Math has an unfortunate reputation. Ask the average person how they feel about math and they will tell you how thankful they are they never have to deal with it again, how they always "sucked at math" in school, or, one I find especially saddening, they will have hardly any opinion at all! There is a saying about politics that essentially goes like: "You're not into politics? Well, politics is into you!" I feel this also applies to math. While most people hardly go beyond simple arithmetic in their daily lives, the world they depend on, interact with, and reason with is largely built on the language of mathematics. Familiarizing yourself with this language can open your eyes to new perspectives on how the world you live in is structured. It gives you a powerful tool for contextualizing and describing more things than I could hope to list. Perhaps, even more important to my argument is that this new perspective is deeply satifying and strengthens your mind.
The way so many people will scrunch up their face at the mere mention of mathematics is disappointing, and the outright refusal to engage with the subject for any period of time is frustrating. There is no DNA strand that codes humans to be averse to math. There was never some mathematical predator lurking in the night as ancient humans slept, killing us off and causing us to evolve to run at the sight of an equation. So, what causes this behavior? Ironically, being taught math seems to be what has entrenched this hatred for the subject in most people! Yet, do we see a near universal habit for people to exclaim "Oh, geography? I always hated geography!" or to refuse to even write a simple paragraph all because they suffered through English classes? No. So, merely being taught the subject doesn't ingrain a distaste for it. Instead, it is how the material is taught. It is how these people remember the way learning math made them feel: the boredom, the teacher frustrated with you that you just cannot understand how to factor a polynomial, the fear of answering a question wrong and being perceived as "stupid." These emotions and experiences become linked to math since, after all, it happened in "math" class. We have a PR problem for math since so many people had a bad time with it in school. I am no expert in education, especially mathematics education, but I know there is an ongoing effort to rethink how we teach math. Some ideas seem to cause more problems than they solve (see common core math programs) and others thankfully bring math pedagogy into the 21st century (think about the wonderful visualization tools online calculators and computer graphics have given us for communicating math). I hope we can find a way to teach children math that will foster a respect and appreciation for the subject, but I want to speak to those with a math phobia that has stuck with them through the years, or even decades, since leaving formal education. Why should these people learn math?
Mathematics has been likened to strength training for the mind. I find this to be an incredibly apt description. Thinking about math problems requires you to call on many skills such as logical thinking, spatial reasoning, and creativity. Also, if you are learning a topic with lots of word problems, say algebra, probability, or calculus, it enhances your ability to distill textual information and apply critical thinking. This is a powerful tool. I think that, unlike puzzles and wordgames (which can also call on some of these skills), mathematics is more challenging. Yes, math is hard! There is no denying that, but it is precisely the fact that math is challenging that makes it so worth doing. If you are trying to learn math you will reach a point where the problems are no longer routine. You may need to take a while to really digest the problem and come up with a plan of how to solve it. Frankly, this can be time consuming and so when it doesn't work out it can become frustrating, but sticking it through and reaching the correct solution (or the best solution if there are multiple) can be a way to practice your tenacity, your "stick-to-itiveness." I feel that there is a special benefit to math being almost purely a mental exercise as well. There are so few barriers for you to begin learning math. The materials are out there, often enough to get a college level education in math for free! You can start at any level, find an abundance of resources to support your learning, and take as much time as you would like. With these resources being free for the public, there is a complete lack of upfront cost. Additionally, math can be a hobby for anyone barring any impedements to mental function. If someone is homebound or disabled, recreational mathematics is as valid of a hobby for them as for anyone else. The playing field is much more level. Plus, it does not require a partner, any special equipment/facilities, or for you to pay dues to a club (but I must emphasize math is better done together). Math is for everyone. It is a beautiful human endeavor that stretches back millenia. As long as humans have been thinking critically, we have been grappling with mathematical problems, and you should be excited to share in that uniquely human experience!
Studying mathematics for its own sake is completely valid. The pursuit of mathematical knowledge for the understanding of the field of math is what many would call "pure math." The study and application of mathematics for understanding physics, engineering, computer science and other problems is what is known, quite fittingly, as "applied mathematics." One is not better than the other, they are both valid approaches to understanding the mathematical world. Many people who take a recreational approach to math may find the applied approach to be more compelling though. This is particularly where my own bias shows. Mathematics is the language of physics, therefore if you have a strong mathematical background it will be much easier to understand physics. In fact, the deeper your knowledge of math, the more intuition you can build for physics problems. Don't get it twisted though, if you want to study physics that will be a separate pursuit, but if you approach it with a solid foundation in math you will absorb the material much more deeply. This deep grasp of the math behind physics will allow you to see why things behave at a more fundamental level. It will give you a new perspective on how much complexity is hidden in the world around us. For example, if you study partial differential equations you can have a better grasp of heat transfer phenomena or how radio waves propagate through space (e.g., the wifi signal that is currently allowing you to read this). If you went even further and studied differential geometry and tensor analysis you could understand Einstein's Theory of General Relativity, which describes the curvature of spacetime! Having the language to describe and communicate these facets of the world around us will give you an appreciation for just how wonderfully complicated the things we take for granted truly are. Having this new perspective, this way of grappling with what you perceive around you, is so satisfying. Much like when people who study a second language start to think in that language as they become more proficient, you too will start to think in terms of mathematical expressions and logical reasoning as you explore how the world around you works.
This pursuit is not something that can be achieved in a month or two either. Depending on where you start and where you'd like to go, studying math can take years. But why fret? There is no teacher asking for you to turn in assignments, there are no looming exams you have to study for, and there are no 8:30 AM lectures to attend. You can take this at your own pace and find what truly speaks to you and stimulates your mind. There are many types of math that your typical high school student will never see or know about, but that the self-learner can approach and find enjoyment in. The fact that learning math becomes a long-term adventure, a dedication you must hold yourself to, is another reason why studying this subject is so perfect for someone who wants to strengthen their mind. If you can stick with it and gradually make your way into more advance material, mathematics will reward you with revelations that will have you looking at the world a bit differently. You will have more confidence in your ability to commit yourself to hard tasks. You will know that you possess a strong problem-solving mindset, and this will pay off well in your daily life. Mathematics pays dividends, you just need to make those regular investments.