Why Math Modeling Needs More Than Numbers: The Power of Interdisciplinary Skills

Sometimes people strongly or even zealously champion certain things, especially when they are of great significance. As a mathematics teacher, I am more aware of the value of mathematics, and the same applies to mathematical modeling. When I understand a solution to a problem, I more easily see the "indispensable" and "crucial" role that mathematics plays. Of course, there are famous quotes that "prove" this point, such as Hua Luogeng saying: "The universe is vast, particles are tiny, rockets are fast, chemical engineering is clever, the earth changes, biology is mysterious, the sun and moon are abundant; mathematics is used everywhere," and Engels saying: "A science is only complete when it successfully employs mathematics."

However, these statements were appropriate in their original linguistic context, but extracting them and repeating them repeatedly can cause the speaker to overemphasize the importance of the discipline itself. In other words, it becomes a "die‑hard fan" or even a "sole fan" of mathematics.

This is not good.

In actual problem‑solving, multiple abilities and interdisciplinary knowledge are often required. For example, consider how to study the change in bee colony numbers. When first encountering this problem, many students think "this is a biology question" and believe that knowing more about bees will make the problem easier; after acquiring sufficient bee knowledge, they attempt to describe the quantity change, which indeed requires mathematical modeling, commonly using differential equations; after modeling, parameters must be chosen and solved, which is often difficult by hand and requires computer assistance; finally, to present the results well, writing skills are needed.

From the above process we can see that solving a problem involves many abilities and disciplines; which knowledge gets the most credit? It reminds me of a skit "The Five Senses Compete for Credit." The result is that all are indispensable; only cooperation works.

We cannot claim that mathematics alone is important; mathematical modeling shows that the more comprehensive one's abilities and knowledge, the stronger the problem‑handling capability. Mathematical modeling is a method and approach to problem solving; its difficulty lies in its comprehensiveness, and comprehensiveness is endless—you can always integrate more knowledge.