How to Fall in Love with Hard Math: Writing Letters to Killer Problems

 

[MATH ESSAY & STRATEGY] THE POWER OF MINDSET

"Fall in Love with Math" — How Writing Letters to Hard Problems Created a Miracle

Hard math problems are not merciless enemies trying to destroy your score. When you replace fear with genuine curiosity and approach them as friends you want to understand, even the most terrifying killer questions become your most reliable allies.

📐 Freezing Before Tough Questions: Fear and Hostility

Whenever I see students freezing up in front of high-difficulty questions right before major exams, I close the test paper and ask them one simple question:

"Are you looking at this problem as an enemy you must destroy, or as a partner you want to get to know?"

For most students, high-stakes math questions feel like traps designed to pull down their grades. But through eyes clouded by fear and resentment, you can never see the organic beauty of formulas or the subtle clues the examiner intentionally planted. No one can ever understand the heart of someone they despise.

A few years ago, a high school senior came to me completely overwhelmed. Whenever an infinite geometric series with fractal geometry appeared, his mind went completely blank. He memorized all the formulas for the initial term a and the common ratio r, but a slight twist in shape would cause him to freeze. With trembling eyes, he told me: "Teacher, no matter what it takes, I want to conquer this exact problem on the final exam."

What I handed him was not another stack of drill worksheets. Instead, I gave him an unusual prescription: "Starting today, write an observation journal and a daily letter to this concept."

🔍 Making a New Friend: "Today, I Discovered This About You"

How do you become close with an intimidating classmate on the first day of school? You observe them with curiosity: 'I noticed you like this,' 'Underneath that quiet look, we actually have a lot in common.' Math works the exact same way.

From that day on, sincere and humble daily conversations began filling the margins of his notebook.

💌 A Letter to Initial Term (a)

"At first, you looked like a terrifying irregular polygon. But once I drew a single auxiliary line, you were just two isosceles right triangles facing each other. You wore a scary mask, but inside, you were neat and simple."

💌 A Letter to Common Ratio (r)

"I almost lost my way again, but then I noticed the circular symmetry you hid. Forcing formulas never worked, but calmly looking into you revealed the rhythmic square of similarity ratio. Tomorrow, I will greet you with a smile."

Hidden symmetries, shrinking geometric rhythms, and auxiliary line paths—things invisible during blind mechanical calculations—gradually surfaced through genuine curiosity.

Then, the breakthrough happened. On mock exam days, no matter how intricate the shapes were twisted, he never panicked. Instead, he smiled and said: "Teacher, today's problem put on a dramatic disguise, but once I stripped the layers away, it was the gentle friend I write letters to every night." The higher the difficulty, the faster and cleaner he solved it.

📌 [Action Plan] The Split-Page Protocol: Turn Hard Problems into Allies

Mindset alone is not enough. Here is the concrete, metacognitive training framework you should put onto your desk tonight.

STEP 1 Left Page: Unmasking (List 3 Core Conditions)

Write down at least three geometric or algebraic clues (special angles, symmetry axes, tangency slopes) in complete sentences before calculating.

STEP 2 Right Page: Bottleneck Diagnosis (Document Missed Properties)

Ask honestly: "Where did I blindly jump into calculations?", "What geometric symmetry did I overlook?" Document your blind spots candidly.

STEP 3 Blank Paper Mastery: Solve Until It Becomes Your Loyal Problem

Do not rely on the textbook's polished solutions. Fight through the solution path in your own logic until you can reproduce it on blank paper without hesitation.

This method works beyond infinite series. Whether it is trigonometric graphs, implicit differentiation, or composite function calculus, call your hardest topics to your desk and talk to them first.

💌 A Word from Yulcho

To those who push it away with fear, math remains a cold, unyielding wall. But to those who persist in understanding its true nature, math becomes an unbreakable shield on exam day.

Do not slam the notebook shut or hide behind solution manuals when you get stuck. When you strip off the intimidating armor of killer problems, they are nothing more than three or four basic concepts harmoniously linked together.

Fall in love with math. The one intimidating question you turn into a loyal ally will redefine your confidence and change your destiny.