“When Will We Ever Use This?” Calculus’s Surprising Uses in Personal and Professional Development.
Why Everyone Should Learn Calculus
Calculus as a branch of mathematics isn’t easy. Limits, derivatives, and integrals are all quite difficult concepts that many high school and college students struggle to understand when they first encounter them. New formulas and theorems appear abstract, and as a result, often beget the omnipresent complaint about calculus’s usefulness. How can a subject revolving around infinitesimal change be relevant to necessary real-world skills like writing a resume or the classic example of filing taxes?
After my experience as a high schooler taking Calculus BC and creating a project applying my calculus knowledge, I’ve realized several surprising practicalities in studying calculus.
Calculus Concepts are Useful
The most common response that I’ve heard in my experience is a claim regarding its usefulness in complex calculations. Nearly all STEM-related fields like engineering and economics use or borrow concepts from calculus.
Let's take a look at building a bridge, as an example. To find the weight a suspension bridge can carry requires mathematical calculations that use force vectors, a concept introduced in calculus. On the other hand, maximizing the bridge’s structural strength with limited resources requires optimization functions that use derivatives. These are just two specific areas out of many in the example bridge-building. When extrapolated for the field of engineering in general, calculus is no doubt essential in its mathematical calculations.
With my calculus-applications final project focused on taxes, I realized that even filing taxes surprisingly uses some calculus. Income tax laws usually use marginal tax brackets, meaning that different portions of your income are taxed at different rates. This approach can be quite confusing for taxpayers, as the multiple different marginal tax brackets on their income are difficult to manage and calculate. To find the total amount of income tax to be paid, a simple integration can be used to find the area under the function. This can then be used to simplify the marginal tax brackets into a single average tax rate as a function of income.
At the same time, just because its a useful concept doesn’t mean it has to be boring or inaccessible to the general public. As explained by a recent book, “Everyday Calculus: Discovering the Hidden Math All Around Us” by Oscar Fernandez, calculus concepts are so ubiquitous that they can even be observed in our daily lives.
The Learning Process
While calculus has proved its usefulness in STEM-related areas like complex engineering and economics, calculus for those who weren’t going into the STEM-field still seems simply impractical to many, despite its position in the common core of many high schools and colleges. So what does calculus offer to everyone regardless of his or her area of interest?
The answer lies not in the hidden benefits of the calculus’s actual content, but rather the skills acquired in the process of learning the difficult and abstract subject.
In the modern skill-based economy, the rapid rate of progress and change means that it’s no longer just having skills that make you stand out, but rather the ability to quickly adapt and learn new skills…What you can do matters more than what you know.
Calculus is a hard subject to learn and fully comprehend. It is built on years of algebra and is filled with subtle concepts. By training your brain to understand such difficult, abstract concepts-like the infinitesimal-you not only improve your mental capacity for logic but also, put plainly, your capacity to learn hard things. And that training for learning hard things is perhaps the most valuable and practical asset for calculus beyond the material learned.
In the modern skill-based economy, the rapid rate of progress and change means that it’s no longer just having skills that make you stand out, but rather the ability to quickly adapt and learn new skills. With the deepening complexity of work in the future, these skills will only grow more abstract and difficult. The experience of learning difficult things will allow those who have experience taking calculus to thrive in such an environment.
Below is an article on the new skill-based economy written by
In other words, studying subjects like calculus is an effective proxy to develop essential workplace-related skills. In the professional sphere, building an efficient and powerful learning process is as important if not more important than the actual skills you have.
What you can do matters more than what you know. Thus, even those who hate calculus-or math in general-may find the skills picked up in learning it to be quite useful in whatever interest that they may pursue.
Conclusion
Beyond calculus, there are a wide variety of subjects out there that will help develop similar essential skills: English for critical thinking and improved communication, History for juxtapositional understanding, and World Language for broadening perspective. Like these other subjects, we must remember that there is a practical reason applicable to nearly all students beyond the pursuit of erudition for placing calculus within the common core.
So next time you wonder, “When will I ever use this?”, focus on the skills learned, not just the content understood.
Thanks for reading! My name is Phillip, and I’m an editor for left | right, a high-school student-run Medium publication dedicated to providing a platform to promote diversity of thought through both analytical and creative pieces.
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