A colleague once asked me what I thought about the relationships between science and math. He was confounded by the seemingly shifting relationship between these disciplines, as he innately understood that there was a significant connection there, but could not quite make sense of it all.
Why does physics seem to use so much mathematical theorem, while biology does not? Why did chemistry invent a mathematical language all its own?
Because I have more free time than he did, I went on a journey for truth. I found some damn interesting facts!
The nature of each of these sciences and the answers each science looks for determines the level of mathematics involved. The amount of mathematical precision required in each question and answer determines its method. Scientists seek answers about the natural world, and each of these sciences requires a style of communication with varying levels of mathematical depth.
The language of Biology is heredity and adaptation. It is best described with phylogenetic trees and anatomical drawings. It is highly qualitative in nature.
The language of chemistry is chemical equations. It is best described with letters and subscript numerals which represent reactions of electron exchange. It is both qualitative and quantitative in nature.
The language of Physics is mathematics expressed as physical equations. It is best described with symbols for numerical values and representative graphs. It is highly quantitative in nature.
Considerations for this argument:
It’s difficult to get very far in any one of these sciences without involving the others. They’re all inextricably linked, and are all concerned with the study of nature.
Generally speaking, however, Biology is a science which examines patterns of behavior and evolutionary mechanisms of living things. This requires a scientific experimentation process which is focused on description-based, rather than numerical, results.
Chemistry, on the other hand, is a molecular study of matter and energy. It looks closely at reactions between molecules and elements in a way that makes a special math-type language necessary, especially when evaluating bond- and force- reactions between molecules.
Physics, like chemistry, examines reactions and forces, but on a much more diverse scale. It attempts to describe, through formulae, the nature of matter and energy. It encompasses the study of many types of forces, as well, such as electromagnetism, gravity and light. Physics also asks about molecular reactions, but goes beyond the (relatively) limited scope of chemistry and elements. This complexity in scope requires a much more meticulous and complex sort of mathematics skill to describe. Conveniently, many laws of nature can be expressed through mathematics. It might even be fair to say that physics is very like chemistry in the types of forces and phenomena it attempts to explain, but the study of physics does not stop at the molecular level; it actually encompasses laws of motion and attraction for all forces of all sizes and types in the entire known universe, from subatomic particles to galaxies. Much of our theory on math comes from our understanding of the physical universe in terms of mass and energy.
Not surprisingly, all of these sciences become much more meaningful (and applicable) when combined, as with biochemistry or physical chemistry.