How are physics and math related?
Yes, indeed they are. Whatever you learn in maths is definitely gonna be used in physics. As a matter of fact, physics is reliable on maths to prove theories proposed based on observations. For example, you may consider differential equations which we learn to mug up the formulas in our Intermediate, this concept is reflected in order to explain rate of change in physics. All the concepts which look like void in maths are going to look like miracles in physics. As far as I understand, physics employs all kinds of subjects in order to arrive at a solution. We have always seen a theory is first proven mathematics before applying it to the real world. A perfect instance which drives home the answer to this question is the famous formula E = mc^2, which had a great impact on the field of science when it was practically applied. There is no disagreement in saying that physics and maths are closely related which run hand in hand.
The phenomena behind the workings of the natural processes are indebted to the investigations of physics. Mathematics is the language of devising the empirical laws of nature.Mathematics is instrumental in understanding the laws of physics. Learning physics requires mathematical knowledge. Mathematical formulas can be applied to define how physical objects interact and the kind of the relationships among them. Physics, on the other hand, is also considered to be a "rich source of inspiration and insight in mathematics."
A chunk of mathematics is dedicated in perceiving and defining the relationships between objects. Therefore, the application of mathematics in physics is undeniable if you consider this aspect common in both the subjects.
The topics of physics that espouses various mathematical principals are- Measurements(Ranging from the measurement of the length of an object using Vernier Calipers to the measurement of the speed of light), Kinematics, Newton's law of motion, Work-energy-power, motion of system of particles and rigid body, gravitation, oscillation and waves.
Thus it may be concluded that mathematics and physics are almost twin brothers, working hand in hand creating scientific revolutions from the time immemorial.
The science of physics is a special case (albeit a rather fundamental one) of mathematical modelling. Physicists attempt to understand aspects of the universe by constructing models, which go through successive refinements (and occasionally a major overhaul) to take into account data from experiments. Seen in isolation from the observations that justify them, physicists' models are entirely mathematical constructs. (Note: the model is not a direct simulacrum of reality, but rather an attempt to produce a distilled explanation of the ‘laws' by which reality apparently operates.) The way that observations are used as evidence is also mathematically sophisticated, because for a lot of physical phenomena, the evidence we have access to is limited and indirect. I think it's safe to say that physics research would not get very far in the effort to understand reality if it couldn't use advanced mathematics.
In the other direction, mathematics does not formally rely on any understanding of the physical universe, nor are pure mathematicians' motivation and thinking anchored in a desire to understand physical phenomena. Mathematicians have a different notion of what is ‘fundamental' than scientists, since mathematics is an intellectual project in its own right. However, a significant amount of deep mathematics has been inspired and driven by the demands of theoretical physics, and often developed by physicists themselves. (Probably the most famous example is Newton's development of calculus, but there are more recent examples as well, such as the major role played by physicists and physical motivations in developing the theory of operator algebras.) The notable feature of fundamental results in mathematics is that they have consequences all over mathematics, including applications that would otherwise seem unrelated to each other. This goes both ways, and it's likely that sufficiently sophisticated mathematics that has been developed for a particular application will give clues leading to some more mathematically fundamental results.
The behavior of a quantity of interest, be it infinitesimal or infinite is reasoned by Physics. The only language through which these reasons could be theorized is Mathematics.
Although, Mathematics can encompass non-physical situations too making it the ‘Language of Nature and beyond' (even if "beyond" is real/unreal and/or exists/doesn't exist).
Math is the language through which you understand physics. Though not quite one and the same, they are VERY MUCH related.
In chronological order, Pythagoras, John Wheeler and Max Tegmark (and Neo) have all maintained that physics i.e. the world, is made of numbers.