1.
Thought and Mathematics
＊ Numbers and symbols
Awards / Big and small numbers / Base / Decimal system / Number system / Zero, zero, blank
＊ In the beginning was the Word - Pythagoras and Logos
Pythagorean theorem / Proof of the Pythagorean theorem / Co-measurement /
Descartes / Pythagorean triples / Fermat's last theorem

2.
Art and Mathematics
＊ Harmony of the Celestial Spheres
Chords / Triads / Pure temperament / Twelve-tone scale / Frequency / Handclapping / Pythagorean comma
Mean temperament / logarithmic function / pitch / cent / trigonometric function / timbre / vibration
＊ Picture, reborn
Vanishing point / Horizon / Distance point / Drawing a square / Harmonic mean / Mean quadrilateral
2-point perspective / 3-point perspective / shadow of a circle / metamorphosis
＊ All things in the universe - appearance and classification
Side-by-side gluing / regular gluing / single-sided gluing / Conway standard
Multi-faceted gluing / Non-periodic gluing / Symmetry

3.
Social Studies and Mathematics
＊ A society where we live together, democracy - voting and election
Ranking system / Pairwise comparison method / Borda counting system / Least vote-getter system / International Olympic Committee / Condorcet paradox
Majority criterion / system independent of resignation / monopoly criterion / rational electoral system / social choice
Belling the Cat / Tournament / Ranking / Multiple-choice Election System / Weighted Voting System / Power Index
＊ We are one - fair distribution
Divided-choice method / parallel-partitioning method / multiple-person distribution / lonely-partitioning method / lonely-choice method
Final reduction method / Moving knife / Parallel division method / Weighted distribution / Envious distribution
Solomon's Wisdom / Choosing in Order / Merging / Natural Number Assignment / Hamiltonian Assignment
Alabama Paradox / Population Growth Paradox / Oklahoma Paradox / Transformative Gardens / Rounding

4.
Technology and Mathematics
＊ Light in the Darkness - Password
Law Mountain / 9-Normal Line / 10-Law Mountain / Error Correction / 11-Law Mountain / Euclidean Algorithm / Coprime
Fermat's Little Theorem / Discrete Logarithms / The Cowherd and the Weaver Girl / Public Key Cryptography / RSA Public Key Cryptography
＊ Rules of the game
Hex / Combination game / Egg collection / Rubik's Cube / Politician / Von Neumann game / Zero-sum game
Lying Game / Minimax Theorem / Fox's Den / Black and White / Guessing Game / Non-Zero-sum Game
Prisoner's Dilemma / Simsung and Alji / Games with Nature / Inductive Games

supplement
References
Search

Next is analog, and then math
Professor Kim Hong-jong of Seoul National University, famous for teaching mathematics in a fun and engaging way, is also a well-written mathematician known for his lectures and writings on topics ranging from science to art and music.
In his previous work, “Viewing Science through Mathematics” (2005), he presented a link between mathematics and science, which evoked a fresh response.
There is a lecture he has been teaching for eight years, and it is 'Mathematics in Civilization', which was established as a core liberal arts subject in 2001 when Seoul National University underwent a large-scale curriculum reorganization with no clear precedent.

“It was only in the 1930s that humanity began to understand what the number meant.
Since then, mankind has developed artificial languages ​​and learned to understand natural languages.
The idea of ​​right and wrong was replaced by the coming and going of electric lights, giving birth to digital civilization.
Today, highly developed arithmetic systems play a key role in the development of these civilizations.
But this kind of calculation, this kind of digital thinking, is a very rudimentary stage in human development.
Therefore, we must encourage greater imagination in schools and prepare for the 'analog revolution' that lies ahead.”

The author emphasizes that the problem of 'existence (1)' and 'non-existence (0)', which has been passed down from ancient civilizations, is the beginning of the current digital revolution, and that our young people must have mathematical knowledge to get ahead. He asserts that after the digital revolution, 'analog' will become the new paradigm and mathematics will play a more important role than it does now.


The power to turn back the darkness: mathematics
Mathematics pursues properties that do not change anywhere.
The sum of the interior angles of any triangle is 180°, and the square of the length of the hypotenuse of any right triangle is equal to the sum of the squares of the lengths of the other two sides (a2+b2=c2), etc. are truths.
Some people question the usefulness of mathematical knowledge.
But if we look a little deeper, we discover that mathematics provides humanity with a 'quality that extends to or connects to everything', that is, universality.
Because the spirit underlying mathematics is so pure, it explains the various and surprising results that can be obtained from it in a way that anyone can understand.
When entering elementary school, children begin to distinguish objects and count by one or two, and in middle and high school, they learn abstract thinking through unknown numbers such as , x, and y instead of specific numbers.
And in college, as you understand the symmetry of shapes and equations, you realize that things that seem very different often come from the same principles.
There is proof in all of this.
The author compares 'proof' in mathematics to the process of following a distant light when lost and wandering in the dark night.
Because you can not only verify the truth for yourself, but also explain what you have discovered so that others can understand it.
But more important than proof is how to find the light to seek.
What is needed here is the training to recall so-called inspiration.
In that sense, mathematics is a highly mental activity.


The world's answer was mathematics.
The author has consistently emphasized that mathematics is not separate from our lives.
Just as climbing a large mountain brings us to trees, rocks, flowers, and butterflies, the book shows, through various examples, that the various experiences we encounter in our daily lives are closely connected to mathematics.
Unfortunately, this book does not include more exciting topics such as infinity, language and logic, space, time, networks, fractals, the golden ratio, natural laws, and machines. However, it does connect mathematics with various perspectives, such as thought, art, society, technology, nature, science, language, psychology, and play.
We will outline the prototype of mathematics through ancient Greek philosophy and Pythagoras, and examine in detail the role mathematics played in the development of music and art through various materials.
In addition, we meticulously and mathematically examine the electoral system and how it guarantees our rights and respects the rights of others in a democratic society.
In addition, it empirically presents the true nature of mathematics through cryptography, which played a crucial role in determining victory or defeat in war, and game theory, which had a profound impact on economics.