At this time, not only Napoleon's heart was shocked, but he was not good at all. Even Laplace and the others were shocked. Why? President Bonaparte had a way to prove this weird geometry? But this is normal. If anyone in this world can quickly solve this problem, "Joseph who never makes mistakes" is of course the most likely candidate.

At this time on the podium, Joseph slowly greeted Fourier: "Mr. Fourier, well, please help me and distribute my paper to everyone. I can take a break and drink some water. When they finish reading it, we will continue our discussion."

After saying this, Joseph slowly returned to his seat, picked up the teacup and drank tea. At this time, Fourier also distributed a paper to everyone.

Napoleon also posted a paper by Joseph. Napoleon lowered his head and saw a topic like "Experience of the Non-Euclidian Geometry". He opened the paper in despair and tried to find out if there were any loopholes in this round of papers. Although he knew that the paper that Joseph threw out at this time was in a loophole, which was less likely to be against less than the Prussians in field battles he brought 100,000 French troops to fight against less than a thousand Prussians in the field, and the entire army was wiped out. (After all, there is still a possibility that a few meteorites fell from the sky, just like the possibility of them being smashed)

Napoleon's mathematics was actually pretty good. Although to be honest, it was still much worse than the academician's level, among ordinary people, it was definitely a top student. Therefore, he would not have the problem of not being able to understand the paper.

Napoleon quickly read the paper with a lucky mentality. This paper is indeed a typical Joseph style, with strict arguments and no gaps left. It also comes with a deduction of one or two new mathematical tools.

"Is this the differential geometry used? The whole argumentation process seems to be fine." Napoleon raised his head and looked at Laplace and the others next to him. He saw that they all had their eyes wide open, but none of them seemed to have to speak.

"It's over, most of the time, I can't see the problem. This guy, Joseph, really realized such a triangle on a hyperbolic surface. This... I'm so stupid. I actually ran to Joseph's base to tell him about the signs of leaving him. I thought he really wouldn't take revenge, but forgot that this guy has always been petty..."

Laplace and the others finally finished reading this paper. They read it more carefully than Napoleon, but like Napoleon, they could not find out any errors in the paper.

"Joseph, who never makes mistakes." Many people's minds came to their minds, and at the same time they felt that the mountain pressing on them was a little heavier.

Joseph had finished drinking the tea in the teacup and added two more cups. At this time, seeing that everyone had basically finished drinking, he put down the teacup and said slowly: "Everyone seems to have finished reading it? Now, do you have any doubts about Mr. Lucien Evans's paper?"

No one said anything.

Joseph said again: "In fact, in addition to my method, there is a more clever proof, which was also completed by my friend, Academician Gauss. You can also take a look."

So Fourier sent Gauss' paper to everyone again.

Gauss's paper is also called "Experience of the Interpretation of Non-Euclidian Geometry", but his argumentative ideas are indeed different from those of Joseph. His ideas are simpler and more special. He used the concept of projection to prove the compatibility of new geometry and Euclidian geometry in unit circles. If Euclidian geometry is established, then the new geometry will definitely be established!

This concise deduction and wonderful proof are full of mathematical beauty, and for Laplace and others, there is nothing more shocking than it.

"I think you should have no doubts about the paper by Mr. Lucien Evans, who is actually anonymous?" Joseph said, "If so, I will announce the result of this hearing. Well, I think Mr. Fourier made the correct evaluation in his review of this paper. Now, who do you agree and who object?"

So everyone, including Napoleon, agreed.

"Very good, I'm very happy to see that our Academy of Sciences is a Academy of Sciences after all, and everyone is willing to reason. Whether it is right or wrong, everyone is willing to speak with the paper. Well, Mr. Fourier, you made a judgment that made this paper pass before you see the perfect proof. And we all know that in this paper, there are many things that transcend our common sense and make us unacceptable. Now, I want to ask you to talk about why you made this paper pass before you see the perfect proof."

Fourier nodded and walked onto the podium.

"Dear academicians, in fact, when I first saw this paper, I felt absurd, unbelievable, and firmly believed that there must be some error in this paper. But at that time, I felt that although the creator of this paper produced an absurd essay, the mathematical level he showed in the paper was very amazing. I think anyone who really seriously restrained his disgust and read this paper seriously should

It should be discovered. I thought at the time: Even if this paper is really wrong and absurd. It is also a more advanced mistake and absurd. Just like the Zeno paradox (Achilles will never catch up with a turtle a little before him), it is obviously absurd, but it is likely to be absurd with very profound connotations. It is absurd that deserves serious consideration. Just as the study of Zeno paradox leads to in-depth research on finite and infinite, continuous and discrete.

So I carefully studied this paper. To be honest, this kind of research made me very scared. My heart told me that this thing must be wrong, and there is no such truth in the world. But my brain told me that this paper is mathematically wrong.

This is really a terrible thing, because it almost means that our mathematics is in conflict with reality. It is very likely that our mathematics is wrong from the root. At that time, I was so scared that I couldn't even eat it."

Even Laplace couldn't help but nod in agreement with this statement. Because, this is indeed too scary. It's as scary as the sudden fluctuation of the amplitude of the universe's 3k microwave background radiation on the whole, or the universe flashes.

"But, at this moment, I suddenly remembered something. It was the Dean's "Bonaparte bright spot experiment" that seemed completely contrary to common sense. Doesn't that experiment also sound completely unrealistic? But as long as the conditions are right, it will really appear in reality. So I got a little comfort. Maybe it is not that math is wrong or reality is wrong, but that I have misunderstood my own understanding of reality. The real world is so grand, and the range we can reach is so limited. Why should we decide what is in line with reality and what is not in line with reality? Maybe, under some special conditions, this strange geometry can really be realized? Just like as long as the conditions are suitable, we can really see a bright spot in the middle of the shadow left by an opaque object.

So, I discussed this paper, as well as my ideas with the Dean and Academician Gauss. They all agreed with my ideas and tried to find out the conditions in reality that could make this strange and intuitive geometry different. The final result was the two papers that everyone just saw.

This incident touched me very much." Fourier listened and continued, "We should be more cautious about what reality is. Don't think we really know what reality is. Many times, the real real world is different from what we think. In contrast, I think that what comes out of mathematical deduction may be more reliable than the reality we see. I remember Dean Bonaparte said before that our eyes will deceive us, our ears will deceive us, and our imagination will deceive us, but mathematics will not. This is what I think, thank you everyone."

So everyone applauded.

At this time, Joseph also stood up. As the host of the conference and the president of the French Academy of Sciences, he would make a summary statement.

"Sir, Mr. Fourier's speech just now gave me great inspiration. I suddenly remembered a pagan story. In faraway India, there is a story that a king led an elephant to touch a few people who were born blind. Then he asked them: "What does an elephant look like?" A blind man who touched the body of an elephant said: "The elephant is like a wall." Another person who touched the legs of an elephant said: "The elephant is like a pillar." A man who touched the nose of an elephant said: "The elephant is like a snake." But we know that they were wrong.

As for us, when we mock the blind man touching elephants, have we ever thought of ourselves? The universe is much larger than the elephants. Compared with the universe, we are far inferior to bacteria. The range that the blind man can touch with his hands accounts for a proportion of the entire elephant, which is much higher than that of all humans in all our ways and the universe itself. Our situation is actually more difficult than that of the blind man. The blind man cannot see the light, but we cannot see all the light. Many lights and many sounds, which clearly exist, but we cannot see and hear. In this sense, aren’t we also blind? What we have to face is a universe much larger than that of the elephants. In this case, we still regard our limited touch as the basis for judging reality. Isn’t this ridiculous?

Therefore, in the face of nature and the world, we must be humble and not think that we really understand what the real world is. Otherwise, it may at any time use a phenomenon that we cannot understand temporarily to make our heads explode with a bang.

Therefore, we must reduce our prejudices as much as possible, reduce the rules and regulations of self-identification, and do not self-righteously determine what the world looks like.

Finally, Mr. Fourier mentioned just now that he felt that mathematical deduction may be more reliable than our vision and hearing. This makes sense. After all, our eyes will ignore some light, our ears will turn a deaf ear to some sounds, our touch has no sense of vibration below certain thresholds, and our sense of smell also has a limit. Only mathematics seems to be the truth that is suitable for the universe." At this point, Joseph paused for a moment, then smiled, "But at the end, please allow me to tell another story to scare everyone.

There was a chick who discovered a rule through countless observations. That is, whenever a peasant woman appeared, delicious millet fell down to let him eat. He observed countless times, without exception, so he was sure that this could be used as a basis for understanding the world, an axiom. That is, when a peasant woman appeared, there would definitely be millet to eat. As a result, one day the peasant woman appeared again, but she did not bring the millet, but a knife. The chick that was greeted according to the axiom turned into chicken soup.

Don’t the axioms of our mathematics also depend on the so-called intuitive laws discovered through repeated observations? Who knows that we would not be that chick? The real world may be very different from our hearts. Therefore, we must be cautious, have more doubts, and must not have too many prejudices. Everything depends on the actual reaction of the real world to judge."

So everyone applauded.

"Today's hearing was really inspiring." Mr. Monge sighed beside Napoleon, "I think I should give my students the story today and let them also be educated."

Napoleon curled his lips and thought to himself: "Joseph will definitely tell this story in the new issue of Mathematics magazine. How could he not promote such things? Well, there are so many factors in this story. People who are self-righteous and bound by old opinions; people who are modest and cautious, who can defeat their prejudices; people who wake up and can change their past mistakes; people who insist on the truth and are not afraid of power... Is there anyone who can better reflect the scientific spirit of the French Academy of Sciences and the Roman Academy of Sciences than this story? The only painful thing is that I have to be a counterpoint in this story. No, my image in this story must be respectful of science, respect the truth, be brave to correct mistakes, and have a broad mind..."
Chapter completed!