The Fox of France

Since Napoleon had not changed his stance, Fourier naturally did not change his stance either. So a few days later, at the French Academy of Sciences, a formal hearing began.

Before the hearing, Napoleon and his think tank carefully studied the paper, hoping to discover any hidden errors in its argumentation. However, despite their efforts, they could not find any such loopholes.

"I don't even know how this terrible paradox came about. But his mistakes are unquestionable. Therefore, in the debate, I suggest we focus solely on attacking the paper's inconsistencies with reality and its lack of achievable models," Laplace and others finally proposed.

Although Napoleon felt that this approach was not enough to completely defeat his opponent, he now had no choice but to resort to it. With this approach, at least he could maintain his undefeated record.

The weather on the day of the hearing was fine, and Napoleon and his allies arrived at the entrance of the small auditorium where the hearing was to be held on time. They happened to encounter Joseph leading a group of people, including Gauss and Fourier.

"Mr. Fourier, why would you support such a strange paper?" Laplace approached Fourier and asked.

"Ah, Mr. Laplace, what's strange about this paper?" Fourier said, "I think it's the best, most innovative, inspiring, and discussable paper in recent times. In fact, this is not only my opinion, but also Mr. Gauss's and Dean Bonaparte's."

In fact, Laplace's conversation with Fourier at this time was largely a military tactic, intending to put pressure on Fourier. However, Fourier dragged Gauss and Joseph out, making Laplace feel quite pressured instead. Because although Gauss was young, his series of achievements in mathematics were truly impressive, and his talent and ability to handle difficult problems were admired by everyone. As for Dean Bonaparte, he had the reputation of "Joseph who never makes mistakes." So when he heard that they both thought highly of this paper, although Laplace was very confident in his academic level, he still felt quite pressured. As for Napoleon, he already had a premonition of being tied to the guillotine.

At this point, Joseph spoke up: "Since everyone is here, let's go in and get ready to start."

So everyone entered the small auditorium and took their seats. Joseph then began: "According to the usual procedure, we should invite the author of this paper, Mr. Lucien Evans, to the scene. However, Mr. Lucien Evans's provided address does not exist. So this hearing can only proceed without the presence of the party."

"He must know that his paper cannot withstand questioning, so he's hiding and dare not come, right?" Napoleon couldn't help but say.

"Academician Napoleon, haven't you read the 'Rules of the Academy Meetings'? Please abide by the rules of the meeting. If you want to speak, please raise your hand first, and then speak after getting permission from the meeting chairman," Joseph said.

Napoleon remained silent.

"Since the author is absent, let's skip this step and proceed directly to the next step. First, let the opposition raise questions and point out errors. Alright, Academician Napoleon, please come forward to state your reasons."

Napoleon looked around and then walked towards the platform. Meanwhile, he thought to himself, "It's a bit nervous to give a speech without a fully armed guard around."

But regardless of his nervousness, he had to speak. So Napoleon began: "As we all know, the reason mathematics is respected as a science is because it accurately describes our world. We can even say that mathematics is the most fundamental rule of the world, it is the language with which God created the world. Therefore, mathematics and reality are inseparable. Mathematical conclusions cannot and should not exist apart from reality. However, this paper has such a problem.

For example, if this paper is correct, then there would exist triangles with internal angles smaller than one hundred and eighty degrees. I want to ask, can any of you draw such a triangle?

Similarly, based on this paper, we see the conclusion that perpendicular and oblique lines on the same line do not necessarily intersect. Then who can draw such a figure? It's impossible, just like triangles with internal angles smaller than 180 degrees, the situation where perpendicular and oblique lines on the same line do not intersect does not exist in reality. Obviously, the person who wrote this paper completely ignored the real world, ignored the foundation on which mathematics exists. He degraded mathematics into a meaningless logical game. That is why I judge this paper to be unacceptable."

After saying this, Napoleon glanced at Fourier and then said, "I'm done speaking."

The mathematicians from the Paris College clapped together. Napoleon bowed slightly to them and then stepped down from the platform.

According to the rules, it should be Fourier's turn to speak when Napoleon finished. But at this moment, it was Joseph who walked up to the platform.

Seeing Joseph stepping onto the platform, Napoleon suddenly trembled all over, his hands and feet turning cold.

"Gentlemen, in fact, before Mr. Fourier made that judgment, he had discussed this paper with me. His evaluation of this paper is actually my evaluation as well. I believe that this is a groundbreaking, epoch-making paper of extreme importance. I predict that the significance of this paper is no less than that of Euclid's 'Elements.' Now, I will respond to the questions raised by Academician Napoleon just now."

"First of all, Academician Napoleon mentioned earlier that mathematics is not a meaningless logical game; it must have real significance. I very much agree with this point. However, I also want to remind Academician Napoleon that reality is not something he can subjectively determine." Here, Joseph glanced triumphantly at Napoleon.

"We know that if the frequency of sound is slightly higher or lower, we cannot hear it at all. But that does not mean that the sound does not exist. Bats use ultrasonic sounds that we cannot hear to navigate. Through photometric experiments, we can also find that in areas beyond violet light and beyond red light, where we appear to have no light, iodine silver can still undergo photochemical reactions. So what we hear with our ears is not necessarily complete reality, and what we see with our eyes is not necessarily complete reality either. Therefore, do not think that you can define reality. Reality may not be what you imagine."

Napoleon wanted to retort, "Then find a triangle with internal angles smaller than one hundred and eighty degrees!" But after a moment's thought, he remained silent.

"Well, let's look at this paper, starting with the first part," Joseph said, while conveniently projecting the first part onto the curtain hanging on the wall using a projector.

"Academician Napoleon, could you please tell us if there are any errors in this section?" Joseph asked.

This section mainly consisted of the five axioms of Euclidean geometry, the first four postulates, and a later assumption: "Through a point not on a line, there are two or more lines parallel to that line."

Napoleon was surprised, he looked at the content being projected, then hesitated and replied, "The previous ones are fine, but the last one is absurd and inconsistent with reality."

"Napoleon," Joseph said with a sarcastic tone, "I remember teaching you what proof by contradiction is when you were ten, right

?"

Napoleon hurriedly said, "Then there is no problem here." He knew that he had misspoken earlier, and if he continued to talk about "proof by contradiction," he would really appear as if he hadn't finished elementary school.

Since Napoleon didn't speak up, Joseph continued to display the content on the projector, and every time he showed a slide, Joseph would ask Napoleon, "Academician Napoleon, is there any problem with this part of the argument?"

Of course, there was no problem. If there were any issues, Napoleon and the group from the Paris College wouldn't have been busy for so long these days and still couldn't find any. So, every time, Napoleon could only answer dejectedly, "No, there isn't."

The projector continued to project the paper, and with Napoleon's repeated answers of "no problem," it finally reached the last section.

"Napoleon, is there no problem here either?" Joseph asked.

"Yes, there is no problem, but it doesn't match reality..." Napoleon wanted to salvage the situation.

"Napoleon, what you call reality is not equal to true reality!" Joseph responded.

"Then you draw a triangle with internal angles smaller than one hundred and eighty degrees!" Napoleon couldn't help but counterattack. He also knew that if he didn't retaliate now, he would be utterly defeated.

"Hehe, Napoleon," Joseph smiled and said, "you see, the entire process of argumentation conforms to the rules. If the premise is correct and the entire argumentation process is correct, but it still doesn't match what you assume to be reality. Reality cannot be wrong, so where is the mistake? Is it possible that the entire mathematical method, the entire mathematical system is wrong? Napoleon, your judgment is really brave, you are trying to overturn almost the entire mathematical system."

"I'm not... I'm not trying to... I just want to see a triangle with internal angles smaller than one hundred and eighty degrees." Napoleon could only cling to the triangle with internal angles smaller than one hundred and eighty degrees as a lifeline.

"No problem, I'll show you now." Joseph looked confident. Seeing Joseph's expression, Napoleon's heart trembled, he knew: a devastating blow was about to fall.