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Among the five postulates, the fifth one was the source of much interest for being very prolix and looking more like a theorem that needs to be proved rather than a postulate. But it was, in fact, equivalent to a proposition that was popular on the Earth: In a plane, through any point not on a given line, only one new line can be drawn that’s parallel to the given line. Since the establishment of the Congress of Magic, with the fast development in mathematics, more and more sorcerers, who pursued the sense of aesthetics that values simplicity in math, attempted to prove the results without using the postulate. However, no one had succeeded yet.

In Eric’s eyes, Levski was one of them who failed. Levski tried to use proof by contradiction to support the fifth postulate and started with the assumption that: In a plane, through any point not on a given line, at least two new lines can be drawn that’s parallel to the given line.

However, the result he got was surprising. By combining the assumption, the five axioms, and the rest of the four postulates, Levski drew up a geometry system that was logically consistent yet at the same time greatly conflicted with reality. The arcanists from Tower all believed that the system was absurd and treated it indifferently.

After Levski submitted his paper against the oppositions, the criticism of his reasoning was like a fierce storm. Without a doubt, his paper failed to pass the review.

"Eric, have you carefully read my paper? Do you see how I demonstrated it? Both the premise and the derivation are correct! Why you just can’t accept it?" Levski’s body was trembling from anger. Years of criticism and poverty had not made him yield: For more than ten years, his magic level and researches remained paused, countless mockery and satire were directed at him, but Levski never gave up his theory.

Eric raised his hand, signaling Levski to lower his voice. "Yes, I admit that your use of proof by contradiction and your logic reasoning are absolutely correct. But Levski, open your eyes and see this world. This table, the room... They all look different from what your geometry describes! They are real, my friend. And you tell me what we should believe! You’ve tried so many years, even printed out numerous copies and propagated them to the other arcanists, but has anyone believed in your geometry system so far?"

"No..." Levski lowered his head, dispirited. In the past, he thought that his paper was rejected because the members of the Arcana Review Board and the arcanists from Tower were too conservative, so he submitted his paper directly to the younger arcanists and to the authorities in mathematics including Douglas, Hathaway, and Paris. However, the younger arcanists still mocked his proposition, calling it "lacking common sense".

Meanwhile, the authorities in mathematics also chose to keep silent.

"I’ve modified it..." Levski hurriedly emphasized; his tone softened for only a single second. "This time it should be able to pass. Eric, please."

Eric sighed. "But you can’t keep acting like this, Levski... You’ve submitted this paper multiple times in the past ten years. And you never succeeded. Also, we have regulations. You can’t submit the same paper for multiple times. It’s a waste of the board members’ time. You’re already in your forties... I have to remind you. You’re still a junior-rank mage... "

"This time is different! I’ve perfected it. Eric, please... Let Mr. Evans read it... I promise I’ll focus on studying magic in the following years." Levski begged with hope in his eyes.

Eric’s serious face slightly twitched. "Mr. Evans only reads those subversive papers... You know, those that will make sorcerers’ brains explode. But yours only discusses the pure theories in math, and it won’t affect one’s cognitive world. So I’m afraid..."

A sorcerer’s cognitive world was based on his or her exploration into the truth of the world. Math was just their tools and thus could not affect its stability.

Before Levski kept insisting, Eric sighed again. "What about this... I’ll put ’subversive’ and ’math’ on the front page of your paper. So your paper will be sent to two board members specializing in mathematics, and Mr. Evans as well."

Eric understood that it was Mr. Evans who brought Levski the gleam of hope. The board members had not changed much within the past several years, and they were all quite annoyed with Levski’s paper. If it were not for newly-joined Mr. Evans, Levski would not have been so determined to submit it once again.

At least there was still hope!

"Thank you, Eric..." Levski became speechless from the surprise.

Eric waved his hand. "Go back and wait for the result. Hope your life can back on track as soon as possible."

Levski nodded seriously, feeling anxious but also full of hope. He had no idea if Mr. Evans would treat his paper fairly.

......

On the fifteenth floor of the magic tower, in a bright and spacious room.

Arms extending from both sides of a magic circle were busy sorting the papers.

"Math, Subversive..." The cold, metal voice paused a bit before making a final decision. "To Mr. Neeshka, Ms. Milina, and Mr. Evans."

......

In his cognitive world, where strings of starlight hanged down while elements and electrons revolved, Lucien spread out his spiritual power in waves and let the power fuse with starlight, elements, ice, and snow. Then he carefully vibrated his spiritual power waves to add the properties of spiritual particles onto time’s instantaneity.

Lucien was being extremely careful with the tiny modifications, for if his spiritual power went out of control, his entire cognitive world could be ruined within a second.

After a long time, Lucien finally ended his early morning meditation and left his bedroom to enjoy breakfast. Then he walked to the Congress of Magic’s headquarter tower as part of his physical exercise.

As soon as he stepped into the institution, he saw Lazar, who never came to the institution early, was walking back and forth in the office with a big smile on his face.

"Hey, Lazar, what makes you so happy today?" Asked Lucien.

"You come so early, Lucien!" Lazar was quite surprised, and then he said in a triumphant tone, "I can fly now!"

As he spoke, Lazar started flying in the office, almost hitting the ceiling.

"I see... So you’re a middle-rank now. Gotta celebrate that." Lucien grinned.

Lazar, whose landing still lacked some balance, laughed. "Of course! We’re having a party!"

Then he said to Lucien with gratitude, "Thank you, man. I’ve learned a lot in the past several months doing experiments with you. Your advanced research in the field of Element, especially the discovery of the electron, helped me gain a better insight. My cognitive world has become more stable since then, so I am able to make such a progress while I am still working on math."

"That’s why we are always exploring the truth of the world." Lucien smiled, but then his tone became a bit more serious. "But Lazar, you still have to work hard on your math. The more progress you make, the heavier you will rely on math as your tool."

Lazar nodded seriously. "I know where my problems lie. Also, since joining the institution, we’re all making great progress. Annick, Sprint, Katrina have told me that they are almost ready to become real sorcerers. They just still need some time to build up their spiritual power and to get some potions as aids."

When Lucien was absent, Lazar and the students followed their prior plan and kept working on studying cathode ray and cryogenic materials. But their schedules were not that tight anymore, so they could have some time to do their own experiments.

"I’m glad to see their progress." Lucien nodded in satisfaction.

After chatting for a while, Lazar suddenly jumped to a new topic. "So Lucien, how do you think of Mr. President’s recent experiment?"

This was a heated topic for almost every arcanist recently, and it had to do with the long-time debate over waves vs. particles. Lucien answered briefly, "If Mr. President’s theories are proven correct, we should be able to abandon the theory of Ether as a medium."

Of course, many would still try hard to come up with all kinds of theories to mend it.

"This’s the Evans I know. Lucien Evans is always sharp and loves to see people’s brain explode." Lazar joked. This comment was agreed by many arcanists.

"Maybe I’ll get a title because of this... Lazar, I’ll go and check out the Review Board first, and go to visit my teacher. When I’m back, I’ll celebrate for you." said Lucien.

Seeing that the other students were showing up one by one in the institution, Lucien decided to spend some time in his office of the Arcana Review Board. Although even if he did not show up, the golem would always send the papers to his place in the early evening. But since he was here in the headquarter tower, Lucien decided to take a look in the office so that it wouldn’t be empty forever.

......

As soon as Lucien stepped into the luxury office on the fifteenth floor, the golem welcomed him and said in its cold voice, "Master, a paper has just been sent to you."

"Paper?" Lucien was a bit surprised, since rarely were there papers qualified for being subversive.

Taking over the paper from the golem, Lucien saw the two words: Math and Subversive. Instantly, he had some expectations, since there were just a few possible findings in math that could be regarded as subversive within the current level of study.

"New Principles of Geometry with Complete Theory of Parallels...."

Lucien quickly browsed the paper and noticed that it was an improved version. Slightly frowning, Lucien said to the golem, "Go and get me the previous papers submitted by this person... together with the review comments of the board members."