Several people (PeterLue springs to mind yesterday) have commented and it seems to be a widely held view that pre-1900 the mathematics of physics was considerably more streamlined and simplistic. Newton's physics didn't require machinary that relativity and quantum mechanics. That physics should return to this 'simpler' and perhaps more 'elegant' times.

Unfortunately this is complete nonsense and is probably the result of the fact the slightest tip of the iceberg that is 'Newtonian physics' is teachable in school, so too many people assume that is the essence of said physics. Just as with every other topic in every subject, school gives you nothing more than the shortest of simplistic glimpses at some enormous topics.

The main formalism in both quantum field theory and relativity, from which equations of motion are computed is the Lagrangian, with the equations of motion known as "The Euler-Lagrange equations". As the names imply, this area of work was derived by Euler and Lagrange. Two people who very much predate 1900. Euler predates 1800. Both of them were prompted to develop this formalism for Newtonian physics. Why? Because sometimes Newtonian equations of motion are just not right for the job. Yes, they work but they are not elegant and do not cut directly to questions like "What are the symmetries of the system?" or "What physical quantities are conserved". The Lagrangian formalism does just that.

Here is an example sheet on classical dynamics, all physics which is very much Newtonian. Th use of Lagrangians is constantly mentioned within the questions and the solutions read very much like various general relativity questions. Infact, in the preceeding example sheet here the first question involves deriving, in classical dynamics, the general Euler-Lagrange equations. To anyone whose studied general relativity, the result, Equation 2, is the equation of motion for a particle in Einstein's space-time! It's all one and the same formalism because precisely the same machinary is used, just the Lagrangians are different.

And in quantum field theory? Such as some of these questions. More Lagrangians. You'd find their equations of motion in precisely the same way, variational principles. String theory works precisely the same way, you do variational principles on a particular Lagrangian.

How about something else in quantum mechanics? Commutator relations. The notion that AB-BA is not zero. Was this some shocking, out of the blue, notion that Dirac dreamt up and everyone was appauled at? Nope. Non-commuting systems are well known to anyone who knows anything about matrices. For most of the previous century enormous work had been done in such areas by people like Lie. But x and p aren't matrices. Not to worry, Dirac actually got his idea about commutators from 'Poisson brackets'. Poisson lived around 1800 by the way. In his system, {x,p} = 1. Dirac remembered his work, read up about it and stuck in a factor of ih.

So you see, the vast majority of the mathematical machinary employed within quantum mechanics and relativity, even up to now, has some or even all of it's origins pre 1900, in other parts of physics. Physicists didn't suddenly make things 100 times more mathematical, they put preexisting mathematics to new uses and the success of those new models and their ever increasing range of description puts them at the forefront of our minds when someone says "Physics".

Up until Newton's time, hardly any maths was used. Relations between physical quantities were said in sentences such as "Increasing the pressure of a vessel while keeping it's temperature constant results in a decrease in volume in the same ratio as the pressure has increased" (but in Latin). We'd now write that at PV/T = constant.

Should we all hark back to the pre-Newton days and wish that all the mathematics be removed from physics? Or are all the "I hate post 1900 physics" people drawing the line in the sand just because they don't realise how mathematical pre-1900 physics was?

Mathematics has been an essential tool in physics for more than 350 years. It didn't just spring from nowhere because Einstein hated everyone or whatever conspiracy theory some of you call into existence to try to support your claims. You're taught simple Newtonian physics because it's easily taught and you can relate it to everyday life. When you're 14, that's important. When you're 18 and at university doing physics, you're taught more complicated Newtonian physics and basic electromagnetism. When you're 19 you're taught even more complicated Newtonian physics, relativistic electromagnetism and basic quantum mechanics. When you're 20.... well you see where I'm going with this.

It's just that every single one of the people who I refered to in my opening sentence never got to the university part I mentioned and so have no information upon which to make informed statements.

It's also important to recognize how many scientific ideas do not predate mathematical physics. For example, the concept of mass did not really exist before Newton. Perhaps it is possible to pay more attention to an intuitive idea of weight that one can somehow relate to mass, but this does not forgo the need to continue to explain for all the observations that we have around the concept of mass found in mathematical physics.

We had Kepler's Laws, but they were general statements which didn't have a foundation or explainations within a more fundamental model. The distance from the Sun and the period of orbit is related but why that relation and not something else?

Newton realised that it's a force, gravity. He realised gravity behaved a certain way. He invented calculus (alongside and indepedently of Leibnitz) and then put his ideas into precise mathematical statements and explained all the motions of the solar system they could observe at the time.

Pre concise mathematical description, our view of the universe was fuzzy. Newton and the people who used his calculus brought it sharply into focus.

But I have my doubts on how many people here, who claim relativity and QM are too mathematical, could actually use Newtonian dynamics to compute such results. I wonder how many of them could do questions from the example sheets I've linked to. Perhaps they consider 3rd year questions too hard. Well there are some 1st year Newtonian dynamics questions on simplistic things (spinning spheres on rough surfaces, comet orbits, collisions etc) here : 1 2 3 4.

Anyone competant in high school mechanics (if you're British, I'm talking about M1~6 Mechanical Maths A Level) can have a good go at most of those questions. But we know the "Relativity is too complicated mathematically!" crowd will be realising that they find Newtonian physics too mathematically complex.

It's a case of ignorance breeding presumption. They've seen some Newtonian dynamics, it's just F=ma and speed = distance/time, so Newtonian physics is fine and dandy. Relativity is Lorentz transforms and curved space-time, it must be nonsense. Where's F=ma and intuitively obvious physics? How dare the universe be more complicated than everyday life! It must be the fault of physicists.

Not once do they stop to consider it might be their fault. It might be that the universe isn't going to be transparent and mundane as their boring lives. No, it's everyone else's fault but theirs.