The Fox of France

At this moment, not only did Napoleon's heart skip a beat, silently calling out that this wasn't good, but even Laplace and the others were startled. What? President Bonaparte already had a method to prove this peculiar geometry? But this was normal. If there was anyone in the world who could quickly solve this problem, "Never Wrong Joseph" was undoubtedly the most likely candidate.

At this moment on the podium, Joseph leisurely greeted Fourier, "Mr. Fourier, hmm, could you please help distribute my paper for everyone to see? I could also use a break and have some water. Once they've finished reading it, we can continue our discussion."

With that said, Joseph slowly returned to his seat and picked up his tea cup for a drink. Fourier then distributed a copy of the paper to everyone.

A copy of Joseph's paper also landed in front of Napoleon. He lowered his head and saw the title "An Attempt to Explain Non-Euclidean Geometry." He despairingly flipped through the paper, trying to find any flaws in it. Although he knew that at this moment, the possibility of Joseph's paper having flaws was smaller than leading a hundred thousand French troops against less than a thousand Prussians in battle and still being completely defeated. (After all, there was still the possibility of meteorites falling from the sky and hitting them.)

Napoleon's mathematics was actually quite good. Although it was still far from the level of an academician, among ordinary people, he was definitely at the top. So, he didn't have any problems understanding the paper.

With a hopeful mentality, Napoleon quickly skimmed through the paper. This paper was indeed in Joseph's typical style, rigorously argued, leaving no loopholes, and even included one or two new mathematical deductions as a bonus.

"Is this using differential geometry? The entire argument process seems to be flawless," Napoleon raised his head and glanced at Laplace and the others beside him. He saw that their eyes were wide open, but none of them seemed to have anything to say.

"Damn, most likely they can't find any problems either. Joseph has really managed to construct such a triangle on a hyperbolic surface. This, this... I'm really foolish, really, I actually ran into Joseph's stronghold expecting him not to retaliate, forgetting that this guy has always been petty..."

Finally, Laplace and the others finished reading the paper. They scrutinized it more carefully than Napoleon, but like him, they couldn't find any errors in the paper.

"Never Wrong Joseph," many people couldn't help but think of this phrase, feeling that the burden weighing on them had increased slightly.

Joseph had finished his tea and poured two more cups. Seeing that everyone had almost finished drinking, he set down his teacup and leisurely said, "It seems like everyone has finished reading? Now, does anyone have any doubts about Mr. Lucien Evans's paper?"

No one spoke up.

Joseph continued, "In addition to my method, there is also a more ingenious proof, completed by my friend, Academician Gauss. You can also take a look at it."

Fourier then distributed Gauss's paper to everyone.

Gauss's paper was also titled "An Attempt to Explain Non-Euclidean Geometry," but his approach was indeed different from Joseph's. His approach was simpler and more unique. He used the concept of projection to prove the compatibility of the new geometry with Euclidean geometry on the unit circle. If Euclidean geometry held, then the new geometry must also hold!

This concise derivation, this wonderful proof, was full of the beauty of mathematics. For Laplace and the others, there was nothing more shocking than this.

"I think, regarding Mr. Lucien Evans, who is actually an anonymous author, everyone should no longer have any doubts about this paper, right?" Joseph spoke up, "If that's the case, I'm going to announce the result of this hearing. Hmm, I believe Mr. Fourier made the correct judgment in evaluating this paper. Now, who agrees, and who disagrees?"

So everyone, including Napoleon, expressed their agreement.

"Very good, I'm glad to see that our Academy of Sciences is indeed an academy of science, and everyone is willing to reason. Whether it's right or wrong, everyone is willing to use papers to speak. Hmm, Mr. Fourier, you made the judgment to pass this paper before seeing the perfect proof. And we all know that in this paper, there are many things that surpass our common sense and are difficult for us to accept. Now, I would like to ask you to explain why you made the decision to pass this paper before seeing the perfect proof."

Fourier nodded and walked up to the podium.

"Respected academicians, actually, when I first saw this paper, I also felt absurd and unbelievable, and firmly believed that there must be some error in this paper. However, at that time, I felt that although the author of this paper had produced a ridiculous composition, the mathematical level demonstrated in the paper was extremely astonishing. I think anyone who truly restrains their disgust and carefully reads this paper should be able to see this point. I thought at the time: even if this paper is really wrong, really absurd. It is a higher level of error and absurdity, just like Zeno's paradox (Achilles never catches up to a tortoise ahead of him), which is clearly absurd but may have very profound implications. It's a ridiculousness worth taking seriously. Just like the study of Zeno's paradox led to a deep investigation into finite and infinite, continuity and discreteness.

So I carefully studied this paper again. This kind of study—honestly, it frightened me. My heart told me that this thing must be wrong, where in the world does such reasoning exist? But my brain told me that there was no error in this paper mathematically.

This was truly a terrifying thing because it almost meant that our mathematics contradicted reality. It was possible that our mathematics was fundamentally wrong. At that time, I was so scared by my own thoughts that I couldn't even eat.

Even Laplace couldn't help but nod in agreement with this statement. Because it was indeed terrifying. It was as scary as the sudden fluctuation in the amplitude of the cosmic microwave background radiation between one and five percent, or as if the universe suddenly began to flicker.

However, at this moment, I suddenly remembered something. It was the President's seemingly completely unreasonable 'Bonaparte Bright Spot Experiment.' Wasn't that experiment also completely unrealistic? But as long as the conditions were right, it would actually appear in reality. So, I found some comfort in that. I thought, maybe it's not that mathematics is wrong, or reality is wrong, but rather my own understanding of reality is wrong. The real world is so vast, yet our scope of interaction is so limited. What right do we have to determine what is in accordance with reality and what is not? Maybe, under certain special conditions, this strange geometry can really be realized? Just like how, as long as the conditions are right, we can really see a bright spot in the shadow cast by an opaque object.

So, I discussed this paper and my thoughts with the President, as well as with Academician Gauss. They all agreed with my thoughts and joined me in trying to find the conditions in reality that would allow this strange and counterintuitive geometry to hold. The

results of our discussion are all written in this paper."

Fourier bowed slightly to everyone and said, "That's all I have to say."

At this moment, the entire Academy of Sciences fell into a strange silence. Everyone's hearts were filled with complex emotions.

After a long time, Laplace finally said, "Mr. Fourier, your words make sense."

Fourier smiled slightly, not saying anything more.

Napoleon looked at Laplace, then at Joseph and Gauss, and finally at the two teacups on the table, quietly saying to himself, "The true power of science and mathematics... it's not about being always right. It's about being willing to admit when you're wrong and to seek truth wherever it leads."

At this moment, he suddenly felt a sense of relief in his heart.

Maybe, this world is not as terrifying as it seems. As long as there are people like Joseph and Gauss, as well as Fourier and Laplace, the light of reason will continue to shine, dispelling the darkness of ignorance and fear.

And as for him, Napoleon Bonaparte, maybe it's time for him to focus on being a leader, not just a conqueror. Maybe it's time for him to lead his nation not only to victory on the battlefield but also to greatness in the fields of science, technology, and culture.

Yes, maybe it's time for him to lead the surrender.

And with that thought in mind, Napoleon stood up and said, "Gentlemen, I have made up my mind. I am going to implement the policy of 'L'Ecole Polytechnique,' where the most talented individuals from all walks of life will be selected and trained to serve our nation. We shall invest in education, research, and innovation, and strive to make France not only the strongest but also the most enlightened nation in the world!"

And thus began a new chapter in the history of France, a chapter filled with hope, progress, and enlightenment.

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