Although the voice was soft, it was like a bolt from the blue when it was heard by Nessica, Mirina and others, deafening.
They have studied mathematical knowledge and won the Arcane Scepter Award, and they will inevitably have a sense of pride in mathematics, but in reality, mathematics is only a tool for arcane exploration and spell analysis, and they are their vassals.
The arcanists in the tower who like the field of mathematics have more or less thoughts similar to the meaning in Lucian's words, but this is only occasional arrogance, occasional flashes of inspiration, and occasional casual complaints, no one has ever used such an impactful statement under such a shocking argument to tell the side of mathematics that is higher than intuitive understanding and higher than real experience, and elevates the importance of mathematics to a status they have never hoped for.
Even if they knew very well that Lucian was adding weight to Levsky's thesis, it did not prevent them from being excited and boiling their blood for a long time.
Levsky was even more excited and trembling, yes, mathematics will not deceive me, so there is "Strict Proof of Geometric Principles and Parallel Line Theorems"! In this seemingly boundless sea, in this sea where the storms never stop, it is precisely by grasping mathematics and relying on it wholeheartedly, and not being "deceived" by the outside world, that you can break through the ups and downs, cross the vast sea, not be blown over by the wind and waves, and not be sunk by despair!
Fernando still did not praise his students, but nodded slightly, the deeper meaning of these words is more worth exploring than the surface content.
Lucian withdrew his right hand, put away the papers surrounding the entire conference room, put another thick stack of papers he had just taken out of the storage bag in the magic circle, and said with a gentle smile: "Next, let's try to start from another road and see if there can be an unusual scenery."
Although Mirina and other committee members were still extremely resistant in their hearts, they did not want to deny themselves and admitted that they had made mistakes, and they had been wrong for more than ten years, but they had to initially agree with this new geometric system. At this point, if they want to overthrow Levsky geometry, they must overthrow the tower geometry that is compatible with it accordingly, which is completely contrary to their original intention.
In addition, they were hit by Lucian's words, and they were emotionally complex but relatively stable at this time, looking at the paper without any prejudice.
"Another Assumption for the Parallel Line Theorem"? Her hair was up, and the graceful and luxurious Mirina read the question in a low voice, vaguely guessing something.
"Another hypothesis...... Levsky seemed to feel that the fog in front of him was dispelled, and he saw the problems he had ignored in his persistence for more than ten years.
Lucian was like a magic school class, pointing his finger at the projected paper and showing the content line by line: "Mr. Levsky first assumed that 'a little outside the line, at least two straight lines can be drawn parallel to the known straight line', and then together with the original axioms and postulates, he deduced a new geometric system that is logically rigorous and self-consistent, so why don't we make another assumption? Another assumption that forms a complete set with Levsky geometry and tower geometry is that 'a point outside the line, no line is parallel to the known line'."
"Next, let's do deductive reasoning and see what happens."
Levsky took a soft breath, his emotions agitated again, as if he understood something, and Nessica, Mirina, and other committee members also looked solemnly at Lucian's projected paper.
Page by page of papers, paragraphs of discussions given, because he was facing an authority in the field of mathematics and science, Lucian explained very quickly, and many places were briefly explained, but the faces of Nesika and the others became more and more serious and confused, and suddenly, Mapel blurted out and whispered to himself: "I actually deduced a proposition that is different from Levsky's geometry but is equally bizarre and bizarre......"
"What the hell is going on......" her voice elicited Salghero's response.
"Is it another new geometric system that is fundamentally different from the geometry of the tower?" Mirina was at a loss, just a few hours ago, she was firmly believing that it was impossible to have a new geometric system that was fundamentally different from the geometry of the tower, but in less than a day, this view seemed to be ruthlessly shattered, and it was shattered twice in a row.
She was confused and glad that fortunately, this was a point of view in the field of mathematics and science, and it did not involve the composition of the cognitive world, otherwise she would have exploded her head with a bang, worthy of Lucian Evans, who secretly had the titles of "Skull Crusher" and "Brain Eater".
Levsky was not puzzled, but fell into deep contemplation, why did this happen? Why do we get different geometric systems from the different negations of the fifth postulate and the fifth postulate itself, each of which is complete, independent, logically rigorous and self-consistent? Why is this? Is this relevant to the real world?
Under the influence of His Excellency Speaker Douglas, the arcanists who grew up in the Magic Council inevitably like to ask why, but there are very few like Lucian.
"It's interesting......" Fernando nodded slightly.
Time flies, and Lucian's thesis turns to the final part, proving the feasibility of the previous content with a spherical-like model.
Nesika sighed deeply: "Sure enough, it's a new geometric system, Evans geometry."
"Mathematics really doesn't lie......"
It is because of arrogance and prejudice that he missed an opportunity to name the entire geometric system with his own surname.
Lucian did not finish, but showed the last few pages of the paper: "I defined the concept of curvature in the paper, and from the calculations it can be concluded that when the curvature is zero, it is tower geometry, when the curvature is less than zero, it is Mr. Levsky's new geometry, and when the curvature is greater than zero, it is the geometry I just mentioned.
Mirina exhaled softly, and now the two new geometry systems seemed to be a little more acceptable.
Levsky suddenly realized, and just as he was about to applaud with joy and excitement, he saw Lucian pressing his hand down and signaling everyone to be quiet.
What else does he want to say?
The same question appeared in the minds of different commissioners, in Levsky's mind.
Lucian no longer roared as fiercely and aggressively as before, but said in a very soft and soft 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, and can only move forward with difficulty."
"Therefore, we can try to separate mathematical knowledge from reality, temporarily do not consider their physical models and practical meanings, and simply start from the most primitive, fundamental, and simple concepts and axioms, and develop a rigorous and self-consistent mathematical system through reasoning and deduction. As for what this system does and what it represents, we will wait until we encounter new problems in specific arcane exploration and need this system."
"This is my personal opinion."
Lucian briefly mentioned the concept of axiom system, but did not discuss it in depth, or wait for the arcanists to slowly accept this concept, and it is not too late to develop it with the consciousness to think in this direction, everything needs to be done step by step.
Crackling, sparse applause sounded, from Levsky, he felt that he and Commissioner Evans had too much common language, and every word he said was something he vaguely felt but could not express, and at the same time, his understanding, support, and proof of his new geometric system were no less than saving his own life, and his deafening speech made him even more excited to think about it now.
In the applause of a person, Nessica's face changed again and again, and all the previous things came to mind, and finally, he hesitated and raised his hand and applauded gently.
With the response of the first person, Mirina, Mapel, Salghero and others also followed suit, gradually changing from hesitation and resistance to sincerity.
"Now, is there anyone who objects to Commissioner Evans' high evaluation of Levsky's paper?" Fernando asked after the applause stopped.
Nesikara lowered his long white eyebrows, stood up suddenly, looked at Levsky and said, "Please accept my apology, this is a thesis worthy of the 'Arcane Scepter' award, my arrogance and prejudice have prevented me from accepting this new geometric system before. I fully agree with Commissioner Evans' assessment."
"I also apologize to you for the indifference, slander and attacks of the past ten years, Levsky, you are a genius, outstanding, great mathematician, my stubbornness and shallowness have blinded my eyes and made me look ugly, Commissioner Evans' evaluation results and the Arcane Scepter Award are the best praise for you." Mirina also got up after Nesica and bowed deeply with the mysterious forehead support ceremony.
Levsky expected that Nessica, Mirina and others would no longer object, but he did not expect them to apologize directly in public.
Are you aggrieved? Of course it's wronged!
Is it painful? Of course it's painful!
But at this moment, these all seem to have paid off because of belated affirmations!
Nesica looked at Levsky, whose eyes were red and his lips trembled but he couldn't speak, sighed understandingly, and then looked at Lucian: "Commissioner Evans, I apologize for the previous question, you are an undoubted mathematical genius, you are an undisputed authority in the field of mathematics, and your new geometric system and the proof of Mr. Levsky's geometric system will surely make you win the 'Arcane Scepter' award!"
"Thank you for your recognition." Lucian replied softly.
Mirina noticed that Lucian was a bit abnormal and asked suspiciously: "Commissioner Evans, what's wrong with you?"
Lucian smiled bitterly: "My voice is hoarse......"
The storm lord is not so easy to learn!
It has been changed.
(End of this chapter)