How can you not love math?
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Description
Book Introduction
★Why study math? The power of mathematics to clearly solve life's complex philosophical problems.
★ Professor Emeritus of Mathematics at Vienna University and a pioneer in game theory share the beauty of rational thinking.
★“Recommended to the countless ‘dropouts’ in this country.” Highly recommended by Choi Jae-cheon, Kim Sang-hyun, Song Yong-jin, and Jeon Hye-jin!
Contrary to popular belief, mathematics is not simply calculations or playing with numbers.
In the history of human thought for over 2000 years, mathematics has been 'philosophy'.
It's not a romantic metaphor, but in reality mathematics has been a useful tool for philosophy, and philosophy has been a useful tool for mathematics.
Thoughts like Plato's "What is truth?" or John Rawls's "How should we divide things fairly?" ultimately encounter mathematics. What is the basis for this? Carl Sigmund, a lifelong mathematics lover and pioneer of evolutionary game theory, offers a fascinating insight into these questions in "How Can You Not Love Mathematics?"
For example, chance and probability are confusing but interesting topics.
The author examines history and tells us how much humans love to play with chance.
The ancient Egyptians played dice, Gutenberg opened a printing press and immediately put out tarot cards (after printing the Bible)… .
Meanwhile, mathematics cannot be left out of artificial intelligence, the hottest topic these days.
The author asks GPT-4 a tricky question: “Can you write a proof that there are infinite prime numbers, with each line rhyming?” To GPT-4’s surprise, it answers quickly.
What principles underpin these remarkable advancements in AI? This book also offers a fascinating and colorful mathematical narrative.
“Why on earth do we have to learn this?” There’s a joke that says math turns us into philosophers.
This is because students who struggle to solve seemingly difficult math problems end up asking themselves, “Who am I, where am I, and what am I doing now?”
Unfortunately, at this point, if education fails to provide meaning to mathematics, we stop thinking and simply give up.
This book shows what the value of mathematics is, how mathematics provides answers to life's questions such as morality, happiness, cooperation, and contracts, and why studying mathematics is enjoyable.
If you, too, have fallen into the path of a math dropout, yet still harbor a vague yearning for mathematics, and are wondering how to love it, this book will provide a clear solution.
★ Professor Emeritus of Mathematics at Vienna University and a pioneer in game theory share the beauty of rational thinking.
★“Recommended to the countless ‘dropouts’ in this country.” Highly recommended by Choi Jae-cheon, Kim Sang-hyun, Song Yong-jin, and Jeon Hye-jin!
Contrary to popular belief, mathematics is not simply calculations or playing with numbers.
In the history of human thought for over 2000 years, mathematics has been 'philosophy'.
It's not a romantic metaphor, but in reality mathematics has been a useful tool for philosophy, and philosophy has been a useful tool for mathematics.
Thoughts like Plato's "What is truth?" or John Rawls's "How should we divide things fairly?" ultimately encounter mathematics. What is the basis for this? Carl Sigmund, a lifelong mathematics lover and pioneer of evolutionary game theory, offers a fascinating insight into these questions in "How Can You Not Love Mathematics?"
For example, chance and probability are confusing but interesting topics.
The author examines history and tells us how much humans love to play with chance.
The ancient Egyptians played dice, Gutenberg opened a printing press and immediately put out tarot cards (after printing the Bible)… .
Meanwhile, mathematics cannot be left out of artificial intelligence, the hottest topic these days.
The author asks GPT-4 a tricky question: “Can you write a proof that there are infinite prime numbers, with each line rhyming?” To GPT-4’s surprise, it answers quickly.
What principles underpin these remarkable advancements in AI? This book also offers a fascinating and colorful mathematical narrative.
“Why on earth do we have to learn this?” There’s a joke that says math turns us into philosophers.
This is because students who struggle to solve seemingly difficult math problems end up asking themselves, “Who am I, where am I, and what am I doing now?”
Unfortunately, at this point, if education fails to provide meaning to mathematics, we stop thinking and simply give up.
This book shows what the value of mathematics is, how mathematics provides answers to life's questions such as morality, happiness, cooperation, and contracts, and why studying mathematics is enjoyable.
If you, too, have fallen into the path of a math dropout, yet still harbor a vague yearning for mathematics, and are wondering how to love it, this book will provide a clear solution.
- You can preview some of the book's contents.
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index
Recommendation
Translator's Note│On the Philosophy of Numbers, Shapes, and Symbols
preface
Part 1: History of Reason
1 Geometry│Memories of the Nameless
2. Create numbers
3 Infinite│Dive into the infinite pool
4 Logic│How Strong Is Logical Necessity?
Operation 5│Ghost in the Machine
Part 2: A Baffling Riddle
6 The Road to Zero
7 Probability│Random Walk to St. Petersburg
8 Randomness│Superstitions of the Common People
Part 3: Problems of Practical Philosophy
9 Votes│Mad Sheep and Dictator
10 Decisions│A Bet in the Dark
11 Cooperation│How I see myself, how I treat others
12 Social Contract│Punish or Die
Process 13│Monopolizing and Sharing
Part 4 How can you not love math?
14 Languages│Speaking in Code
15 Philosophy│Plato's Shadow on Jurassic Park
16 Understanding│You have to taste the pudding and the proof to know its taste.
Acknowledgements
Translator's Note│On the Philosophy of Numbers, Shapes, and Symbols
preface
Part 1: History of Reason
1 Geometry│Memories of the Nameless
2. Create numbers
3 Infinite│Dive into the infinite pool
4 Logic│How Strong Is Logical Necessity?
Operation 5│Ghost in the Machine
Part 2: A Baffling Riddle
6 The Road to Zero
7 Probability│Random Walk to St. Petersburg
8 Randomness│Superstitions of the Common People
Part 3: Problems of Practical Philosophy
9 Votes│Mad Sheep and Dictator
10 Decisions│A Bet in the Dark
11 Cooperation│How I see myself, how I treat others
12 Social Contract│Punish or Die
Process 13│Monopolizing and Sharing
Part 4 How can you not love math?
14 Languages│Speaking in Code
15 Philosophy│Plato's Shadow on Jurassic Park
16 Understanding│You have to taste the pudding and the proof to know its taste.
Acknowledgements
Detailed image
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Into the book
Mathematics is a useful extension of both theoretical and practical philosophy.
For example, epistemology deals with topics like space and chance, which are central to geometry and probability theory; ethics borrows from game theory to deal with concepts like fairness and social contracts; and there are many other fields as well.
On the other hand, mathematics itself is one of the most puzzling and fascinating sources of philosophical questions.
Why is mathematics so practical, even though it is clearly not an empirical science?
---From the "Preface"
Geometry was the first field of mathematics to make great strides.
Perhaps because it has obvious utility for architects, sailors, and surveyors.
A more plausible reason is beauty.
Geometric shapes, even the simplest ones like triangles, are fascinating.
The musical triangle is a humble instrument hidden somewhere at the back of the orchestra, but the mathematical triangle shines in the front row.
---From "Chapter 1 Geometry"
Why does negative multiplication by negative result in positive? You may have learned a useful analogy in school.
“The enemy of my enemy is my friend.” But since the foundation of arithmetic is not Machiavelli, this metaphor is a bit out of place.
If we consider negative numbers as the mirror image of positive numbers, multiplying by -1 can be interpreted as flipping around the point 0.
Therefore, (-1)×(-1) is flipped twice, so it returns to its original position and becomes 1.
An explanation like this might be enough to allay a child's doubts.
But mathematicians would say that the 'real' reason for "negative times negative is positive" is that we want to preserve the same rules as for natural numbers.
---From "Chapter 2"
Pebbles have been used for counting since very early times.
One pebble represents one head of cattle.
This makes it easy to check that all livestock have returned from pasture.
The Romans called these pebbles 'calculus', which comes from 'calx', meaning 'chalk'.
Therefore, the origin of our calculations is pebbles, and in mathematics departments around the world, calculations are still written on blackboards with chalk and erased at dawn the next day.
---From "Chapter 3: Infinity"
Wittgenstein ridiculed “mathematicians’ superstitious fear and worship of contradiction.”
He asked:
How can we find contradictions? How can we exploit them? What if (whether desired or not) an inconsistency arises? Are we prepared to abandon all our hard-won mathematical theorems? No way! Formalization is just a game.
Whenever it becomes apparent that the rules of a game lead to a contradiction, mathematicians will change the rules to resolve the contradiction.
---From "Chapter 4 Logic"
Mathematics is considered a bastion of skepticism.
In mathematics, nothing is taken on faith.
This is precisely why all theorems must be proven.
If doubt were impossible, then faith would be unnecessary.
If there is one thing in the world that is certain, it is mathematical knowledge.
But for two hundred years, this certainty was the certainty of a sleepwalker.
Oddly enough, this was the very period when hermeneutics and astronomy joined hands to usher in the Age of Reason.
The foundation upon which hermeneutics achieved victory was the concept of the infinitesimal.
A number that is greater than 0 but less than any positive number, and therefore less than itself.
---From "Chapter 6: Limits"
Today, physics, chemistry, economics, and biology are unthinkable without probability theory.
James Clerk Maxwell hailed probability theory as “the true logic of the world,” and Pierre-Simon Laplace called it “the most important problem in life.”
Of course, it is true that Albert Einstein claimed that “God does not play dice” (someone wittily countered,
“But if I had played dice, I would have won”).
But quantum physics sees coincidence everywhere.
---From "Chapter 7 Probability"
In virtual betting, the probabilities of various events are generally well known.
But in everyday reality, such cases are rare.
We don't know the probability.
To quote an American politician, “There are things we know we don’t know, and things we don’t know we don’t know.” We often don’t even vaguely know the probabilities of our various choices.
Still, the decision cannot be postponed.
Such decisions are called 'decisions under uncertainty', in contrast to decisions under risk (where the probabilities are known).
---From "Chapter 10 Decisions"
The tragedy of the commons is widely known.
Commons is a pasture that belongs to the entire village.
This land is often overgrazed and becomes a wasteland.
If a herdsman feeds more cattle than his quota on common land, the milk and meat he obtains will benefit only him, while the damage to the pasture will be borne by everyone.
These days, there isn't much public land left.
Common goods include clean air, golden fishing grounds, and public transportation, but these are always prey to free riders.
---From "Chapter 12: The Social Contract"
Mathematics itself is a language.
This is a widely accepted view.
Let me quote two of the greatest mathematicians of our time, Yuri Manin and Alain Cohn:
Manin says.
“Language is the basis of all human civilization, and mathematics is a special form of language activity.” Cohn goes further.
“Mathematics is undoubtedly the only universal language.” Physicists since Galileo have taken this view for granted.
“The universe is written in the language of mathematics, and the letters of this language are mathematical figures like triangles and circles.”
---From "Chapter 14 Language"
Of all the fields a philosopher can choose, few are better than the philosophy of mathematics.
The philosophy of mathematics is full of grand questions.
First, let me quote Kant.
“How is pure mathematics possible?” Let’s continue.
What is mathematics? What is it about? What do mathematicians mean by "truth" or "existence"? What is proof? What convinces us? What is a number? What is a set? What is logic? What is discovered and what is invented? Why is mathematics useful? Why is it so unique? But the most important question is this:
Why should we care about mathematics?
---From "Chapter 15 Philosophy"
What kind of pleasure does mathematics offer? Above all, there's no doubt that it offers the joy of insight.
It usually comes after a period of rising, disappointing, and even painful stagnation.
Sometimes you just have to give up and try again another day.
Math teaches perseverance.
It also teaches humility.
There are so many people in the world who are much smarter than me!
For example, epistemology deals with topics like space and chance, which are central to geometry and probability theory; ethics borrows from game theory to deal with concepts like fairness and social contracts; and there are many other fields as well.
On the other hand, mathematics itself is one of the most puzzling and fascinating sources of philosophical questions.
Why is mathematics so practical, even though it is clearly not an empirical science?
---From the "Preface"
Geometry was the first field of mathematics to make great strides.
Perhaps because it has obvious utility for architects, sailors, and surveyors.
A more plausible reason is beauty.
Geometric shapes, even the simplest ones like triangles, are fascinating.
The musical triangle is a humble instrument hidden somewhere at the back of the orchestra, but the mathematical triangle shines in the front row.
---From "Chapter 1 Geometry"
Why does negative multiplication by negative result in positive? You may have learned a useful analogy in school.
“The enemy of my enemy is my friend.” But since the foundation of arithmetic is not Machiavelli, this metaphor is a bit out of place.
If we consider negative numbers as the mirror image of positive numbers, multiplying by -1 can be interpreted as flipping around the point 0.
Therefore, (-1)×(-1) is flipped twice, so it returns to its original position and becomes 1.
An explanation like this might be enough to allay a child's doubts.
But mathematicians would say that the 'real' reason for "negative times negative is positive" is that we want to preserve the same rules as for natural numbers.
---From "Chapter 2"
Pebbles have been used for counting since very early times.
One pebble represents one head of cattle.
This makes it easy to check that all livestock have returned from pasture.
The Romans called these pebbles 'calculus', which comes from 'calx', meaning 'chalk'.
Therefore, the origin of our calculations is pebbles, and in mathematics departments around the world, calculations are still written on blackboards with chalk and erased at dawn the next day.
---From "Chapter 3: Infinity"
Wittgenstein ridiculed “mathematicians’ superstitious fear and worship of contradiction.”
He asked:
How can we find contradictions? How can we exploit them? What if (whether desired or not) an inconsistency arises? Are we prepared to abandon all our hard-won mathematical theorems? No way! Formalization is just a game.
Whenever it becomes apparent that the rules of a game lead to a contradiction, mathematicians will change the rules to resolve the contradiction.
---From "Chapter 4 Logic"
Mathematics is considered a bastion of skepticism.
In mathematics, nothing is taken on faith.
This is precisely why all theorems must be proven.
If doubt were impossible, then faith would be unnecessary.
If there is one thing in the world that is certain, it is mathematical knowledge.
But for two hundred years, this certainty was the certainty of a sleepwalker.
Oddly enough, this was the very period when hermeneutics and astronomy joined hands to usher in the Age of Reason.
The foundation upon which hermeneutics achieved victory was the concept of the infinitesimal.
A number that is greater than 0 but less than any positive number, and therefore less than itself.
---From "Chapter 6: Limits"
Today, physics, chemistry, economics, and biology are unthinkable without probability theory.
James Clerk Maxwell hailed probability theory as “the true logic of the world,” and Pierre-Simon Laplace called it “the most important problem in life.”
Of course, it is true that Albert Einstein claimed that “God does not play dice” (someone wittily countered,
“But if I had played dice, I would have won”).
But quantum physics sees coincidence everywhere.
---From "Chapter 7 Probability"
In virtual betting, the probabilities of various events are generally well known.
But in everyday reality, such cases are rare.
We don't know the probability.
To quote an American politician, “There are things we know we don’t know, and things we don’t know we don’t know.” We often don’t even vaguely know the probabilities of our various choices.
Still, the decision cannot be postponed.
Such decisions are called 'decisions under uncertainty', in contrast to decisions under risk (where the probabilities are known).
---From "Chapter 10 Decisions"
The tragedy of the commons is widely known.
Commons is a pasture that belongs to the entire village.
This land is often overgrazed and becomes a wasteland.
If a herdsman feeds more cattle than his quota on common land, the milk and meat he obtains will benefit only him, while the damage to the pasture will be borne by everyone.
These days, there isn't much public land left.
Common goods include clean air, golden fishing grounds, and public transportation, but these are always prey to free riders.
---From "Chapter 12: The Social Contract"
Mathematics itself is a language.
This is a widely accepted view.
Let me quote two of the greatest mathematicians of our time, Yuri Manin and Alain Cohn:
Manin says.
“Language is the basis of all human civilization, and mathematics is a special form of language activity.” Cohn goes further.
“Mathematics is undoubtedly the only universal language.” Physicists since Galileo have taken this view for granted.
“The universe is written in the language of mathematics, and the letters of this language are mathematical figures like triangles and circles.”
---From "Chapter 14 Language"
Of all the fields a philosopher can choose, few are better than the philosophy of mathematics.
The philosophy of mathematics is full of grand questions.
First, let me quote Kant.
“How is pure mathematics possible?” Let’s continue.
What is mathematics? What is it about? What do mathematicians mean by "truth" or "existence"? What is proof? What convinces us? What is a number? What is a set? What is logic? What is discovered and what is invented? Why is mathematics useful? Why is it so unique? But the most important question is this:
Why should we care about mathematics?
---From "Chapter 15 Philosophy"
What kind of pleasure does mathematics offer? Above all, there's no doubt that it offers the joy of insight.
It usually comes after a period of rising, disappointing, and even painful stagnation.
Sometimes you just have to give up and try again another day.
Math teaches perseverance.
It also teaches humility.
There are so many people in the world who are much smarter than me!
---From "Chapter 16 Understanding"
Publisher's Review
Why should you read a math book now?
"It is the only discipline that has steadily developed over thousands of years and represents the intellect humanity has accumulated over that time." _Song Yong-jin (Professor of Mathematics, Inha University)
We read science books because they give us the strength to live.
Quantum entanglement, the Big Bang theory, the emergence of life, and other mysteries so vast and profound that they cannot be fathomed by the human mind, humble us.
The country experiences a sense of absolute alienation, a sense that its existence is nothing more than a tiny insignificant thing in the cosmic perspective and that its current intense struggles are trivial.
This allows us to observe life and realize that we don't have to struggle, which paradoxically becomes the driving force of life.
So why read math books? Whether it's elementary particles, black holes, or mutations, the mysteries science books address ultimately reflect thoughts about the real world that exists outside of us.
But it can be considered natural, even coincidental, that reality is so incomprehensible, and in some ways it is not so surprising.
But there is one discipline that allows us to experience the same alienation within ourselves without having to look at the outside world: mathematics.
Mathematical concepts are much more abstract than tangible, tangible objects, and so math books are sometimes considered more difficult than science books, but they also offer deeper and richer insights.
"How Can One Not Love Mathematics?" is a book on the philosophy of mathematics written by Carl Siegmund, an emeritus professor of mathematics at the University of Vienna, Austria, and a pioneer in evolutionary game theory.
Having taught and researched philosophy for nearly 50 years, he explains in this book how mathematics applies to all kinds of philosophical issues, from logic to politics and morality. He also tells the fascinating story of the long history of how the two disciplines developed together, and finally explores the fundamental questions many people ask about mathematics.
“Why do we learn math?” “Why does math bring so much joy (to some of us, but not all of us)?”
"Unraveling the grand narrative of mathematics, logic, and philosophy step by step, from the ground up." _Kim Sang-hyun (Professor, Department of Mathematics, Graduate School of Advanced Science)
A fascinating historical exploration that reveals the meaning and value of mathematics.
Is there a single field today that is not connected to mathematics? Just look around.
The GPS in car navigation tracks location by solving Einstein's field equations, and credit cards are encrypted through factorization.
In economics, game theory is used to analyze rational decision-making, and in public health, probability theory is used to estimate virus infection rates.
This book explains that mathematics always helps us when we want to talk about something.
Because mathematics is a language that makes “inaccuracy impossible.”
Let's look at history.
In 18th-century France, 'political arithmetic' even exposed the obvious flaws in democracy.
Nicolas de Condorcet, a member of the Academy of Sciences at the time, was a radical Enlightenment thinker who publicly called for women's suffrage and even proposed the abolition of slavery.
He discovered the paradox that the candidate who could win every runoff election never made it to that position.
The runoff voting system is a system in which, if no candidate receives a majority of votes in the first round, the two candidates with the most votes compete in a second round. It has been used in French elections since 1789.
“If our Condorcet had known this, he would have sighed in his grave,” the author says, wittily unraveling the mathematical ‘story.’
Long ago Galileo said this:
“The universe is written in the language of mathematics, and the letters of this language are mathematical figures like triangles and circles.” As if in response, a message was sent from Earth to aliens in 1974.
The sender was the Arecibo Observatory in Puerto Rico, and the message was arranged into a 1679-bit image that looked like a crossword or nonogram puzzle.
In the hope that the recipient would quickly realize that this number was the product of two prime numbers, 23 and 73, the numbers 1 through 10, as well as the number of protons in the hydrogen, nitrogen, oxygen, carbon, and phosphorus atoms that make up DNA, were written inside.
The author explains the significance of mathematics as follows.
"If we want to communicate with aliens, what else can we use besides mathematics? If they want to understand our messages, they don't need fingers, ears, or musicality, but they do need to know a little arithmetic."
"Hidden mathematical talents will be rekindled, and philosophy will be seen differently." _Choi Jae-cheon (Professor, Department of Eco-Science, Ewha Womans University)
Liberal studies that develop clear and detailed thinking skills
The author examines mathematical theories and principles that have been discovered by numerous scholars over 2,000 years, from ancient Plato and Pythagoras to modern-day Schopenhauer and Turing, and develops them into philosophical thought.
If you read it calmly, chewing over the descriptions and formulas, you can sharpen your rational thinking.
This will be a sword that cuts the Gordian knot for us who are wandering around in the ambiguous and complex problems of life.
Especially now, when explosively developed artificial intelligence threatens to topple the tower of intelligence built by humanity, let us undertake the important task of discovering the power and beauty of human reason through this book.
Even the concept of negative numbers (-), which is very familiar to us, confused philosophers in the past.
The number zero represents "nothing," so how can something less than nothing exist? "There may be one or two apples in a basket, but there can't be minus three!" Today, this concept is easily understood through familiar metaphors like reduction, deficiency, and debt, but there's one rule that remains puzzling even today.
Why does negative multiplying negative by negative result in positive (+)? Why is (-1)×(-1) 1?
The author says that while the metaphor “the enemy of my enemy is my friend” is useful, it is a bit out of place because the foundation of arithmetic is not Machiavelli.
It is often explained to children that negative numbers are the mirror image of positive numbers, and that multiplying by -1 means flipping the number around 0.
(-1)×(-1) means that it is flipped twice, so it returns to its original position.
But mathematicians would say the real reason is this:
“Because we want to preserve the same rules as in natural numbers.”
Let's follow the book's explanation closely.
For any natural numbers a, b, c, d, the following rules hold.
(ba)×(cd)=b×c+a×d-(a×c+b×d).
Then, (-1)×(-1) is no different from (1-2)×(1-2), which by rule should be equal to 1+4-(2+2), which is 1.
Therefore, (-1)×(-1)=1.
Rather than racking their brains over the true nature of concepts, such as asking, "What is a number?", mathematicians seek to preserve the rules of computation, known as the "permanence principle."
This is a moment to experience Wittgenstein's philosophy that the meaning of a word is determined by its usage.
The author examines mathematical theories and principles that have been discovered by numerous scholars over 2,000 years, from ancient Plato and Pythagoras to modern-day Schopenhauer and Turing, and develops them into philosophical thought.
If you read it calmly, chewing over the descriptions and formulas, you can sharpen your rational thinking.
This will be a sword that cuts the Gordian knot for us who are wandering around in life's ambiguous and complex problems.
Especially now, when explosively developed artificial intelligence threatens to topple the tower of intelligence built by humanity, let us undertake the important task of discovering the power and beauty of human reason through this book.
“Reason is the most important human quality, and thinking is our noblest activity.”
"It is the only discipline that has steadily developed over thousands of years and represents the intellect humanity has accumulated over that time." _Song Yong-jin (Professor of Mathematics, Inha University)
We read science books because they give us the strength to live.
Quantum entanglement, the Big Bang theory, the emergence of life, and other mysteries so vast and profound that they cannot be fathomed by the human mind, humble us.
The country experiences a sense of absolute alienation, a sense that its existence is nothing more than a tiny insignificant thing in the cosmic perspective and that its current intense struggles are trivial.
This allows us to observe life and realize that we don't have to struggle, which paradoxically becomes the driving force of life.
So why read math books? Whether it's elementary particles, black holes, or mutations, the mysteries science books address ultimately reflect thoughts about the real world that exists outside of us.
But it can be considered natural, even coincidental, that reality is so incomprehensible, and in some ways it is not so surprising.
But there is one discipline that allows us to experience the same alienation within ourselves without having to look at the outside world: mathematics.
Mathematical concepts are much more abstract than tangible, tangible objects, and so math books are sometimes considered more difficult than science books, but they also offer deeper and richer insights.
"How Can One Not Love Mathematics?" is a book on the philosophy of mathematics written by Carl Siegmund, an emeritus professor of mathematics at the University of Vienna, Austria, and a pioneer in evolutionary game theory.
Having taught and researched philosophy for nearly 50 years, he explains in this book how mathematics applies to all kinds of philosophical issues, from logic to politics and morality. He also tells the fascinating story of the long history of how the two disciplines developed together, and finally explores the fundamental questions many people ask about mathematics.
“Why do we learn math?” “Why does math bring so much joy (to some of us, but not all of us)?”
"Unraveling the grand narrative of mathematics, logic, and philosophy step by step, from the ground up." _Kim Sang-hyun (Professor, Department of Mathematics, Graduate School of Advanced Science)
A fascinating historical exploration that reveals the meaning and value of mathematics.
Is there a single field today that is not connected to mathematics? Just look around.
The GPS in car navigation tracks location by solving Einstein's field equations, and credit cards are encrypted through factorization.
In economics, game theory is used to analyze rational decision-making, and in public health, probability theory is used to estimate virus infection rates.
This book explains that mathematics always helps us when we want to talk about something.
Because mathematics is a language that makes “inaccuracy impossible.”
Let's look at history.
In 18th-century France, 'political arithmetic' even exposed the obvious flaws in democracy.
Nicolas de Condorcet, a member of the Academy of Sciences at the time, was a radical Enlightenment thinker who publicly called for women's suffrage and even proposed the abolition of slavery.
He discovered the paradox that the candidate who could win every runoff election never made it to that position.
The runoff voting system is a system in which, if no candidate receives a majority of votes in the first round, the two candidates with the most votes compete in a second round. It has been used in French elections since 1789.
“If our Condorcet had known this, he would have sighed in his grave,” the author says, wittily unraveling the mathematical ‘story.’
Long ago Galileo said this:
“The universe is written in the language of mathematics, and the letters of this language are mathematical figures like triangles and circles.” As if in response, a message was sent from Earth to aliens in 1974.
The sender was the Arecibo Observatory in Puerto Rico, and the message was arranged into a 1679-bit image that looked like a crossword or nonogram puzzle.
In the hope that the recipient would quickly realize that this number was the product of two prime numbers, 23 and 73, the numbers 1 through 10, as well as the number of protons in the hydrogen, nitrogen, oxygen, carbon, and phosphorus atoms that make up DNA, were written inside.
The author explains the significance of mathematics as follows.
"If we want to communicate with aliens, what else can we use besides mathematics? If they want to understand our messages, they don't need fingers, ears, or musicality, but they do need to know a little arithmetic."
"Hidden mathematical talents will be rekindled, and philosophy will be seen differently." _Choi Jae-cheon (Professor, Department of Eco-Science, Ewha Womans University)
Liberal studies that develop clear and detailed thinking skills
The author examines mathematical theories and principles that have been discovered by numerous scholars over 2,000 years, from ancient Plato and Pythagoras to modern-day Schopenhauer and Turing, and develops them into philosophical thought.
If you read it calmly, chewing over the descriptions and formulas, you can sharpen your rational thinking.
This will be a sword that cuts the Gordian knot for us who are wandering around in the ambiguous and complex problems of life.
Especially now, when explosively developed artificial intelligence threatens to topple the tower of intelligence built by humanity, let us undertake the important task of discovering the power and beauty of human reason through this book.
Even the concept of negative numbers (-), which is very familiar to us, confused philosophers in the past.
The number zero represents "nothing," so how can something less than nothing exist? "There may be one or two apples in a basket, but there can't be minus three!" Today, this concept is easily understood through familiar metaphors like reduction, deficiency, and debt, but there's one rule that remains puzzling even today.
Why does negative multiplying negative by negative result in positive (+)? Why is (-1)×(-1) 1?
The author says that while the metaphor “the enemy of my enemy is my friend” is useful, it is a bit out of place because the foundation of arithmetic is not Machiavelli.
It is often explained to children that negative numbers are the mirror image of positive numbers, and that multiplying by -1 means flipping the number around 0.
(-1)×(-1) means that it is flipped twice, so it returns to its original position.
But mathematicians would say the real reason is this:
“Because we want to preserve the same rules as in natural numbers.”
Let's follow the book's explanation closely.
For any natural numbers a, b, c, d, the following rules hold.
(ba)×(cd)=b×c+a×d-(a×c+b×d).
Then, (-1)×(-1) is no different from (1-2)×(1-2), which by rule should be equal to 1+4-(2+2), which is 1.
Therefore, (-1)×(-1)=1.
Rather than racking their brains over the true nature of concepts, such as asking, "What is a number?", mathematicians seek to preserve the rules of computation, known as the "permanence principle."
This is a moment to experience Wittgenstein's philosophy that the meaning of a word is determined by its usage.
The author examines mathematical theories and principles that have been discovered by numerous scholars over 2,000 years, from ancient Plato and Pythagoras to modern-day Schopenhauer and Turing, and develops them into philosophical thought.
If you read it calmly, chewing over the descriptions and formulas, you can sharpen your rational thinking.
This will be a sword that cuts the Gordian knot for us who are wandering around in life's ambiguous and complex problems.
Especially now, when explosively developed artificial intelligence threatens to topple the tower of intelligence built by humanity, let us undertake the important task of discovering the power and beauty of human reason through this book.
“Reason is the most important human quality, and thinking is our noblest activity.”
GOODS SPECIFICS
- Date of issue: May 30, 2024
- Page count, weight, size: 492 pages | 682g | 145*220*22mm
- ISBN13: 9791155817254
- ISBN10: 1155817257
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