Think of it like this:

You can use a tennis ball machine to measure how far away a house is by firing the tennis ball at a constant velocity, timing how long it takes the tennis ball to come back to you, multiplying that time by the velocity, and dividing by 2 (since you measured the distance for a round trip). This works pretty darn well for measuring the distance to houses.

But now try this same trick to measure the distance to another ball. When your measuring ball hits the ball you want to measure, it doesn't stay resolutely planted in the ground like that nice friendly house. The energy from your measuring ball bounces the ball being measured off into the distance. Even if you could get your measuring ball to return, the ball you measured isn't in the place you measured it.

Replace that tennis ball with a photon, and you have the basic picture. There's no such thing as passive observation. Measuring something interacts with that thing. Conventional measurement is like in the case with the house, the thing being measured is so much bigger and more stable than the thing we're measuring with that the effect is negligible. But once you start trying to measure something on the same scale as your measuring tool, the ensuing chaos makes it basically impossible to get useful measurements.

Every road leads to Plato's cave

My teacher had a good comparison for this: observing macroscoping reality like we do microscopic reality would be like throwing a car at another car to measure its speed or position. Obviously you alter the course of events this way.

Fortunately light doesn't do much in the macroscopic world, so we can use it to observe stuff.

Not quite - observability in quantum mechanics is about the event producing an interaction that could potentially be measured, regardless of whether we actually attempt to measure it. By interacting with other things the superposition is collapsed and we can determine it's current properties, but it's still the "real" behaviour of things, because we can only determine things behaviours from their interactions with other things - not knowing what they do when left alone isn't just about there not being a human around to interacts with them, but about there not being any other particles - no atoms, no electrons, no quarks - for them to interact with either.

Great distinction.

The big problem isn't that the math is hard, or that's often impossible to visualise. The problem is that a whole bunch of charlatans intentionally misinterpret what "observing" is in QM, to make money off of gullible victims.

To elaborate on this, the Schrödinger equation, which describes the dynamics of a single particle, is a wave equation and hence a lot of classical intuition from e.g. electrodynamics can be applied. It is many-body systems, i.e. systems composed of many interacting particles, which is not only mathematically complex but can also defy classical expectations due to emerging phenomena, etc.

The problem of quantum mechanic is that the physics it shows us is not intuitive, and it sometimes breaks other laws of physics.

Quantum intrication means that information travels faster than light for example. Counterfactuality also breaks causality.

It's not the maths that are the problem, it's that it doesn't make physical sense in the world we currently understand. And the equations explain nothing. They merely describe a a world that doesn't make sense.

Quantum mechanic is like having a machine from the future that does cool things, but you don't understand how it works. It's like people did chemistry before they understand what chemistry was. We do uber cool things with it, but it is a spotlight on our ignorance at the same time.

You have to think of it as "Waves + extras". It then, suddenly makes logical sense.

Unless you observe the double slit experiment, and then suddenly it's particles again

If you mean that we make cities and culture and science with our minds, then yes.

If you mean we control reality by squeezing our butt cheeks real hard and wishing for parking spaces, then no.

Most of the time I hear this, it's stupid people promoting the second.

The term they should have used from the get-go is "measurement" instead of "observation". Humans will always tack on mystical mumbo jumbo if given a chance, muddying up the waters for us laymen trying to learn, and "measurement" sounds much more neutral to me.

God doesn't play dice, he surfs, got it.

What would oceanic philosophy be then? Dilute everything?

The various interpretations help in processing the math, but isn't the same as understanding - there are a bunch of fundamental facts about quantum mechanics that we just don't understand, even though we know the elements exist, that they happen, and even how we can take advantage of them.

The difference between quantum mechanics and other high level theories like relativity is actually quite large, because the higher level interactions all derive from quantum level states and interactions. At the point where question marks really start popping up (weak and strong nuclear forces, gravity, dark matter &/ energy) it's almost always a matter of quantum mechanics getting involved and being weird.

My quantum mechanics professor started our first lecture with "if you think you understand quantum mechanics you do not understand quantum mechanics", because there are still some really big question marks around our understanding of it. Especially what in the fuck spin actually is.