I have always wondered, whether math is really necessary for understanding Biology. This question had eluded me since my high school when I took Math and Biology both as my elective subjects.
When I see this question raised again, I think I have an answer. Math is not essentially needed to understand Biology. It is useful and may be helpful sometimes, but that’s about it. You can get away with understanding math. You can learn to do the math if necessary, but you can escape the chains of “understanding it.”
Biology as Wikipedia states is “a natural science concerned with the study of life and living organisms, including their structure, function, growth, evolution, distribution, identification and taxonomy.” It is incredibly broad and rich, as the organisms themselves. When we’re talking about such highly complex systems, systems like millions of cells coordinating among each other, systems as big as thousands of organisms interacting and living in an ecosystem, can such diverse systems be described by just some set of equations?
The key even attempting to writing those equations is having an understanding of the system, an intuition what exactly is happening inside. Mathematics is just a tool, which is making our lives easier, giving us new numbers. But what these numbers mean requires an understanding of the system.
Mathematics is a tool. Sure, there exists complex mathematical formulae and domains like topology, number theory, but do we really need these? Basic math, standard calculus and statistics that we did in high school is more than enough to cover almost most of the math one would need in their Biology research. Understanding bio may require these two topics at some point, but that is all that one would need. And even these make their way into topics like Ecological studies and population dynamics, and a little bit in kinetics/metabolism, but sure you wouldn’t need these in Molecular Biology!
Consider Mendel’s Experiment in Genetics. His discovery of laws of inheritance relied on him spending 12 years in a pea garden, “observing”, making careful observations, and coming up with the classic Mendelian experiment that’d uncover the laws. He later came up with the law of independent assortment, which was a result of him realizing the progeny in a dihybrid cross coming up in the ratio 9:3:3:1 was just a result of his understanding and basic probability.
It was his careful observations, understanding, and his deductive reasoning. The math he used was just probability ( Something along the lines of “probability of a head showing up on a fair coin’s toss”; if you got 1/2 you’re already good at it!)
Even the principles of Evolution by Charles Darwin were a result of pondering over the dynamics of an ecosystem worked, principles that lead to the survival of the fittest. Mathematical formulations came later, but the true manifestation of Evolution was stated in the principle, not in the math.
These and many other examples just speak one thing that understanding and having a physical feel of the problem, of the system to which it is to be applied.math is a powerful tool, but only a tool nonetheless. You can come up with hundreds of equations, highly sophisticated models but it wouldn’t matter unless you can interpret what the results mean. What do these numbers imply?
“You don’t need Math to understand Biology. You need biology to make sense of the math, the numbers.”