Just as we can feel emotion and joy through nature and poetry, we can also feel even greater emotion and joy through the discipline of mathematics.
The most important thing when studying mathematics is to feel beauty and joy in the process of discovering and understanding concepts.
--- p.10

Every day we create a diagram of life made up of dots called moments.
And the form of that figure is completed with death.
Just as dots come together to form lines and planes, and various shapes are created depending on how they are formed, various forms of life are created depending on how we live in the moment.
Therefore, each and every point of the life we ​​are creating now is infinitely precious and valuable. --- p.20

What we ultimately want to know about a function is how it relates to and responds.
For example, you could match each person with their name, their age, or even their country of origin.
The rules for corresponding like this are called functions, and what is of interest in mathematics is when there is a regularity in each corresponding method.
Because the relevance of their relationship can be known through the rules discovered in their relationship. --- p.64

A philosopher asked:
Who is the worst at math? The philosopher's answer was, "People who have no interest in math."
This statement has significant implications for mathematics education in our country.
The importance of mathematics in our country's college entrance exams is increasingly being emphasized.
However, I am concerned that, contrary to its intention, our math education may be turning children into the worst math students.
--- pp.80-81

By looking at the structure of mathematics, we can see what we are truly aiming for.
We are so busy reacting to phenomena and adapting to reality that we don't know what we truly want to be.
Humans have a tendency to pursue beauty in whatever they do.
The pursuit of beauty does not inherently require money or power.
All it takes is an attitude of opening our hearts. --- pp.88-89

He is holding a red apple in his hand.
On the tray are green apples, pears, red bean buns, and a glass cup.
If you were asked to choose the apple on the tray that resembles the apple you're holding, which one would you choose? If you chose the blue apple, would that be the correct answer? If you chose the blue apple as the same as the red apple, you might be mistaken.
You can't say that a blue apple is the same as a red apple unless you define what you mean by same.
--- pp.108-109

We understand phenomena that occur in nature with our brain.
But just because our brains don't perceive it doesn't mean other phenomena don't exist.
Just as a child who has lived only in the mountains cannot imagine the ocean with its rolling waves, it does not mean that the ocean does not exist.
What we perceive is but a speck of dust compared to the vastness of nature.
But mathematics leads us into a vast ocean of knowledge about nature. --- p.119

If two people maintain an appropriate distance between themselves by acknowledging each other's differences, encouraging each other, and learning from each other, their relationship will become richer and more beautiful.
In mathematics, if you can give distance to a space, you say that the structure of that space is rich.
It is not always possible to give distance to a space, so a space that cannot give distance has a very poor structure. --- p.129

Mathematics is not only a way to find out what we want to know about natural phenomena, but also the beginning of an academic discipline that seeks to realize the beauty of the ideas in our minds.
Therefore, studying mathematics is an act of restoring the beauty inherent in our hearts, and through the structure of mathematics, we can vaguely envision what we truly aspire to be. --- p.138

Sometimes I feel a longing for things that I once treasured but have gradually neglected because they are no longer expressed in numbers.
It's inevitable that I feel happy when I see the numbers on my bankbook growing, but I feel a stronger sense of meaning in life when I feel happy without being bound by the numbers.
What is clear is that neither the value of life nor happiness are proportional to the size of the numbers.

--- pp.144-145