A New Theory to Explain the Higgs Mass
quantamagazine.org
quantamagazine.org
Like I said, I sucked pretty badly at physics but my impression is that people tend to jump back and forth between imagining the physics, modelling it in math, making predictions based on the math, imagining again what the physics would look like, ad infinitum. So for complex problems, I don't think anyone has a whole physics problem in their head at once and are reasoning about it at that level. They just have pieces and use the math as a way of swapping parts of the problem in and out of their head (if that makes any sense).
I think that's one of the biggest problems with popular descriptions of physics. It doesn't make any sense without the math, but average people don't have the math background. So the descriptions make absolutely no sense. Often you get people who are interested in the physics (but without training) imagining all sorts of crazy things because they have built their understanding on these kinds of nonsense descriptions.
It's been this way for quite a long time. Newton had use new mathematical techniques (calculus) to understand things like the force of gravity. Even if you go back to Archimedes, I wonder how much of his reasoning about density was based on modelling it with math and how much was based on intuition about the physical universe.
The science fiction author, Jerry Pournelle, who has a measured IQ of 180, once complained to Richard Feynman, "I don't understand quantum mechanics." Feynman replied, "That's okay, Jerry; neither do I."
I get pretty irritated when people say nobody can or does understand quantum physics. Your intuition does no better with classical physics, or any other physics. You build an intuition through study. Almost none of us would probably even be able to discover conservation of momentum without it being laid out by someone else.
Most physicists don't "understand math" in a way that a mathematician would recognize, but rather use math as a natural language (with all the dialectical oddities that implies) to help us think about physical reality. When we get too enamoured of the math, we go off the rails, because the universe isn't very good at math and doesn't obey most equations very well (thus the reason most wave equations require us to throw away half the mathematically allowed but physically forbidden solutions from of the off, for example.)
This is why the search for "naturalness" has been such a loser. Elegance and naturalness are attributes of our descriptions, not attributes of the universe we describe. Newton's laws aren't in any sense "natural": they are counter-intuitive and weird. Einstein's equations even moreso.
Mathematically-minded physicists convince themselves of the "naturalness" of these descriptions and go out seeking the same quality, but they fail to realize that it is something that is bolted on afterwards. Using it is a guide will very rarely work (the Dirac equation is arguably the one time it ever has, which is an equation that actually seems to describe the universe without any extra bits left over.)
Most of the past physics seems much simpler partly because the teaching methods and more direct derivations have been developed in the large span of time since they were discovered.
For a background about the physics discussed, check out The Pool-Table Analogy with Axion Physics http://arxiv.org/abs/hep-ph/9506229