“How will I use this in real life?”

When people encounter some complex concept from mathematics, they often ask this question. So is mathematics actually useful? I offer two answers and some food for thought.

Math is actually useful

Before starting university, I truly loved math. Solving math problems was a source of joy. And I was good at it. Then, something changed. During college, math felt overwhelming and confusing. My grades from math courses went down, and even though I always passed an exam at the first try, I only got Ds and Es.

But my passion for math returned back when I discovered machine learning and AI. Everything suddenly clicked. I realized that higher level math is actually useful — and not just some small part, most of it. Linear algebra, calculus, probability theory, optimization methods — machine learning combines them all.

So, my first answer to the question from the title is that math is actually useful in many fields: AI, engineering, physics, finance, even managerial decision making. If you look at this list, you’ll see some of the most influencial professions of our age.

However, math’s usefulness is often hidden. When students encounter some concepts from higher level mathematics, they don’t see the connection to real world problems right away. I am wondering if they would be less sceptical if curricula changed and relevant math concepts would be introduced together with their applications.

This is not always practical, though. I can imagine that many courses in an engineering major require students to understand basic linear algebra. Introducing this knowledge multiple times in different contexts might not the most efficient use of time.

If you are a student who doesn’t fully grasp the purpose of what you are learning at a math course, my advice to you is patience. It may well be the case that you’ll understand the usefulness of math only later in your studies.

Math as a hobby

The second answer is that for me personally, the question of how is math useful in real life is often simply irrelevant. I often solve math problems simply for its own sake. I like it and it brings me joy.

We do many seemingly irrelevant things every day. We call them hobbies. Most people have some. Some people play board games, others do sports, play a musical instrument, or take care of their own gardens. None of these activies increase our salaries, help us advance in our careers, or make our economy as a whole more productive. Quite the contrary; our hoobies often cost us money and time that we could use to do something else. From the perspective of a rational economist, hobbies make no sense.

Yet, despite this apparent irrationality, we often see value in our hobbies. They make our lives fuller in a way that’s hard to express in words. We create, we connect with and bring joy to others, we overcome our limitations, we discover and capture the beauty of our universe, we connect with something “divine”.

For many people, including me, solving math problems is simply at the same level as playing sports ormusical instruments

What saddens me, is that many people see education as a means to getting a job later in life. This is undoubtelly important. But maybe we should also start seeing education, mathematics included, in a more romantic way — as a way of making our lives richer and more colorful.

Math as a gym for the mind?

I originally planned to include a third answer that presents solving math problems as a workout for our minds: just as a gym workout improves our strength and stamina, a math workout improves our cognitive abilities.

But such a claim requires scientific evidence, and when I started to research the topic, I discovered that we don’t have that many studies supporting this conclusion. Some studies show that there is a relationship between people’s performance at math and later success in life — people good at math get accepted to a good university and they earn more money.

The issue is that correlation is not causation. We don’t know for sure if teaching someone a bit of math or making them solve math problems actually improves their mental abilities. It is entirely possible that people who are good at math are simply also good at other mental tasks. They might have won the gene lottery and are naturally good at math-like thinking, which gives them an “unfair advantage” in life.

Should you learn math?

It might be the case that (higher-level) math won’t be that useful to YOU, because you are predisposed to be good at something else. And that’s okay. But there are also many people who do find math useful. And people who know math influence your world more than you think.

Even if math isn’t the best form of mental workout and you don’t plan being involved in some math-heavy field, it might still be worth it to learn some math for its own sake, to the best of your ability. Mastering percentages, some statistics and probability, or basic geometry is extremely useful in day-to-day life.

The best way to learn math is by solving many math problems by yourself, which means a lot of mistakes and frustration. If learning feels easy, you are not really learning.