The Beauty of Mathematics

Which subject do you find the most challenging?

Mathematical analysis.

I’ve asked many students who have graduated from our major, and the most useful subject they learned in college or the one they wish they had excelled in the most is mathematical analysis.


At a college meeting

This book is a popular science work. Don’t let the word “mathematics” deter you from it. Reading it during college is the best time, as it’s too early to fully understand some things, and reading it later, like me, you’ll wonder why you didn’t discover this book earlier.

I won’t delve into mathematical knowledge here but will highlight a few common scenarios we encounter in our lives.

  1. Search engines: When you search for “Cheng Xiaobai,” how does it present relevant results? Where does the data come from, and why do some pages rank higher than others?

  2. Map navigation: How does it quickly plan various suitable routes, such as the fastest (not necessarily the shortest), the shortest, or tell you which bus or subway to take and where to transfer?

  3. Email: How does your email service provider filter out some spam emails?

  4. Recommendations: Whether it’s shopping, news, or videos, how do they suggest content to you?

  5. Speech recognition: With more and more applications using it, how is what you say recognized?

Mathematics plays a significant role behind these services. Can you think of any of these services that can function without mathematics? Temporarily, yes, but in the long term, significant disparities will arise.

In the field of engineering, sometimes you can get by with blind improvisation to achieve a passable result. However, in the long run, maintaining these ad-hoc solutions comes at a tremendous cost. Not only do they lead to disorganized and ugly structures, but they also make future modifications and corrections virtually impossible due to the lack of understanding behind these ad-hoc solutions. On the contrary, if you abstract the problem at a higher mathematical model level, seeking a correct framework, you can systematically fill in the details and gradually achieve perfection. Such a solution not only meets the requirements but also maintains a clear and understandable structure, making it easier for future maintenance and corrections.

Reading this book doesn’t mean learning advanced mathematical knowledge or programming skills. Instead, it made me realize how the knowledge I acquired can be applied and how it can have such a profound impact. Mathematics in the computer industry is no longer merely abstract algorithms; it genuinely influences our internet-driven lives.

In fact, the earlier you read this book, the better. One of the biggest failures of Chinese education is that students from the first day of class to the end of exams have no idea what they are learning is for. “The Beauty of Mathematics” can tell students how the math they’ve learned from childhood can reshape the world.

Many people aren’t lazy; they just can’t find their direction, and, as a result, they waste a lot of precious time.

Mathematical analysis, advanced algebra, probability theory, and linear algebra are full of complex logic proofs and data calculations. Few people discuss how these pieces of knowledge can be applied or leveraged. At the end of my sophomore year, I could still calculate integrals, matrices, and probabilities because I had some impression left from exams. However, as I progressed into computer science courses in my junior year, I only understood the concepts, and now, one year after graduation, when I look at these materials, I can only recognize them and nothing more.

We were once experts at problem-solving, but because we didn’t understand how mathematics could be used, we gradually forgot it.

If, during my junior year, the computer science courses had been integrated with mathematics, with two years of theory and one year of practice, it would have been perfect.

But that’s just an “if.”

So, few people can tell you during your college years how the knowledge you are learning can be applied and have a massive impact in the future.

Many people hold the belief that the knowledge gained in college is useless, leading them to drift aimlessly through their university life. The more people around them with this belief, the more they feel comfortable with this aimlessness. The quality of college life can be seen in the campus atmosphere.

The environment is one factor, but often, self-change is more critical.

No one can help; you can only rely on yourself. You search online, ask others what the application direction is for your major’s courses, and whether you can combine it with your interests.

Each course should have a weight, and the time and effort spent on each course should be different.

Effort is essential, but blind effort is futile. In different scenarios, the criteria for excellence are not the same. Working hard alone will not yield results; you must work hard in the right direction.

However, such self-awareness is relatively rare, and those who possess it often feel anxious, a sense of helplessness.

Awareness brings pressure, not because of the credits and grades that need to be accumulated, but because of the anxiety of not seeing the future, because of the uncertainty, because of not knowing, because of the helplessness that comes from knowing you are wasting time.

Such individuals, full of potential but lacking direction, are only one step away from making significant changes in their lives.

Enlighten your past without blaming it and discern those who come in the future.

Let’s encourage each other.