Sky cleared up after the snow. Sunlight warmed up everything on the ground.

The heavy steps of the steel golem echoed from within the corridor. Pushing open the office door, the golem said to Lucien in its cold rigid voice, "Master, here are the six papers submitted by the same author, as well as the comments by the board members."

This was one of the advantages of being a member of Arcana Review Board — A member did not need to spend any arcana points for checking papers and their corresponding comments. This was for encouraging the in-depth study of arcana and the prudent attitude for writing reviews.

Lucien took over the pile of papers, signaled the steel golem to guard outside his office, and immediately started reading.

From the several papers submitted in the past, it could be seen that the author, Levski, had delved into a geometry system which was contradictory to the current Tower system. In his most recent paper, Levski had developed a brand new system of geometry based on the five axioms, the four postulates, and the premise that in a plane through any point not on a given line, only one new line can be drawn that’s parallel to the original one.

Lucien was very surprised that, a person in this world had worked out Lobachevskian geometry on his own!

Lobachevskian geometry was the first non-Euclidean geometry system developed on the Earth, and it was named after its discoverer Lobachevsky. When Lobachevsky first came up with the system, he was still a widely-recognized, young and promising mathematician. However, the cost of him introducing the new geometry system was life-long criticism and humiliation. The authorities either fiercely attacked the new system or ignored it completely. Even Gauss, the foremost of mathematicians, who in fact saw the rationality of Lobachevskian geometry, chose to remain silent in fear of the great pressure from the whole academic community.

But despite the miserable situation, Lobachevsky never gave up. He kept on trying for the new geometry system that he invented and even published another monograph in geometry in the last year of his life. Unfortunately, by the time he died in great pain and poverty and nearly blind, the academia still refused to recognize the enormous value of his geometry system.

In was only more than a decade after his death that his new geometry system was proven correct on special surfaces by another mathematician. Finally, and the significance of his finding was acknowledged and it was thus highly appraised by the academic world.

It seemed that in the current stage, the study could neither help the progressing of arcana nor the improvement of magic. However, when the development of arcana and magic proceeded further and reached the realm of space and the universe, the current mathematical tools would become insufficient for describing and solving practical problems. By then, development in math studies and new math models would be in need.

For example, another non-Euclidean geometry, Riemannian geometry, was the mathematical foundation for the great General Theory of Relativity which addressed the problems of space and time, while the application of Lobachevskian geometry was seen in human being’s exploration of the universe.

If it could be said that Tower Geometry (Euclidean geometry) was human beings’ direct perception of the world, then the two non-Euclidean geometry systems were closer to the objective truth — In fact, the three geometry systems were just different in curvature.

Compared to studies in magic, subjects that were being used as tools, such as math, faced a more challenging and tough journey for the discovery of subversive theories, for the authorities were even harsher and more conservative. Lucien sighed as he saw the comments given by the board members:

"A ridiculous reasoning has led to a ridiculous result. I’d suggest that the author should look through a window and see the real world. The paper shall not pass."

"... full of mistakes and useless. Fail to pass."

"... this is a vagarious and incomprehensible dream talk. The best and only use of this paper is to be thrown into a fireplace. Obviously, fail."

...

Lucien shook his head repeatedly when he read through the comments. Although his paper had also been looked down upon in the past, the comments were still given in a standard tone, and they were mostly due to the inability to understand the paper or incapacity to verify the results with experiments. Yet the review comments here looked more like attacks and calumniations towards the author, which should never come from a board member, whose duty was to review a paper based only on its theorem and proof.

After informing Fernando, Lucien spent his time reading Levski’s paper carefully from the very beginning to the end, while doing the deductive reasoning on his own. Then, he picked up the quill-pen and started writing down his first review result as a board member.

"A daring hypothesis, rigorous deductive reasoning..."

......

The dusk light in the early evening dyed Allyn with a layer of shining gold-orange color, which made the whole city look stunning.

In a very tall magic tower which rose into the sky, a frowning old man was concentrated on deducting a math problem, over his white eyebrows was the special grey pointed hat of Tower. The several complex magic circles which occupied most of his desk space burst out light from time to time, assisting him with the sophisticated calculations.

At this time, his assistant knocked on the office door.

"Come in," said the level-eight, seventh-circle mage in a bit short-tempered tone, as he hated to be interrupted in the middle of his work.

His assistant was a young beautiful lady who always looked serious. Wearing a traditional Holm dress and holding a pile of documents, she said, "Teacher, the puppet has sent today’s papers over. Please take a look at them."

The old man in his sixties rubbed his brows and nodded. "Give them to me."

If the papers were not that serious or difficult, his students should be able to handle them.

The emotionless young lady approached him with a constant pace and put the papers on the desk beside his right hand.

The old man first took a glance at the title of the paper, and then the look on his face instantly changed. Banging the desk fiercely, he yelled,

"Again! Levski’s submitting his imagination geometry again! Is Eric daydreaming? It’s such a waste of our time! The Board should prohibit him from submitting this paper again forever!

"Samantha, just scribble something based on the comment I wrote last time and throw it back!"

......

Meanwhile, in a villa in Allyn which claimed to have the biggest collection of flowers in the world.

A beautiful and elegant lady, whose hair was tied back, threw the paper in her hands on the ground. "Levski still won’t give up?! What a waste of his talent and life! What’s the point of submitting the same ridiculous paper again?"

With a second thought, she picked up the paper from the floor and grabbed a unique-shaped pretty quill-pen. Within two minutes, she had finished her comments.

Then she said to her servant angrily, "Give it back to the Board two days later, in the evening."

Let this stubborn madman live under the torture brought by hope for two more days!

......

After sending his comments back to the Board, Lucien started working on his own paper with a smile on his face.

Three days after in the morning, as soon as Lucien stepped into Fernando’s office, he saw Douglas, the president of the Congress. Douglas was wearing a black suit and looked kind and easygoing as usual.

"Morning, Mr. President." Lucien greeted, wondering what was going on this morning.

Douglas grinned. "Quite surprised to see me, right? I’m here to talk to your teacher about the two theories published on Arcana and Magic — the two that disproved my experiment."

"You know, I like to talk to Fernando face to face at times like this," Douglas added. "Listening to him roaring against the theories lifts my spirit up."

Lucien almost burst out laughing.

Fernando looked quite pissed. Shaking his head, he said, "I don’t get it... Why these worthless papers could even be published on Arcana and Magic? I know their standards has never been impressive, but now it is becoming unacceptable! What does it mean by ’charged particles are shortened when put against ether, so there would be a deviation in measurement’? Are there any evidence from solid experiments to prove this?"

"Comparatively speaking," Fernando calmed down a bit, "Brook’s paper which throws doubt against your system of celestial body motion is more powerful. After all, those planets only exist in your dreams right now."

Douglas did not feel offended by Fernando’s comments at all. Smiling, he turned to Lucien. "What do you think, Lucien... with regards to my experiment and the debates?"

Lucien was a bit speechless, as he had been asked about the same question almost every day recently. But this time, in front of the president, he had a prepared answer which derived from his careful thinking:

"Mr. President, I do have some thoughts here. The core of your theory is based on the existence of planets, which is also the most problematic part, since we haven’t found a planet yet. Therefore, your theoretical system lacks firm support."

"So what? You can find a planet?" Fernando questioned bluntly.

Lucien looked very serious, and he said firmly, "If we can’t find one, why don’t we make one?

"Why don’t we make a small planet that rotates our world following the orbit that we calculated?

historical

"If it moves as what we expect, and if it can be observed, then gravity system can definitely be proven!"

This was Lucien’s proposal! He had been reflecting on it for a very long time ever since he read the letter from Douglas!

The study suddenly quieted down. Only the sound of the wind shuffling papers could be heard.

......

In Sorcerer Administrative Department, Levski, who wore the same old magic robe, knocked on the door of Eric’s office. His heart was full of hope, but also fear and anxiety.

"You come here quite early..." said Eric stiffly. In fact, he was not surprised at all.

Levski nodded, his face pale from the cold wind on his way here. "Yesterday was the third day. Today the comments should be available..."

Eric had just arrived in his office. Tidying his desk up, he answered, "wait a moment. The earliest results should be available at around a quarter past nine."

"Alright..." Levski sat down. But a few minutes after, he sprang up from the chair and paced back and forth. He wished that he could light a cheap cigarette, but it was in Sorcerer Administrative Department.

Time passed by seconds. Suddenly, the iron cage burst out milky white light.

"Is it...?" Levski hurriedly asked, excited and scared at the same time.

Eric picked up the pile of papers and leafed through, then he looked up abruptly, appearing very surprised. "No, your paper is not here!"

"W-why?" Levski had no idea what was going on.

......

On the fifteenth floor of Sorcerer Administrative Department, in the hall of Arcana Review Board.

Holding the three review results, the alchemical life was in a great dilemma.