A Devastating Blow

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

Before the hearing, Napoleon and his advisors carefully studied the paper, hoping to find any hidden errors in its argumentation. However, despite their great efforts, they were unable to find any such flaws.

"I don't even know how this terrible paradox came about. But its error is undeniable. So, in the debate, I suggest that we can only attack it by focusing on the fact that this paper is inconsistent with reality and has no feasible model." In the end, Laplace and others still put forward this suggestion.

Although Napoleon felt that this approach was insufficient to completely defeat his opponents, it was the only method he could use at the moment. With this method, at least he could remain undefeated.

The weather was fine on the day of the hearing, and Napoleon and his allies arrived on time at the entrance of the small auditorium where the hearing was being held. They happened to run into Joseph with Gauss, Fourier, and a group of others.

"Mr. Fourier, how could you support such a strange paper?" Laplace asked, leaning closer to Fourier.

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

In fact, Laplace's conversation with Fourier at this time was largely a tactical maneuver, intended to put psychological pressure on Fourier. However, Fourier's inclusion of Gauss and Joseph only increased Laplace's pressure. Gauss, though young, had achieved remarkable mathematical success, and his talent and ability to solve difficult problems were widely admired. Dean Bonaparte, on the other hand, was known as "Joseph, who never makes a mistake." Therefore, when Laplace heard that both of them also thought the paper was excellent, Laplace felt considerable pressure, despite his confidence in his own abilities. As for Napoleon, he already had a premonition of being led to the guillotine.

At this moment, Joseph spoke up, "Now that everyone is here, let's go in and get ready to begin."

So everyone went into the small auditorium and took their seats. Joseph then began to speak:

"According to standard procedure, we should invite the author of this paper, Mr. Lucien Evans, to be present. However, the address Mr. Lucien Evans provided does not exist. Therefore, this hearing can only be held in the absence of the person involved."

"He knows his thesis can't withstand scrutiny, so he's hiding and doesn't dare to come, right?" Napoleon couldn't help but ask.

"Academician Napoleon, haven't you read the 'Discipline Guidelines for the Academy of Sciences Meetings'? Please abide by the meeting rules. If you wish to speak, please raise your hand first and speak only after receiving permission from the meeting chair," Joseph said.

Napoleon then fell silent.

"Since the author is absent, we'll skip that step and move directly to the next. First, the opposing side will raise questions and point out errors. Alright, Academician Napoleon, please come up to the stage and state your reasons."

Napoleon looked around, then walked towards the podium. At the same time, he thought to himself, "It's a little insecure to give a speech without a fully armed guard."

Despite his apprehension, Napoleon still had to speak. So he began, "As we all know, mathematics is a respected science because it accurately describes our world. We can even say that mathematics is the most fundamental rule of the world; it is the language of God's creation. Therefore, mathematics and reality are inseparable. Mathematical conclusions cannot, and should not, exist detached from reality. This paper, however, suffers from this very problem."

For example, if this paper is correct, then triangles with an interior angle sum of less than 180 degrees would exist. My question is, can anyone draw such a triangle?

Similarly, based on this paper, we see the conclusion that a perpendicular line and an oblique line to the same straight line do not necessarily intersect. So who can create such a diagram? It's impossible. Just like triangles with interior angles less than 180 degrees, the situation where a perpendicular line and an oblique line to the same straight line do not intersect does not exist in reality. Clearly, the author of this paper completely ignores the real world and the very foundation upon which mathematics exists. He has reduced mathematics to a meaningless logical game. This is why I judge this paper to be unqualified."

After saying this, Napoleon glanced at Fourier and then said, "I have finished speaking."

The mathematicians at the École Normale Supérieure all applauded. Napoleon bowed slightly to them and then stepped down from the podium.

According to the rules, Fourier should have been the one to speak at this point. But instead, Joseph stepped onto the stage.

When Napoleon saw Joseph walk onto the podium, he trembled violently and his hands and feet went cold.

"Gentlemen, in fact, Mr. Fourier discussed this paper with me before making that judgment. His evaluation of this paper is, in fact, my evaluation as well. I believe that this is a groundbreaking, innovative, extremely important, and epoch-making paper. 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 earlier."

"First, Academician Napoleon just mentioned that mathematics is not a meaningless logical game; it must have real-world significance. I completely agree with that. However, I must also remind Academician Napoleon that reality is not something he can subjectively determine." At this point, Joseph gave Napoleon a smug look.

"We know that if the frequency of a sound is higher or lower, we can't hear it at all. But that doesn't mean sound doesn't exist. Bats use higher-frequency sounds, which we can't hear, for navigation. We can also find through photosensitive experiments that silver iodide can still react in areas outside of violet and red light, places that appear dark to us. Therefore, what we hear is not necessarily the complete reality, and what we see is also not necessarily the complete reality. So don't think you can define reality. Reality is not necessarily what you think it is."

Napoleon wanted to retort, "Then find a triangle whose interior angles sum to less than 180 degrees!" But after thinking about it, he remained silent.

"Well, let's look at this paper. Let's start with the first part." Joseph said, as he projected the first part onto a screen hanging on the wall using a slide projector.

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

This section mainly covers the five Euclidean Geometry, the first four postulates, and the final assumption. "Through a point outside a line, there are two or more lines parallel to that line."

Napoleon was taken aback. He glanced at the projection and then hesitated before replying, "The first few are fine, but the last one is absurd and doesn't reflect reality."

"Napoleon," Joseph said sarcastically, "I remember when you were ten years old, I already taught you what proof by contradiction was, didn't I?"

Napoleon quickly replied, "Then there's no problem here." He knew he had misspoke earlier, and if he continued to argue about "proof by contradiction," he would really make himself look like a fool who hadn't even finished elementary school.

Since Napoleon remained silent, Joseph continued to present the remaining content on the slide projector. After each slide, Joseph would ask Napoleon, "Academician Napoleon, is there a problem with the argument in this section?"

Of course there was no problem. If there were, Napoleon and his colleagues at the École Normale Supérieure had been working on it for days; how could they not have found it? So, each time, Napoleon could only answer dejectedly, "No, no."

The slide projector projected the paper slide by slide, and with Napoleon's reply of "No, no problem," it finally reached its last paragraph.

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

"Yes, there's no problem, but it doesn't match reality..." Napoleon still tried to salvage the situation.

"Napoleon, your description of reality is not the same as the actual reality!" Joseph retorted.

"Then draw a triangle whose interior angles sum to less than 180 degrees," Napoleon couldn't help but retort. He knew that if he didn't fight back, he would be utterly defeated.

"Heh heh, Napoleon," Joseph said with a smile, "You see, the entire argument follows the rules. If the premises are correct, the entire argument is correct, but it's different from reality, just as you assumed. Reality can't be wrong, so where is it wrong? Is the entire mathematical method, the entire mathematical system, wrong? Napoleon, your judgment is truly courageous; you're trying to overturn almost the entire mathematical system."

"No, I didn't. I just wanted to see triangles with interior angles less than 180 degrees." At this point, Napoleon could only cling to the idea of triangles with interior angles less than 180 degrees as a last resort.

"No problem, I'll show you right now." Joseph looked confident. Seeing Joseph's expression, Napoleon's heart skipped a beat. He knew: something terrible was about to happen; the most devastating blow was about to fall.