Mathematics and Physics, which is better?

Interestingly, I came upon these questions very often. Not only at school but also on the Internet as well. Like the other day when someone posted the very same thing, and boom, two opposite answers.

And surprisingly, both of them have their point. And the opposite of one’s strength is the other’s strength. And of course, none backs down.

As an observer, I find these discussions particularly interesting. It sure did highlight some of the differences between Maths and Physics, but I also believe that the peaceful coexistence of the two subjects is viable and vital through many interdisciplinary roles. Here are some takeaways

Math is more theoretical, while Physics is more practical:

To begin with, Mathematics is not observation-based. Its very nature is to derive conclusions, in this case, theorems, from a layer of other proven theorems, tracing back to a parent axiom which is universally agreed to be true. You just don’t really “observe” the theorems in real life, which leads to experiments holding minimal value in Mathematics, a feature unique to this particular subject. 

On the other hand, Physics, just like virtually any other science subject, is observation-based. In Physics, there is no axiom decided by humans, because nature does that job. This leads to a need to base theories on facts, and the ones which don’t are either rejected or remain hypotheses. Many times, a whole set of theories has to be rewritten because the foundation is proven wrong. And as more phenomena are observed, physics is always in a constant state of renewal to have fitting explanations to observations.

Physics can be relative, but Math has to be absolute:

Physics is a science that tries to explain nature, and nature, unfortunately, does not always operate by pattern. Therefore, no theory of Physics will ever be absolute truth; they are just not disproved yet. To adapt to this nature, physicians will happily accept theories that predict correctly a large number of observations, and will mostly still accept those theories if only a small number of opposing observations are found, only making small changes such as reducing the theories’ scope or adding exceptions. Logic is still needed but to a lesser degree.

Mathematics does not accept that kind of argument, as every one of its elements has to be logically defined. It deals with all things on a linear basis, and no theorem can be considered true while it is still undefined by preexisting theorems. On the other hand, if a theorem has been proven, that theorem will be an eternal truth – Mathematicians do not look back and revise it in any way. 

Mathematics is an abstract language; Physics is a realistic application

Of course, to sum up all characteristics, Mathematics is in itself a universal tool that can be applied to every other discipline. It proposes theorems without the need to depend on whether it would be useful – it just takes a complete analyses of ideas from their roots, which makes it powerful in terms of flexibility, but limited in terms of application. And while historically Mathematics had been devised from observations, modern Mathematics is increasingly turning to abstraction, and most of the researches nowadays cannot yet be utilized anywhere aside from pure Mathematics. This, however, will not deter them from possible applications in the future.

Adversely, Physics is specific in the very procedure of its operation from observation to theorizing to application. And as stated above, it tries to explain the nature, and none of its theory will, or even need to, go out of this bound. The standard practice of Physics, therefore, can be explained wholly by descriptions and patterns, but as this science explores deeper, this kind of approach proves inadequate compared to usage of Mathematics as a powerful tool. As it stands, applications of Mathematics in Physics are blooming, ranging from simple calculations to advanced probability and discrete Mathematics.

Conclusion:

As seen above, Mathematics and Physics can sometimes be polar-opposites, but are always supportive of the other – I have seen a lot of examples for this. Next time I’m talking more specifically on these applications, so stay tuned!