Although Lucien's voice was low, it was as loud as thunder in the ears of Neeshka and Milina.
Having studied mathematics and won the Arcana Scepter Award, it was natural for them to be proud of mathematics. However, in reality, mathematics was only a tool for arcana exploration and spell analysis. Few arcanists were willing to devote their whole life to the field that was full of unparalleled beauty. For them, it was enough as long as it was enough.
The arcanists in Tower who loved mathematics more or less had the same idea as Lucien, but it was just a moment of pride, a moment of inspiration, or a moment of carelessness. None of them had ever been like Lucien Evans, who used such an impactful argument to describe the fact that mathematics was more important than intuition and experience. Lucien Evans had elevated the importance of mathematics to a position that they had never dreamed of.
Even though they knew that Lucien was trying to prove that Levski's paper was correct, it still did not stop them from feeling excited.
Levski was even trembling with excitement. Yes, mathematics would not lie to him. That was why there was a Rigorous Proof of the Principles of Geometry and the Parallel Line Theorem! In this seemingly boundless ocean, where the storm never stopped, it was precisely by grasping mathematics tightly, relying on it wholeheartedly, and not being "deceived" by the outside world that one could go through all kinds of difficulties, cross the boundless ocean, and not be blown away by the wind and waves, and not be drowned by despair!
Fernando still did not praise his student. He just nodded slightly. The deeper meaning of Lucien's words was more worth exploring than the surface content.
Lucien took back his right hand and put away the papers that surrounded the conference room. He put another thick stack of papers in the magic circle and smiled gently, "Now, let's try another way. Let's see if we can find something unusual."
With the mathematical model and the proof that Levski geometry was compatible with Tower geometry, Milina and the other members of the committee were still reluctant to admit that they had made mistakes for more than ten years. However, they had no choice but to accept the new geometry system. At this point, if they wanted to overthrow Levski Geometry, they would have to overthrow Tower Geometry which was compatible with it, which was completely against their original intention.
Also, Lucien's words had touched their hearts. They had mixed feelings but were relatively calm at this moment. They read the paper without holding any preconceived ideas.
"Another Hypothesis of the Parallel Line Theorem?" Milina, who had her hair tied up elegantly, read the title in a low voice. She seemed to have guessed something.
"Another hypothesis …" Levski felt that the fog in front of his eyes was dispelled, and he saw the problem that he had neglected for more than ten years.
Lucien pointed his finger at the projected paper and showed the content line by line, "Mr. Levski first postulated that 'if you cross a point beyond a straight line, you can draw at least two straight lines parallel to the known straight line'. Then, together with the original axioms and postulates, he deduced a new geometric system that is logically rigorous and self-consistent. Why don't we make another postulate? Another assumption that forms a complete set with Levski geometry and Tower geometry is that there is no line parallel to the known line beyond a point of a straight line. "
"Now, let's do some deductive reasoning and see what will happen."
Levski took a deep breath and became excited again. He seemed to have understood something. Neeshka, Milina and the other members also looked at the paper projected by Lucien seriously.
Pages after pages of the paper were turned, and paragraphs of discussion were given. Since Lucien was an authority in the field of mathematics, he explained very quickly and briefly. However, Neeshka and the other members became more and more serious and confused. Suddenly, Mabel blurted out in a low voice, "He really deduced a proposition that is different from Levski Geometry, but equally strange …"
"What the hell is going on …" Her voice triggered Salgueiro's response.
"Is it another new geometry system that is fundamentally different from Tower Geometry?" Milina was at a loss. Just a few hours ago, she still firmly believed that there was no new geometry system that was fundamentally different from Tower Geometry. However, in less than a day, her view seemed to have been ruthlessly shattered, twice in a row.
She was both confused and relieved. Thankfully, it was a mathematical point of view and did not involve the composition of the cognitive world, or her head would've exploded. Lucien Evans truly deserved to be called "Cranium Crusher" and "Brain Eater" in secret.
Levski was not confused. Instead, he fell into deep thought. Why did this happen? Why did different geometry systems that were independent, logically and self-consistent come from different negations of the fifth postulate and the fifth postulate itself? Why is this so? Did it have anything to do with the real world?
Under the influence of President Douglas, the arcanists who grew up in the Congress of Magic liked to ask why, but few arcanists were like Lucien.
"Interesting …" Fernando nodded slightly.
Time flew. Lucien turned to the last part of the paper, and used a spherical model to prove the feasibility of the previous content.
Neeshka sighed deeply. "Sure enough, it's a new geometry system, Evans Geometry."
"Mathematics really doesn't lie …"
It was because of his arrogance and prejudice that he missed the opportunity to name the whole geometry system with his own surname. If one could accept Levski's hypothesis, then Lucien Evans' hypothesis was actually very easy to come up with.
Lucien did not stop there. Instead, he showed the last few pages of the paper. "I defined the concept of curvature in the paper. According to the calculation, when the curvature is zero, it's Tower Geometry; when the curvature is less than zero, it's Mr. Levski's new geometry; and when the curvature is greater than zero, it's the geometry I just talked about. They have something in common and can be compatible."
Milina let out a sigh. Now the two new geometry systems seemed to be more acceptable.
Levski was suddenly enlightened. When he was about to clap his hands in excitement, he saw Lucien waving his hand, signaling everyone to be quiet.
What else was he going to say?
The same question appeared in the minds of different members, and also in Levski's mind.
Lucien was no longer as aggressive and aggressive as before. Instead, he said in a very soft and gentle voice,
"We can see that, under certain circumstances, the mathematical knowledge we study is beyond our experience and intuition, which constrains us a lot. The development of mathematics is like an eagle whose wings are tied up, and we can only move forward with great difficulty."
"Therefore, we can try to separate the mathematical knowledge from reality. For the time being, we can ignore the real models and practical meanings of the mathematical knowledge. We can start from the most primitive, fundamental, and simplest concepts and axioms, and develop a rigorous and self-consistent mathematical system through deduction and deduction. As for what this system can do and what it represents, we can only consider it when we encounter new problems in arcana exploration. "
"This is my personal opinion."
Lucien briefly mentioned the concept of the axiom system, but did not elaborate further. It would not be too late to develop it when the arcanists gradually accepted the idea. Everything had to be done step by step.
Clap, clap, clap. Levski felt that he had too much in common with Mr. Evans. Every word that Mr. Evans said was something that Levski could not express. At the same time, Mr. Evans's understanding, support, and proof of his new geometry system were no less than saving his life. Mr. Evans's inspiring speech also made Levski very excited.
In the applause of one person, Neeshka's expression changed again and again. All the things that happened before came to his mind. Finally, he raised his hand hesitantly and clapped.
With the first response, Milina, Mabel, Salguero, and the others also clapped. Gradually, their hesitation and resistance became sincere.
"Now, is there anyone else who objects to Mr. Evans's high praise for Levski's paper?" Fernando asked after the applause stopped.
Neeshka pulled his long white eyebrows and stood up abruptly. He looked at Levski and said, "Please accept my apology. This is a paper that deserves the Arcana Scepter Award. My arrogance and prejudice prevented me from accepting this new geometry system. I completely agree with Mr. Evans's evaluation. "
"I also want to apologize to you for my indifference, slander, and attacks in the past ten years. Levski, you're a genius, an excellent, and great mathematician. My stubbornness and shallowness blinded me and made me look ugly. Mr. Evans's evaluation and the Arcana Scepter Award are the best compliments for you." Milina also stood up and bowed deeply to Levski.
Levski knew that Neeshka and Milina would not object anymore, but he did not expect that they would apologize in public. Instantly, a surge of bitterness rushed to his head, making his nose sour and his eyes blurry. He watched the members stand up and apologize one after another, but he could not say anything.
Was he wronged? Of course he was!
Was he in pain? Of course he was!
But at this moment, it seemed that he had finally gotten what he deserved!
Seeing Levski's red eyes and trembling lips, Neeshka sighed and then turned to Lucien, "Mr. Evans, I apologize for my previous doubts. You're undoubtedly a genius in mathematics, and you're the undisputed authority in the field of mathematics. Your new geometry system and your proof of Mr. Levski's geometry system will definitely win you the Arcana Scepter Award!"
"Thank you for your approval," replied Lucien in a very low voice.
Milina noticed that Lucien was a bit strange. She asked confusedly, "Mr. Evans, what's wrong with you?"
Lucien smiled bitterly, "I lost my voice …"
It was not easy to learn the Lord of Storm!
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