Since the publication of "Looking at the World in the Language of Mathematics", it has been widely loved by teachers, parents and students. This book not only has clear and rigorous proofs of mathematical definitions, but also has interesting human history, showing the history of human knowledge and exploration from ancient times to the present. Mathematics as a language is an essential skill to be a free thinker.
Now, the revised version of this book is finally ushered in. Based on the original content, more than 30 interesting stories and proof examples have been added to make the content of the whole book richer and fuller.
Works by Professor Hiroshi Oguri, director of the Institute of Theoretical Physics at the California Institute of Technology, and research director of the Kavli Institute for Mathematical Physics at the University of Tokyo, Japan
Break through the traditional teaching order and methods of mathematics education / Explain the core concepts and principles of mathematics with "language thinking" / Return to the "basic principles" to re-understand the essence of mathematics
Written by Hiroshi Ooguri
Article | " Looking at the World in the Language of Mathematics (Enhanced Edition) " Foreword: A Mathematical Gift for My Daughter
When you were born, I thought that I hope that while you live happily in this world, you can also become a promoter of social progress. Although there are many problems in modern society, I think that now is the most exciting era in human history. Like every parent, I want my children to have the best things in the world. However, this alone is not enough. This wonderful era is constructed by human beings with wisdom and hard work. I hope you are not only the beneficiaries of the achievements, but also the creators, leaving better achievements for future generations.
The 21st century can also be said to be an uncertain era, and the rules of the international community are constantly changing. China has about 1.4 billion people, and India has about 1.4 billion people. The world would be a different place if the majority of these groups received higher education and went on to intellectual careers. Speaking of this matter, some people worry that the status of developed countries of Japan and the United States will be threatened, but I don't think so. If billions of people in developing countries get good educational opportunities, many new ways to solve current social problems will also be born. As the overall education level of the world rises, the "cake" that can be distributed will be bigger. For you born in the 21st century, these situations present both a challenge and a great opportunity.
In this ever-changing world, the ability to think independently is essential. There is an educational tradition of "Liberal Arts" in Europe. Liberal originally means "freedom", which means "never be a slave". In other words, Liberal Arts is a quality that allows people to control their own destiny and become a free person. No matter when you become a leader or when you face unexpected problems, you must exercise the ability to think independently to solve problems.
In ancient Rome, the "seven arts" were logic, grammar, rhetoric, music, astronomy, arithmetic and geometry. The first three items are for honing the language skills of "argumentation". I think the reason why these three items are ranked first is that they are the necessary conditions for the formation of language. Only by learning to use language can we acquire the ability to think.
Both "arithmetic" and "geometry" in "Seven Arts" belong to the field of mathematics, which I find very interesting. Usually, people think that literature in the field of language or foreign language and literature belongs to liberal arts, and mathematics belongs to science, but I think mathematics and language are interlinked. Mathematics can accurately describe things, and this description ability surpasses the expressive ability of natural languages such as English and Japanese. So, if you understand mathematics, you can see the invisible and come up with new ideas that no one else has thought of.
I didn't like the subject of "arithmetic" very much in elementary school, but after entering middle school, "arithmetic" evolved into "mathematics", and I gradually fell in love with this subject. The opportunity for this transformation stems from the pleasure brought to me by independent thinking. When I solve a math problem, there is only one answer and nothing else. When encountering a problem that cannot be answered by the knowledge learned at school and solving the answer with my own thinking, this joy becomes stronger. And I don't need to ask the teacher whether the answer is correct, because I can judge independently. It's like a baby's first steps, with new skills that broaden his experience of the world. I hope you can experience this joy too.
This book is written to enable you to live a meaningful life in the 21st century. Of course, if you want to study mathematics systematically, it is best to use school textbooks. If mathematics is regarded as a language, for example, mathematics is compared to French, then this book does not teach grammar and vocabulary step by step from scratch, but a collection of practical conversations. With it, you can travel to France and order food at restaurants in Paris in French. Even when the waiter introduces "today's recommended dish", you can immediately understand and judge whether you should order this dish. Or when you go to the Louvre and get in touch with the great works of the past, you can lift your spirits. In addition to telling the practical application of mathematics, this book will also tell interesting stories about the development of mathematics from ancient Babylon and ancient Greece.
I am not a mathematician. I received a Ph.D. in Physics from the University of Tokyo in 1989, was hired as a professor at the University of California, Berkeley 5 years later, and has been working in the Physics Department of Caltech since 2000. However, in 2010, the teachers in the Department of Mathematics invited me to serve as a professor of mathematics. At first I rejected it on the grounds that "I have never verified any famous theorems", but they persuaded me that "verifying theorems is not the only way to contribute to mathematics. Your research raises new questions for mathematical research and promotes New developments in mathematics", so I had no choice but to accept their invitation. In fact, I have put forward many conjectures about mathematics, and these conjectures have been accurately proved by mathematicians. So instead of being a theorem-proving mathematician, I am recognized as a user of mathematics. The content described in this book is also the mathematical knowledge from the user's point of view.
