Sabine Hossenfelder in Quanta:
Theoretical physics has a reputation for being complicated. I beg to differ. That we are able to write down natural laws in mathematical form at all means that the laws we deal with are simple — much simpler than those of other scientific disciplines.
Unfortunately, actually solving those equations is often not so simple. For example, we have a perfectly fine theory that describes the elementary particles called quarks and gluons, but no one can calculate how they come together to make a proton. The equations just can’t be solved by any known methods. Similarly, a merger of black holes or even the flow of a mountain stream can be described in deceptively simple terms, but it’s hideously difficult to say what’s going to happen in any particular case.
Of course, we are relentlessly pushing the limits, searching for new mathematical strategies. But in recent years much of the pushing has come not from more sophisticated math but from more computing power.
When the first math software became available in the 1980s, it didn’t do much more than save someone a search through enormous printed lists of solved integrals. But once physicists had computers at their fingertips, they realized they no longer had to solve the integrals in the first place, they could just plot the solution.
More here.