From the Fields Medal: mathematics hollowed out by brush questions, it's time to find its true soul.

RecentlyFields PrizewinnerWang HongInterviews on mathematics learning and Peking University education brush the public opinion field. Many media and education commentators traced back to her study experience at Peking University and mentioned that the time after the transfer was far from smooth for her: in the mathematics department, which gathered gold medalists in the national competition, she had no competition background and was always on the edge of the evaluation system. She had to try her best to catch up with the huge gap in her studies, rarely received positive professional guidance and encouragement, and even had to bear it silently.The implicit bias of "non-competitive origin is difficult to follow the path of pure number research.

Some commentators bluntly said that her depression and unhappiness in those days were precisely the epitome of the general predicament of the top mathematics departments in China.-The whole environment excessively praises problem-solving skills and competition talents, but seldom guides students to touch the essence and beauty of mathematics, and is more stingy in giving enough growth space for slow-heating and non-talented lovers.

Wang Hong's ExperienceIt is not only the plight of top college students that has been broken: many people are skilled in solving problems, but they are at a loss about the essential meaning of mathematics. The competition system trains"Muscle memory", on the contrary, has become an obstacle to the touch of real mathematics.

This discussion once again poked the collective anxiety of the whole society: we have studied mathematics for more than ten years from primary school to university, and most people only remember the pain of brushing questions and scattered and useless formulas., hastily used for exams, muddleheaded answers, but I don't know the power they contain. If you are out of the examination environment, you will completely abandon it.

What is mathematics? Is it a tool for screening IQ or a stepping stone for further studies and employment?There are many more people who are less receptive and have a slower way of thinking, who are rejected because they don't get enough positive feedback.Outside the door of the "mathematical kingdom. These are undoubtedly regrettable. Perhaps, we have gone in the wrong direction on the "root" of learning purpose.

The Lost in Mathematics: From"Feast of Thought" to "Inner Paper of Brushing Questions"

American Mathematical Association（MAA) First Chinese President in 100 YearsFrancis Suein its writingsThe Power of MathematicsinsideOnce upon a timeWrite down a fact that many people do not want to admit: today's mathematics education has completely deviated from its origin.

Once upon a time, mathematics was the vanguard of human exploration of the world. From Euclid's geometric axioms to building the edifice of logic, to calculus pushing the door of modern science, to the mathematical cornerstone behind cryptography and artificial intelligence in the information age, mathematics has always been the pioneer of human cognitive boundaries and a sharp weapon to respond to the real problems of the times.

But what about today? For most people, mathematics is only left with the questions on the test paper, the scores on the answer sheet, and the threshold on the way to higher education. The students practiced repeatedly in the sea of questions, reciting formulas and problem-solving templates skillfully, but they never knew how these theorems came about, what phenomena they could explain, and even less than half the fun of mathematics."People use grades and achievements as a reference to measure personal progress and as a label to flaunt their self-worth." Francis Sue writes this in his book.

When the external benefits of mathematics-grades, rankings, diplomas, jobs-become the only goal, the meaning of mathematics itself is hollowed out. This is exactly the dilemma that Wang Hong observed: even in top universities like Peking University, a large number of students are trapped in the "problem-brushing inertia. They are good at dealing with exams, but they don't really think about mathematics. They care about grade points and rankings, but they have no curiosity and love for mathematics itself. Mathematics has degenerated from a feast of ideas to explore the world into an inner game of zero-sum games.

The Nature of Mathematics: A Journey to Complete Personality

What was the real mathematics in Francis Sue's mind?The core answer of the book, hidden in"Human prosperity" in the four words. In his view, the power of mathematics never lies in the speed of calculation and problem-solving skills, but in that it can respond to the basic desires of everyone's heart and nourish a sound personality and precious character. The book examines twelve innate human desires-exploration, meaning, play, beauty, eternity, truth, struggle, power, justice, freedom, collectivity, love-and mathematics is the perfect response to these desires.

Mathematics is a game. Like all fun games, it has rules, challenges, unexpected solutions, and surprises to discover the truth. Chris, the prisoner in the book, has no teacher to guide him, no superior circumstances, and is immersed in a single copy of God Created Integers, because he experiences the pure intellectual pleasure of deducing the theorem-This is no different from the happiness of children addicted to puzzle solving and chess players.

mathematics teachingWill people"Effective struggle": it is not to repeat the same question type mechanically, but to be willing to try different strategies when facing difficult problems, dare to make mistakes, and deepen the understanding of things through repeated trial and error. This resilience that persists in frustration will migrate from math problems to every difficult problem in life. Mathematics also gives man certainty of truth.

In an era of mixed information and rampant lies, the conclusions of mathematics, once proven, will always be true. "As long as the universe is not destroyed, 2 2 will always be equal to 4", Chris wrote in the letter, which is precisely the most precious security that mathematics gives people: you can hold an eternal anchor in a chaotic world.

In other words, learning mathematics is never to become a mathematician, but to become a more complete person: can think independently, can face difficulties directly, has the will to seek truth, and understands the pleasure of aesthetics. This is the true power of mathematics.

"Mathematical talent theory" is the most hidden injustice

Along with Wang Hong's interview, there are also enduring"Mathematical talent theory": Many people acquiesce that mathematics depends on talent. Only a few "smart people" can learn it well, and ordinary people "can use it".

In his book, Francis Sue directly punctures this widespread illusion.He gave the most powerful rebuttal with Chris's story: aThe 19-year-old man who was in prison, who had no formal higher education and could only gather together two chairs as desks in the open grid of the prison, learned topology and advanced mathematical analysis all the way through self-study after reading the classics of Euclid, Archimedes and Descartes, and helped more than a dozen inmates get them.General Education Development Certificate。

If mathematics really only"Talent", none of this can happen. More sharply, Francis Sue pointed out that the so-called "talent difference" is often just a fig leaf of injustice. In the chapter "Justice", he said that women, ethnic minorities and children from low-income families are often indoctrinated with the stereotype that "you are not suitable for mathematics" in the process of growing up; they lack high-quality educational resources, lack of guidance from role models, and even their courage to ask questions will be suppressed. It's not that they don't have talent, it's that the environment deprives them of the opportunity to get in touch with real mathematics early on.

"Mathematics should have opened its doors to everyone, but it has been artificially built with high walls." When we label people with "talent", we are essentially making excuses for the injustice of education and the gap in resources. Just like today, many people think that "the mathematics department of Peking University is a genius", but those who are really seen are always those who have already got the tickets; those who are persuaded by the talent narrative do not even have the chance to stand on the field.

reconstructing mathematics.Value

Francis SueAlways adhere to the current society shouldRebuild the value of mathematics and let mathematics return.The essence of "achieving people" is to build a mathematical community in which everyone can participate. This requires a shift in the concept of education.

He called on educators to put aside their obsession with scores and look away fromThe "correct rate of problem solving" is moved to "human growth. The classroom should not be a place to instill knowledge points in one direction, but a place to explore, discuss and make mistakes. The teacher's duty is not to screen geniuses, but to ignite the curiosity of each student and give them the freedom to explore, understand and be accepted. It also requires each of us to let go of the "good or bad math" judgment.

Mathematics is not a track with only one direction, but a vast garden: some people are good at logic deduction, some are good at geometric intuition, some like to use mathematics to solve practical problems, and some simply enjoy the fun of puzzles. There is no difference between high and low, everyone can find their own scenery.

In the book The Power of MathematicsAt the end of the book, Francis Sue wrote a gentle but powerful sentence:"You have to believe that everyone in your life, including you, can find their own scenery on the road of mathematics." It sounds like idealism, but Chris's story proves it's possible. In the most closed and barren environment, mathematics can become a person's spiritual harbor, helping him rebuild his dignity and find his direction. That in the wider world, it was supposed to illuminate more people.

Written at the end

Why do we especially need to read The Power of Mathematics today?Because we're at the peak of math anxiety:Olympiad Numbers VolumeStarting from kindergarten, the pressure of brushing questions runs through the whole student age. On the one hand, it isThe emphasis on "mathematics is the foundation of science and engineering" is on the one hand the spit out that "mathematics graduates are unemployed.

We spend the most time on math, but we get the most frustration. The reason why Wang Hong's interview resonated widely is precisely because she confirmed the suspicion of many people from within the top universities: our mathematics education seems to have gone astray. And this book by Francis Sue shows us another way.

For parents, it can help you put down anxiety: the ultimate meaning of learning mathematics is never to get into a prestigious school, but to help children develop the ability to think independently, the toughness to face difficulties, and the character of seeking truth and truth.For educators, it is a reminder that the goal of mathematics education is not to select a few talents, but to enable every student to gain the power to grow in mathematics.

For every ordinary person who has been hurt by mathematics, it is a reconciliation: do you think you"You can't learn math well" may just be because you have never seen real math.

The ultimate power of mathematics is never to divide people into three, six or nine, but to make everyone who comes into contact with it become a better self. When we finally put aside the obsession with grades, talents, and rankings, we can truly see mathematics as it is-that it is a door to freedom and dignity, open to everyone.