In many locations, among others the Wikipedia article of the battering ram and this post on this very subreddit, I see it mentioned that battering rams were used to break down walls, in addition to gates.
While I have no problem accepting the fact that stone isn't very flexible and will crack when struck very hard with a heavy object, I have my doubts that a 'normal-sized' ram (like the one seen in this Youtube video) would be able to break through or significantly damage a 15 meters high, 3 meters thick wall in any realistic time frame, that is to say: before the ram itself, in spite of any protection on it, is destroyed by the defenders. I'm not referring to any specific wall, here, just extrapolating dimensions from looking at the Wikipedia article of known dimensions.
Of course, there were monstrosities such as the ram of Hegetor, but given the ridiculous dimensions of that thing, I wouldn't necessarily call that a standard ram — although of course, I could be all wrong on my assumptions on the size of a standard ram.
So, to reiterate my question: could a standard ram really break down a fortified wall? (Or for a secondary question: are my assumptions of the dimensions of walls and rams anywhere near accurate?)
Go out in the yard, pick a stone about the size of a human head and a normal hammer. Start hitting the stone with the hammer in almost exactly the same place. I've done this myself. And I'm not talking soft limestones and sandstone and shales and that wussy stuff. Red granite, some of the oldest pieces this planet, I have cracked it apart. Now to make it easier, get yourself a chisel. Does it matter how large the stone is to the end result? No it doesn't. The repeated impact of even a small object will eventually crack the stone. This is exactly how you chip a tiny sliver of planet earth to get the stones to stack up as your wall in the first place. Whether that sliver of planet Earth is 50 tonnes or 50 kg or 5 kg. And you can't really get a bigger piece of stone that the crust of the planet right? So that should tell us that the size of the piece of rock worked on is irrelevant to the effect of using concentrated force against it. We are not trying to push the whole thing over, this is not tipping cows.
Gutta cavat lapidem after all.
The next thing to realise is that a wall is not a solid mass. It's not poured concrete with rebar. It consists of lots of small pieces that are mostly held together with gravity and friction of cunningly crafted stone. Especially true for very large and thick walls where we save cost and effort by filling the middle with sand and smaller rock. This is why mining and sapping is so effective. Remove enough support in one go and you get a cascading failure as the wall falls in upon itself of it's own weight. Doesn't really have to be in one go either, it's just more effective that way. Also, you can set it up so you aren't present for the whole tons of stone debris crashing down part.
Obviously not all walls are created equally. Depending on where you are and how it is constructed various methods may be more effective and practical to enact. The aforementioned mining/sapping is one of the more effective ways. But all walls are subject to the same fundamental truth, chip away at the wrong part, the base, and it all falls down eventually. This holds roughly from the invention of walls to keep out nosey neighbours and their cows to the effective deployment of gunpowder weaponry and "siege revolution" that meant high walls were suddenly a liability and not a benefit and we start building low thick walls, ideally without a base to be attacked, i.e. bastion and later so called star fort types.
So in short, yes, battering rams can bring down large and thick walls using exactly the same principle the people who built the walls managed to cut the stone in the first place. It doesn't require absurdly large machines either. You don't have to chip through the entirety of a 3m thick wall, somewhere well before that the 15m above you will fall down and create a convenient ramp for you to get up to the now much lower heap of rubble.
Ancient Siege Warfare, Persians, Greeks, Carthaginians, Romans 546-146 BC, Duncan B Campbell (2005)
Medieval Siege Warfare, Christopher Gravett (1990)