If fundamental physics were making big progress, I'd be all over it - that's what I wanted to do ever since I was a kid. But it's stagnant: the action is elsewhere, like using category theory to design radical new kinds of software. So these days I get some of my physics fix by studying the *history* of physics.
After studying the hell out of particle physics and general relativity, I went back and dug into the history of electromagnetism, which is really just as fascinating. Now I'm going back to medieval physics - because the idea that everyone was an idiot until Galileo is just plain wrong.
"Natural philosophers" in the 1200s and 1300s developed key concepts, utterly necessary for modern physics, but almost invisible now because we're so used to them - except for students, who find physics really hard because we don't bother to CLEARLY EXPLAIN those concepts: we act like children are born knowing them.
I'm talking about concepts like "the speed of an object at a moment of time". What the hell does that even mean? How can you figure out how fast something is going in one instant of time, when doesn't have time to go anywhere?
Well, that was clarified by calculus, and we credit it to Newton and Leibniz. But they had to have the idea already, in order to clarify it! And the idea of "instantaneous velocity" was developed around 1340 by the Oxford Calculators, a school of thinkers like Heytesbury and Swineshead - geniuses we never hear about.
Now I'm going back further. Did you know that back in 420 AD Martianus Capella had a theory where Mercury and Venus revolved around the Sun? And this was known to thinkers in Charlemagne's day... and also Copernicus! Wow!
Is instantenous speed a central example here? I'm asking because I'm surprised to find it's not an intuitive notion: I don't remember fellow classmates struggling with it (and I do remember struggles with abstractions such as a function that happens to be linear. I will probably ask my 6~8yr old "nephews" in the coming days; suggestions on concrete questions that show the difficulty are very welcome.)
I don't think children are likely to start with that worldview based on anecdotal evidence: I don't know anyone who initially considered Zeno's (Xeno's?) paradox to be intuitive (@timorl , did you?). When I first learned of it (sometime in primary school) it seemed contrived to me.
Oof, I wrote a long-ish response and only then remembered that this is not about that Zeno’s paradox – we are talking about the one with the arrow not moving at a specific point in time, right? The other ones always seemed to me more like jokes (i.e. subverting intuitive expectations), but this one did make some sense. Although I think rather than pointing to the difficulty in accepting instantenous speed, it points to the counterintuitive concept of considering a situation at a specific point in time altogether. I think the intuitive approach to understanding everyday mechanics is much more dynamic, and introducing any moment-by-moment abstraction requires some work, including the fact that speed is still associated with objects (even if the fact by itself is not particularly hard to accept).
But these are guesses, our current culture is soaked in this understanding of dynamics to an extent that almost surely influences children even before they get formally introduced to physics, so it’s hard to tell which things are a priori intuitive – for that you really gotta study history like @johncarlosbaez does. 
@robryk @johncarlosbaez
From a certain point of view, it can seem that, instantaneously, nothing moves, therefore, how could there be speed? Zeno's paradoxes.