The way I understand it was that Newton essentially used mathamatics to describe the laws of physics. This is particularly true in terms of describing the movement of "heavenly bodies" such as the planets orbiting the solar system. Newtonian Mechanics are still used today BUT was superceded in part by Einstein's theory of Relativity. The way I remember it is that Newtonian mechanics didn't describe the movement of Mecury accurately, and it was Einstein who suggested that the bending of Space-Time due to the Sun's gravity was responsible for the irregulatities on Mecury's Orbit.
There was a BBC film (Einstein and Eddington) in which Arthur Eddington later demonstrated Einstein's theory by capturing the image of the Sun during a Solar eclipse. What it demonstrated was that the position of the stars changed during the eclipse and therefore that light "bends" around the sun.
I believe this can be stated mathamtically (I'm not smart enough to know how) but this creates a methodological problem in that if we start from mathamatical equations and then build theories on top of it, these later theories are dependent on the assumptions of the underlying models being correct. When you start studying the "extremes" such as the extremely small (quantum mechanics), the extremely large (cosmology, the big bang etc) the validity of these assumptions is stretched. The criticism that can be made is that we start creating theories to reflect these assumptions and then go looking for evidence for it. The "strangeness" and "counter-intutive" nature of many aspects of theoretical physics is down to dealing with the incredably abstract nature of the theories involved.
i.e. Whilst Newton was able to accurately describe the movement of the planets, it was because he already had data and observations to calculate those formulas for. However, what we (appear) to now be doing is creating formulas only
then to go looking for evidence. In other words, we don't know if these equations actually correspond to the observations because we haven't made the observations yet. we are simply assuming the maths is a reflection of real processes.
For the record, this is an "anti-realist" criticism of the use of mathamatics in Science (i.e. maths may not correspond to "real" phenomena) and is widely regarded as pseudo-science or anti-Science and part of the
"Anti-Cosmology" movement. so these criticisms probably would not be well recieved by the "scientific realists" who make up the scientific establishment (and who would argue that the maths does correspond to "real" phenomena because of the historical evidence to support that view).