Why You Should (Or Should Not) Self-Study Mathematics

Mathematics is a fascinating field and a valuable addition to anyone’s arsenal of skills. However, not everyone is able or willing to pursue a formal course of study in math. Perhaps doing so would be too expensive, or too time consuming, or perhaps they are already studying something else in school. Or possibly they are not sure if they want to commit to a full class or degree. Whatever the reason, there is a viable alternative: self-study. Math is one of those subjects which is distinctly suited for self-study. It does not require fancy equipment, large facilities, or journeys into the wilderness. All you really need is some pen and paper, and the will to explore.

There are a variety of reasons why people choose to learn more math: as a hobby, for professional advancement, or as a gateway into other areas of study. The first two reasons are what drew me back into mathematics. It has been a wonderful journey, but not always an easy one. In this article I wish to go over some pros and cons of choosing to study mathematics on your own. I have done my best to remain objective, despite my own positive experiences.

The overall pro of self-learning is that you can customize the experience however you like to fit your goals, your schedule, and your budget. The overall con of self-learning is that you have to do all of the hard work yourself without an expert teacher to guide you or provide directions and encouragement.

Pro: You Can Pace Your Learning However You Like

One of the nicest things about studying on your own is that you have the freedom to pace your learning as you see fit. If you only have a few hours a week to devote to studying, that’s okay! You don’t have to worry about falling behind your peers or looming examinations. On the other hand, if you want to push yourself to grind through material for five hours every day (careful not to burn yourself out!) you can do that, too.

Con: You Are Responsible For Maintaining Your Habits

Life is busy and full of distractions. No matter how much we love learning math, it is hard work and involves its fair share of tedium. There are often other things that sound more fun than pushing ourselves through another exercise set. Without the motivation of deadlines, it is only too easy to push things off until the next day, and then the next day … and so on. If the material you are learning is not exercised regular then your progress will start to slow to a crawl.

Pro: You Are in Charge of Your Own Curriculum

Every person is different and so are their goals. When you self-study, you can tailor what you are learning to align more closely with your interests than formal coursework might. If you are looking to apply your newfound math skills to something specific like economics, engineering, or even archaeology, you can utilize materials specific to those applications. This freedom let’s you discover all manner of knowledge which might be overlooked in a normal course of study.

Con: It is Easy to Get Lost

Math is vast. Unbelievably vast. For all its beauty it remains a rather tangled wilderness of knowledge with relatively few signposts to help explorers navigate. Once you narrow down where you want to go in mathematics, finding a pathway is not always straightforward. Where should you start? Which subjects do you need to cover before you can reach your target subject matter? There are dead ends, twisting detours, and rabbit holes with no bottom.

Pro: It is Cheaper Than Attending School

When you self-study, you only have to pay as much money as you wish to. It is entirely possible to learn mathematics to almost any level without spending any money. Of course, you will have an easier time if you are willing to invest some money, but even if you are loose with your spending you will still spend less than the tens of thousands of dollars that a formal education can cost.

Con: It is Difficult to Find Good Materials

It’s not so much that there is a shortage of good materials, rather it is that there is such a vast quantity of materials to choose from that makes the process challenging. Plus, if you are looking for resources to learn from then you likely don’t yet have a solid grasp of the subject matter which makes it even more challenging to determine which materials are good and which are not. It is a bit of catch 22. You need quality resources to learn from, but you have to already know something about the subject in order to find good resources. Unfortunately, the solution is often simply to not be afraid of trying many different books and resources to see which work and which don’t. See my advice on how to choose a good math book.

Pro: There are Many Good Online Support Communities

Mathematicians and people who enjoy math are a (sadly) small portion of the population. Outside of academia and professional circles, it used to be difficult to find other people who shared a similar passion for mathematics. However, with the internet it is now easier than ever to find like-minded people to connect with. There are a variety of online communities for math enthusiasts and learners at all levels. Some links to different communities can be found on the resources page.

Con: You Are Still Missing Out on the Social Side of Math

While there are many great communities for connecting with other math enthusiasts, it is just not the same as being physically surrounded by other math students, professors, and professionals. Mathematics is more than just the information kept in books. It lives in the people who do it and love it. It has a culture all its own. As you learn more mathematics you will find yourself more excited to talk about it, but sadly most people are not that interested in it and your excitement may fall on deaf ears.

Pro: There is No Limit on How Far You Can Go

In the formal education system there are many rather artificial barriers to advancement, especially at the higher levels. You must apply to get into programs. There are qualifying exams. You have to take the courses in a certain order. You must maintain certain grades. There are good reasons for these barriers to exist and I am not saying they shouldn’t, but they can be frustrating obstacles when all you want to do is learn some math. With self-study, there are no barriers like that. If you can find materials on a topic, you can dive into it (even if you are not conventionally ready).

Con: No Official Recognition of Your Knowledge

YouTube does not give diplomas, and textbooks do not come with certificates of completion. If you hope to convince others of the knowledge you have gained, such as for a job or for school, your word that you have studied the material may not be sufficient. In an ideal world it would not matter how your skills were acquired as long as you could demonstrate them, but we do not live in an ideal world. If you are hoping to learn math in order to get a better job or gain admission to a school, make sure to know what sort of proof of skills will be required from you.

This issue is not insurmountable, but is something you should take into consideration as early as possible. Your primary goal is to get people to pay attention to you long enough that you can demonstrate your skills and your legitimacy. Things like letters of recommendation, related experiences, and other certificates/degrees will go a long way in this regard.

Pro: No Judgement

Judgement comes in many forms, benign and malicious. When you are self-studying a topic you are protected from judgement and criticism until you decide you are ready for it. No one else has to see your first attempts at solving something and Google will never judge you for the questions you search for. There are no classmates to zoom by you or comment that the topic you’re struggling with is soooo easy. This lack of judgement can ease any math anxiety you may normally feel.

Con: No Feedback

While it is not a great feeling to have your work handed back to you covered in corrections and comments, that feedback is invaluable for learning. Having someone there to not only tell you when you did something wrong but also why what you did was wrong is a luxury that is only able to be fully appreciated once it is no longer there. When you are studying on your own there is no one to pat you on the back and say good job, and there is also no one to tell you that you need to slow and work harder. You must be your own cheerleader and your own critic.

Pro: Satisfaction and Pride for Your Accomplishments

When you reach a milestone such as mastering a new concept, completing a textbook, or applying your knowledge to the real world, the satisfaction can be immense. The pride you feel will be made all the more sweet with the knowledge that you were responsible for every step of the journey. When you self-study you know that you were the one who set your goals, found your materials, held yourself accountable, identified and corrected your mistakes, and ultimately achieved the goals you set.

Con: Frustration

The same things that can make self-study so satisfying can also make it all the more frustrating. When things go wrong or get difficult, as this list should convince you they can, you may have no one to turn to but yourself. Building a support network for yourself is crucial, especially for those times when you feel discouraged. Developing coping mechanisms and having other interests and hobbies to turn to is also important. Learning mathematics is a marathon, not a sprint.

Conclusion

Choosing to self-study mathematics is not a decision to take lightly. It requires hard work and dedication. It can be a long and lonely path, but however great the challenges, the rewards for persevering are even greater. Studying on your own is a solid alternative or supplement to a formal education when it comes to learning mathematics and applying it to your life. I encourage you to give it a shot.