Mathematics. Once it becomes hard to visualize, caring about learning it can become a real struggle of internal nagging questions like…

- “Why do I need to learn this?”
- “How will this ever be useful in my life?”
- “What is the point of knowing how to solve these problems?”

These thoughts are perfectly understandable. I wondered too, if I would ever “use” math regularly. In high school, I saw it more as puzzle-work and not applicable to most common situations. In certain careers, sure, but in my day-to-day life? I was not so sure.

Now, I understand the impact of learning math better. Not just because I have seen its use in industry and academia, but because I see how logical reasoning as a skill is remarkably useful and applicable to ordinary scenarios. And the development of logical thinking skills is a major effect of engaging in the process of learning and doing math.

Viewing math as just formulaic puzzle-work misses the mark of what the actual impact is. **Memorizing formulas and knowing how to apply them is not the long term takeaway. Developing the deductive and logical thinking skills involved in solving the problems is.** Because of the field’s strict logical rules, solving mathematical problems requires the application of logical reasoning skills. These skills can be applied during real-life situations.

Consider being challenged with the task of creating a method to practice applying logical thinking. Certainly you couldn’t plan exercises that work through every scenario that you may face that would require logical reasoning, so the method must generalize to be applicable to a range of situations. Creating this would be very difficult.

Mathematics solves this challenge. It provides problems that can only be solved in a logical way. The process of learning math requires actively practicing logical reasoning to solve mathematical problems.

“Even if you don’t remember the quadratic formula, the process of learning it made you a clearer thinker. That’s how the entire world teaches math.” - Svetlana Jitomirskaya, Math Professor, U California Irvine

Concepts and features of mathematical problem solving that are applicable in real-world scenarios:

- Understanding the concept of multiple factors influencing a problem
- Understanding how different initial circumstances lead to different outcomes
- Solving the same problem in different ways / from different viewpoints
- Contextualizing a problem’s scope, limitations, and nuances
- Developing, organizing, and applying a process structure while working towards solutions
- Saving solution strategies and methods internally to apply later on similar problems
- Prioritizing correctness and punctuality based on what is known to be true, not believed
- Checking other’s work by thinking for yourself using logical reasoning
- Analyzing a problem quantitatively and objectively

Furthermore, understanding the concept of “quantitative proof” and being able to do math is empowering in the sense that it gives people the power to recognize when they are being manipulated - by a lengthy car loan that will cost them much more over the long term - by the statistics fed to them by politicians and PACs - by the “scientists have proven” articles that have zero quantitative foundation. **In a world of clickbait and endless manipulation of the regular person, understanding mathematics and quantitative logic, and applying it appropriately, functions like a strong piece of armor against such forces.**

Short and sweet. I just wanted to put this in writing somewhere. Math is extraordinarily “pure” in its logical foundations, but similar arguments could be made for numerous other fields like rhetoric, computer science, and more. There are other ways to view the impacts than my descriptions here, it is just my two cents. My undergrad degree is in applied mathematics.

Cheers,

Daniel