Throne of Magical Arcana

Although the voice was soft, it was like a thunderbolt in the ears of Nesska, Mirina and others, deafening.

Those who have studied mathematics and science and won the Arcane Scepter Award will inevitably feel proud of mathematics, but in reality, mathematics is only a tool for arcane exploration and spell analysis, and it is their vassal. Arcanists are willing to devote their entire lives to this field of unparalleled beauty, and for them, enough is enough.

The arcanists in the tower who like the field of mathematics and physics have more or less thought similar to the meaning of Lucien's words, but these are just occasional pride, occasional flashes of inspiration, and occasional casual complaints. No one has ever described the side of mathematics that is higher than intuitive understanding and higher than real experience under such a shocking argument with such powerful arguments, and raised the importance of mathematics to a level like Lucien Evans. A status they never expected.

Even though they knew very well that Lucien was adding weight to the correct weight of Levsky's thesis, it didn't stop them from being excited and their blood boiling for a long time.

Levsky was trembling with excitement, yes, mathematics will not deceive me, so there is "Strict Proof of the Principles of Geometry and the Theorem of Parallel Lines"! In this seemingly limitless sea, in this stormy sea that never stops, it is precisely by grasping mathematics, relying on it wholeheartedly, and not being "deceived" by the outside world, that one can overcome the ups and downs , cross the vast sea, not to be blown over by wind and waves, not to be sunk by despair!

Fernando still didn't praise his students, but just nodded slightly. The deep meaning of these words is more worth exploring than the superficial content.

Lucien withdrew his right hand, put away the papers surrounding the entire meeting room, and placed another thick stack of papers just taken out of the storage bag in the magic circle, and smiled gently: "Next, let's try Start from another road and see if there is an unusual scenery."

There is a mathematical model and a proof that Levsky's geometry and the tower's geometry are compatible. Although Milina and other committee members are still extremely resistant, they don't want to deny themselves and admit that they have made mistakes, and they have been wrong for more than ten years. I have to initially agree with this new geometric system. At this point, if you want to overthrow Levsky geometry, you must overthrow the tower geometry that is compatible with it, which completely violates their original intention.

In addition to being hit by Lucien's words, they were emotionally complicated but relatively stable at this time, and they looked at the paper without prejudice.

"Another Hypothesis for the Theorem of Parallel Lines"?" The graceful and luxurious Milina read the title in a low voice, her hair curled up, and she vaguely guessed what it was.

"Another hypothesis..." Levsky seemed to feel that the fog was being dispelled before him, and he saw the problems he had ignored in the past ten years.

Lucien is like attending a class in a magic school, pointing his finger at the projected thesis, and letting the content be displayed line by line: "Mr. Levsky first assumes that 'passing a point outside the straight line, at least two straight lines can be drawn parallel to the known straight line' , and then together with the original axioms and postulates, a logically rigorous and self-consistent new geometric system is deduced, so why don't we make another assumption? In addition to forming a complete set with Levsky geometry and tower geometry An assumption, 'There is no straight line parallel to a given line through a point outside the line'."

"Next, let's do deductive reasoning and see what happens."

Levsky took a deep breath, feeling agitated again, as if he understood something, while Nesska, Mirina and other committee members also looked solemnly at the thesis projected by Lucien.

Pages of papers were flipped through, and paragraphs of discussion were presented. Since he was facing an authority in the field of mathematics and science, Lucien explained very quickly, and many places were briefly mentioned, but the expressions of Nessica and others became more and more serious. The more serious he became, the more puzzled he became. Suddenly, Mapel blurted out and murmured to himself: "It actually deduces a proposition that is different from Levsky's geometry but equally bizarre..."

"What the hell is going on..." Her voice elicited a response from Salgueiro.

"Could it be a new geometric system that is essentially different from the geometry of the tower?" Mirina was at a loss. Just a few hours ago, she firmly believed that it was impossible to have a geometry that was essentially different from the geometry of the tower. The new geometric system, but in less than a day, this point of view seemed to be ruthlessly shattered, and it was shattered twice in a row.

She was confused and thankful, fortunately, this is a point of view in the field of mathematics and science, and does not involve the composition of the cognitive world, otherwise she would have exploded her head with a bang, and she deserves to be a road with the titles of "skull-crusher" and "brain-eater" secretly Sean Evans.

Levsky was not puzzled, but fell into deep contemplation, why did this happen? Why starting from the different negations of the fifth postulate and the fifth postulate itself, can we get different geometric systems that are complete, independent, logically rigorous and self-consistent? Why? Does this have any relevance to the real world?

Under the influence of His Excellency Speaker Douglas, the arcanists who grew up in the Magic Council would inevitably like to ask why, but there were very few of them like Lucien.

"It's interesting..." Fernando nodded slightly.

Time passed quickly, and Lucien's thesis turned to the last part, using a model similar to a sphere to prove the feasibility of the previous content.

Nesska sighed deeply: "Sure enough, it is a new geometric system, Evans geometry."

"Mathematics really can't lie..."

It was because of arrogance and prejudice that I missed an opportunity to name the entire geometric system with my own name. If Levsky's hypothesis can be accepted, then Lucien Evans' hypothesis is actually easy to think of.

Lucien did not end, but showed the last few pages of the thesis: "I defined the concept of curvature in the thesis. From the calculation, it can be concluded that when the curvature is zero, it is a tall tower geometry. When the curvature is less than When it is zero, it is Mr. Levsky’s new geometry, and when the curvature is greater than zero, it is the geometry I just talked about. They have something in common in essence and can be compatible.”

Milina exhaled lightly, and now these two new geometric systems seem to be a little easier to accept.

Levsky suddenly realized that, just as he was about to applaud excitedly, he saw Lucien pressed his hand to signal for everyone to be quiet.

What else is he going to say?

The same question appeared in the minds of different committee members, and it appeared in the mind of Levsky.

Lucien no longer roared aggressively and aggressively like before, but said in a soft and gentle voice:

"We can see that under certain circumstances, the mathematical knowledge we study exceeds our experience and intuitive feelings, which makes us subject to many constraints, making the development of the field of mathematics like an eagle with its wings bound. Go hard."

"Therefore, we can try to separate mathematical knowledge from reality, ignore their physical models and practical significance for the time being, and simply start from the most primitive, most fundamental, and simplest concepts and axioms, and develop rigorous and self-awareness through reasoning and deduction. A consistent mathematical system. As for what this system does and what it represents, it will not be considered until the specific arcane exploration encounters new problems and needs this system.”

"This is my personal opinion."

Lucien briefly mentioned the concept of the axiom system, but did not discuss it in depth. It would not be too late for the arcanists to slowly accept this concept and develop the awareness of thinking in this direction. It needs to be done step by step.

Clap, clap, sparse applause, from Levsky, he felt that he and Commissioner Evans had too much in common, and every word he said was something he felt vaguely but could not express At the same time, his understanding, support, and proof of his new geometric system are no less than saving his own life, and his deafening speech makes me even more excited when I think about it now.

In the applause of one person, Nesska's expression changed again and again, and all the previous events came to mind. Finally, he hesitated and raised his hand, applauding lightly.

With the first person's response, Mirina, Mapel, Salgueiro and others followed suit and applauded, gradually changing from hesitation and resistance to sincerity.

"Now, is there any objection to Commissioner Evans' high evaluation of Levsky's paper?" Fernando asked after the applause stopped.

Nessika frowned at his long white eyebrows, stood up abruptly, looked at Levsky and said, "Please accept my apology, this is a paper that is good enough to win the 'Arcane Scepter' award, my arrogance and prejudice prevented me from accepting this new geometry before. I fully agree with Commissioner Evans' assessment."

"I also apologize to you for the ten years of indifference, slander and attack, Levsky, you are a genius, excellence, great mathematician, my stubbornness and shallowness blinded me , make me look ugly, the evaluation results of Commissioner Evans and the Arcane Scepter Award are the best compliments for you." Milina also stood up with Nessica, and bowed deeply with the mysterious forehead lifting ceremony.

Levsky expected that Nesska, Mirina and the others would no longer object, but he did not expect that they would directly apologize in public. Suddenly, a sour emotion surged into his head, making him His nose became sore and his eyes became blurred. He watched the committee members get up and apologize, but he couldn't speak.

Are you wronged? Of course I am wronged!

pain? Of course it hurts!

But at this moment, it all seems to be paying off with a belated affirmation!

Nesska looked at Levsky, whose eyes were red and his lips were trembling but unable to speak, sighed understandingly, and then looked at Lucien: "Commissioner Evans, I apologize for the previous doubts, you are Undoubtedly a genius in mathematics, you are an undisputed authority in the field of mathematics, your new geometric system and the proof of Mr. Levsky's geometric system will surely win you the 'Arcane Scepter' award!"

"Thank you for your approval." Lucien replied softly.

Milina noticed that Lucien was a little unusual, and asked suspiciously: "Commander Evans, what's wrong with you?"

Lucien smiled wryly: "My voice is hoarse..."

Stormmaster is not so easy to learn!

changed.