"Under the Umbrella of Mathematics: The Joy of Understanding the World" is a popular science masterpiece by Mikael Launay, winner of the "D'Alembert Prize" of the French Mathematical Society. Using mathematics as a link, from algebra, geometry to relativity, from thermometers to black holes, he vividly interprets a new perspective on the world.
Picking up this book will stimulate your curiosity and lead you to appreciate the beauty and charm of mathematics. Recommend this book! Under the protection of the umbrella of mathematics, you and I will explore the world together, unlock the mysteries of the universe, feel the collision and spark of thinking, and enjoy the most vivid journey of wisdom.
"Under the Umbrella of Mathematics: The Joy of Understanding the World", written by Mickaël Launay, uses mathematics as a tool and enjoys thinking; develop your own thinking and observation skills, and become a real thinker.
introduction
In 1980, teachers at the Institute for Mathematical Education (IREM) in Grenoble, France, posed the following riddle-like question to a group of children:
There are 26 sheep and 10 goats on a boat, how old is the captain?
This question is very strange. What could the age of the captain have to do with the number of sheep and goats? But 75 percent of the nearly 200 7- to 8-year-old elementary school students who were asked gave the answer without expressing confusion. Many children add two numbers and get 36. But when the same test was given to 9- and 10-year-olds, most began to protest and refused to answer. Only 20% of the children answered without reservation. During two years, the children's critical thinking becomes more refined. These children develop insight and learn to step back and objectively understand what they are doing.
I must admit that I was quite interested in brain teasers when they were their age. Questions that tease your brain are, in the end, more jokes than math questions. One of my favorites is the following question.
An orchestra of 50 musicians performed Beethoven's Ninth Symphony in 70 minutes. So how long would it take an orchestra of 100 musicians to play the same piece?
Of course, the duration of the symphony does not depend on the number of musicians, 70 minutes will still be 70 minutes. I also particularly like this question: which is heavier, 1 kg of feathers or 1 kg of lead? Neither will be heavier because they both weigh the same: 1 kg.
Little did I know then, that the process of domesticating the meaning of things took far longer than I had imagined. The more I went along, the more I discovered the subtleties of word meaning and the holes in my understanding of the world. Of course, as adults, we don't fall into the traps of being kids. But it would be a mistake to think that we are henceforth immune to the prejudices of other prying eyes. Our intuition can deceive us, and things we take for granted are sometimes wrong. I think I can say this at the age of 35, and every year of my life, starting in elementary school, I realize that my self-righteous understanding of some things is wrong.
We are often overwhelmed by our desire to understand the world, by our curiosity about the universe that surrounds us. After all, the great wise men of human history have all done what the children who learned to refuse to answer the captain's age did. These wise men doubt what they see and try to see beyond. They rose up against the established order. Science is the wondrous realm of inquiry, and mathematics is one of its most powerful tools.
To study mathematics is to spy on the secrets behind the scenes of this world, to sneak into the background to observe the huge gears that drive the universe. The spectacle was dizzying, but also unsettling. Reality challenges our senses and intuition. It's not what we thought it would be. It overturns our priors and sweeps away our most secret shoulds. Great mysteries can hide in the least surprising details, and a child's puzzle can sometimes be deeper than it appears.
Lo and behold, here's another example.
If 4 hens lay 4 eggs in 4 days, how many eggs will 8 hens lay in 8 days?
I'll let you think about it first, and we'll come back to that later. All I can tell you is that when I first saw this problem at the age of 10, I was far from imagining that it would one day help me understand the most famous mathematical equation of all time.
Well, if you'd like to come with me, let's go on an adventure together. During this journey, we may encounter difficult moments, but we do not change our thinking at the snap of our fingers, and encounter doubts to overcome and ideas to mature. But please hold on, the joy of understanding will pay off a thousandfold for your efforts. After turning this page, our mathematical journey has officially begun. Together, we will discover some of the most beautiful hidden mechanisms in this world. Lift your eyes and look around: after our tour is over, you may not see this universe—your universe—in the same way again.
recommended reading
Author: [France] Mickaël Launay
Translator: Ou Yu
Popular science masterpiece of the winner of the "D'Alembert Prize" of the French Mathematical Society
Mathematics is a tool for understanding the nature of the world and the relationship between all things. It can create two compass: one is called "practical" and the other is called "elegant". If you don't understand the meaning of mathematics, you can't really learn and understand mathematics.
Why are scientists so smart? Because they have extraordinary ways of thinking.
Use mathematics as a tool, take thinking as joy; cultivate your own thinking and observation skills, and become a real thinker.
