Am-E7-Am. It is much easier to play a pieces if you know the patterns involved. Many people I guess just learn by focusing on muscle memory. I find that my muscle memory is not that good and that I need to play by ear as well. I would perhaps play an accompaniment with simple chords.
Do tradional piano lessons focus too much on muscle memory and too little on playing by ear? Am I "weird" as I cannot play without trying to understand the music? My thinking is that most students stop taking lessons as they need more playing by ear. It's hard to play without any understanding.

For learning a piece, you list knowing patterns, muscle memory, and ear, but you've left out learning by reading the score. You don't need to understand the music, or have heard it, to play by reading the score.