Opening Remarks: Why We Study Mathematics

Part 1: Warming Up with Math

Why study math? │ Various solutions for even simple calculations? │ Creative calculation methods that play with numbers │ Multiplication methods that are not taught even in school │ Understanding bases through groups of numbers │ Unconventional thinking for solving area problems │ Develop spatial sense by dissecting shapes │ Become familiar with shapes by cutting and putting them together │ Learning the basics of math with triangles

Part 2: Thinking and Proving with Mathematics

Breaking stereotypes reveals the solution │ Proof can be found just by drawing a picture │ Why does 1+1=2? │ Why can't we divide by zero? │ The principles of fraction calculation that even elementary school students can understand

Understanding Math Formulas Without Memorizing Part 3

How to easily determine the multiple of any number │ How to understand and use the root formula │ The secret of the formula for finding the area of ​​a trapezoid │ The secret of the formula for finding the area of ​​a circle │ How to find the volume of a round solid

Part 4: Discovering Mathematical Principles in Everyday Life

How to become familiar with mathematics through origami │ The secrets of mathematics hidden in the rules of patterns │ The principles of mathematics used in artificial intelligence │ The beautiful meeting of mathematics and humanities

Part 5: Teaching the Math I Learned in a Fun Way

Let's create problems instead of just solving them │ There are multiple answers to one problem, and various solutions to one answer │ Even the same question can be interpreted differently │ The world of shapes and numbers created with a ruler and compass │ The true meaning of commonly used mathematical terms

Conclusion: Learning Mathematics: The Optimal Tool for Problem Solving

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“There is no more ‘giving up on math’ in my dictionary!”
Math class where you learn with your eyes and think with your head, without memorizing.

The secret to studying math is unfounded confidence.
Insights from Professor Jun-i Heo, 2022 Fields Medalist

Professor Heo Jun-i, who became the first Korean to win the Fields Medal, often called the Nobel Prize of mathematics, in July 2022, is constantly in the spotlight.
Professor Heo Jun-i's achievement of solving the '11 mathematical problems', which are considered lifelong challenges even for mathematicians, is expected to be utilized in very important research that will take responsibility for our future.
The fact that Professor Heo Jun's research findings are being applied to many modern technologies, including information and communications, semiconductors, statistical physics, and big data, clearly demonstrates that mathematical thinking is becoming an essential virtue in our daily lives, surrounded by increasingly complex networks and rapidly developing artificial intelligence.

However, in a reality where there are still many ‘math dropouts’, Professor Heo Jun-i chose ‘unfounded confidence’ as the secret to being good at math.
How can one promote "unfounded" virtues in mathematics, a field that, more than any other discipline, relies on causality and logical thinking? Professor Heo Jun emphasizes that the secret to excelling in mathematics lies in the "courage" of persistent study, even when you can't immediately obtain the answers required by exam questions, fail to find the right answer, or face an uncertain future due to a lack of established skills.
Memorizing formulas and repeatedly solving hundreds of problems in the 'problem bank' just for the entrance exam will only reduce interest in math.
Professor Heo Jun-i emphasizes that the first step in studying mathematics is to understand the principles of the problem in your own head, even if it means solving just one problem, and to try to discover mathematical principles in everyday life.

“Math that you can understand through principles, without having to memorize.”
The magical study of mathematics where problems are solved as they appear

Beyond simply learning math through rote memorization, how can we understand and apply its principles? Professor Park Man-gu, who has long developed optimal math education methods for those struggling with math, has captured the fundamentals of mathematical thinking for both adults and children in his new book, "Visible Math."
From mathematical formulas and concepts you've likely learned at school to mathematical ideas that connect with our everyday lives, this book uses a variety of visual tools to explain the logical foundations of mathematics, focusing on the question "why" that has often been overlooked in our mathematics studies.
For those of us who have studied by memorizing the solution process using 'problem-solving books' or 'math practice books', this book guides us to understand and apply mathematical principles 'with our heads' in a single breath through the process of simply seeing and learning.

From simple calculations to complex formulas
The unique secret of counting that you never learned in school

Even simple additions and subtractions can be solved in a variety of ways if you know the mathematical principles.
For example, when doing 17-8, adults naturally think of borrowing from the tens digit (borrowing) because they cannot subtract the ones digits, but children think of numbers as groups of beads, so they subtract 8 from a group of 10 beads and add the remaining 2 to a group of 7 beads to get the answer of 9.
This book develops this mathematical thinking by introducing a variety of problems and propositions that cannot be resolved into a single answer and require multiple solutions.
This book takes a fresh look at the principles of calculation that we have taken for granted, such as the Poppos game that uses 4 four times to derive the answer, visually understanding the principles of ternary and quinary numbers beyond the decimal system, why you should not divide a number by 0, why division of fractions is multiplication by reciprocals, and how to prove 1+1=2. This book uncovers the rich secrets of mathematical thinking that cannot be left to calculators alone.

From geometry that develops spatial sense to mathematics used in artificial intelligence.
Principles of mathematical thinking used in various fields of daily life

Geometry is used to understand the various characteristics of shapes and to acquire spatial sense in two- or three-dimensional areas.
A sense of geometric space is essential not only for designers, architects, and surgeons, but also for drivers who need to estimate distances or guess the shape of buildings.
This book guides you through understanding and utilizing mathematics in a single step with 'pictures' by visually showing what shapes appear when you cut and dissect a shape, why the formula for calculating the area of ​​various shapes such as circles and trapezoids was created that way, and how to prove the Pythagorean theorem.
Furthermore, it presents ways to utilize mathematics as an engine of logical thinking, from play to cutting-edge industries, such as by teaching mathematics hidden in specific patterns or rules through origami and tessellation games, and by introducing big data learning methods utilized in artificial intelligence.

“Even in mathematics, there can be more than one answer.”
Finding creative learning methods to solve life's problems

The author recommends going beyond solving problems and creating other math problems as a math learning method that encourages creative thinking (this is a math teaching method that Professor Heo Jun-i also frequently uses with his son).
The author, who has participated in various mathematics gifted education programs, emphasizes that mathematical thinking can be further developed when students go beyond the method of finding a set answer and undergo training to accurately understand the intent and principles of the problem and express them in various ways.
It is impossible to solve difficult math problems by simply applying what you learned in textbooks.
By addressing novel and novel problems that challenge our preconceptions, this book provides a foundation for mathematical thinking that empowers us to think and solve problems on our own.

The author emphasizes that even seemingly complex problems in life can be simplified and made clearer if thought about mathematically.
The power of mathematics lies in the ability to reason logically about not only the visible but also the invisible.
This is possible through the beautiful meeting of mathematics and humanities.
For example, the formula for achieving maximum happiness in life can be expressed through the properties of fractions we have learned.
This is the formula: 'The size of happiness = what I have already achieved / what I desire.'
According to this formula, no matter how much you achieve, if what you desire is greater than what you achieve, you will not be satisfied. However, even if what you achieve is little, if what you desire is less than what you achieve, you will be satisfied.
By basing ourselves on mathematical ideas like these, we can discover the secret to happiness that no philosopher has ever easily defined, and we can have the "unfounded confidence" to ultimately find the optimal solution to any difficult problem.