Grothendieck continued: "A lot of people see me and want to talk to me about mathematics. Actually, since 1970, I have preferred to talk about peace, environmental protection, disarmament, or Buddhism. However, it is very realistic that just as people prefer to listen to the coquettishness and pretentiousness of a 20-year-old woman rather than the life advice of a 60-year-old woman, it is obvious that everyone does not want to listen to my whining and complaining. Well, now that I've come to the place where Mr. Johnson worked, I'm going to follow the locals and talk about some of the things I learned about math. ”

The audience finally breathed a sigh of relief. They were really afraid that Grothendieck would be willful and talk about environmental protection and disarmament, so that they would come all the way and be happy.

"When I was a kid, I loved going to school because I never got bored at school, where there was the magic of numbers, the magic of words, the magic of symbols, the magic of sounds, and the magic of rhymes in songs and poems. I always felt that rhyme contained an ineffable mystery, until one day someone explained to me that a very simple trick to rhyme was to make two words spoken in quick succession end with the same syllable, so that it would become a poem as if by magic. I began to write poetry to entertain myself, and for a while, even my every word I said rhymed. Even now, I occasionally write poetry. ”

Okay, Gehuang, we know you're versatile, but let's talk about math!

Grothendieck seemed to feel the complaints: "It turns out that I don't have the talent of Mr. Johnson to be able to excel in multiple areas at the same time." So as the months passed, my obsession with rhyme receded. During my time at school, I was a good student, but not the best student. I would be so desperate to get into what I was interested in, so I would ignore the things I wasn't very interested in and not care much about what my teacher thought. Once the interest fades, I put them aside. For example, when I was in middle school, there was a time when I liked to play crossword puzzles very much, and I used to make crossword puzzles all day and week, combining the magic of shapes with the magic of words, nesting layer by layer, stumping all the answerers. Later, when I got tired of playing, I threw it aside, leaving no trace. ”

Merlin sighed with emotion: "Desperate to devote himself to something that interests him, maybe this is the reason why Emperor Ge can succeed!"

Jiang Shuiyuan was full of malicious speculation: Could it be that he later gave up studying mathematics and lived in seclusion in the Pyrenees, also because of the decline of interest? The old man is really willful enough!

Grothendieck finally got the topic back: "I've been fascinated by math since I was in elementary school, and I'm happiest when I do math problems every day, whether it's in a cramped attic or in a noisy classroom. Soon the things in the textbooks did not satisfy me, because it seemed to me that the topics were almost identical, nothing more than a makeover, and the contents of the textbooks lacked the necessary logic, and felt a bit like the book of Revelation, which did not talk about where they came from or where they were going, as if they had fallen from the sky. Rather than learning these rigid things, I prefer to explore real problems, such as the Helen formula, when the length of the three sides of a triangle is known, the area of the triangle is determined, and I wondered what is the volume of a tetrahedron with six edges of known length? Is there a similar formula? and I spent a lot of time figuring it out. That's how I am, when something gets stuck with me, no matter how many hours or days it takes, I think about it so obsessively that I forget everything else. ”

Merlin, Jiang Shuiyuan and others have already sacrificed their knees: they are worthy of being emperors, and the brain circuits that think about problems are different from those of us ordinary people!

Grothendieck goes on to criticize secondary education: "I think that the secondary mathematics education we receive is completely contrary to mathematics itself, including now. I was very impressed by a math test, the question asked to prove one of several cases of triangle congruence, and the teacher gave me a very low score, not because I answered incorrectly, but because the proof I gave was different from the answer in the book, and the teacher revised the paper based on the answer, and the result was like this. However, I was sure that there was nothing wrong with my proof, and that it was as convincing as the standard answer, but the teacher clearly did not trust his own rational judgment. He must refer to an authority, a criterion to make his own judgments, and he trusts authority more than himself. I thought this kind of thing was absurd, and it should be an exception. When I entered university and started studying mathematics, I realized that this was actually a very common norm, and everyone preferred to trust authority rather than make their own rational judgments. Maybe that's why mathematics is lagging behind?"

Merlin, Jiang Shuiyuan, and others knelt more standardly: Great God, there are not many people in the world who study mathematics in the world, okay? We all know that when you were a student at the University of Montpellier at the age of 17, you spent most of your time making up for the shortcomings of your high school textbooks, trying to redefine length, area, and volume, and rediscovering the concepts of measure theory and Lebegus integrals, but please don't use your standards to demand us mortals!

Please, give us mortals a way to live!

Immediately afterwards, Grothendieck began to complain about the University of Montpellier where he studied. Founded in 1289 and one of the oldest universities in the world, this first-class university in Europa has become "a teacher who reads from a book", "a student who can hardly learn anything", and "almost the worst university in mathematics in France".

Well, did you know that the University of Montpellier has always listed you as a distinguished alumnus in the profile? Do you think your alma mater will open up if you say that?

He then began to criticize the École Normale Supérieure in Paris.

In 1948, at the age of twenty, Grothendieck came from the University of Montpellier to study at the École Normale Supérieure in Paris, where he came into contact with the true mathematical elite and began to realize his own shallow ignorance. However, this little fresh meat who speaks German and has little education is not popular with the Parisian academic community, especially his social skills are a disaster, and he is soon excluded from the circle.

- Perhaps, this is also one of the reasons for Emperor Ge's dissatisfaction.

When he finished complaining about the École Normale Supérieure in Paris, everyone was in high spirits: the drama meat is finally here! What elementary school, Sévenn Lyceum, Montpellier University, and École Normale Supérieure de Paris are just foreshadowing. It was in 1949 when he came to the University of Nancy, the mecca of mathematics in the field of functional analysis. At the University of Nancy, he worked on functional analysis with Dieudonne and others of the Bourbaki school, and at the age of 21 he published six papers in one go, each of which was full of weight, making him an authority on topological vector space theory at the time.

This is also the starting point of the Emperor Godhead.

Who knew that Grothendieck was not going the usual way, and the conversation immediately changed: "The reason why I talk about this today is that I think that our mathematics education has gone astray, and it is going further and further down the wrong path. Whether mathematics is used as a means of selection, competition or livelihood, the study of mathematics with entertainment, utilitarian or competitive purposes has seriously hindered human cognition of the beauty of mathematics. This phenomenon must be reflected on and corrected. Well, that's the end of my speech, thank you!"

Hey, hey, we have pants, no, we have taken out our notebooks, and you ended up telling us about it?

Is there any heavenly reason?

Is there any royal law?

The older audience in the audience was in a mess, if it weren't for the international etiquette and the transcendent status of the emperor, it is estimated that a vote of people would have rushed to the stage and grabbed his collar and questioned him. On the contrary, the students who participated in the Mathematics Olympiad felt that they had gained a lot after listening to it, and many of them began to seriously reflect on their purpose and methods of learning mathematics. Quite simply, Grothendieck's lecture was addressed to them, not to the young and old, middle-aged mathematicians who had already embarked on a career in research.