Seeing the title, Eric heaved a deep sigh. "It's no use, Levsky. No use at all. Your reasoning is chasing a dead end. No committee would accept something so far-fetched — it's completely different from the real world we observe, and it contradicts the foundations of geometry. There's no doubt it's wrong. We've been old friends for years, so I'm advising you: stop wasting your time on this."
Due to the needs of Arcane Magic structural diagrams and the materialization of the Cognitive World, the study of mathematics had been woven throughout the history of Arcane Magic exploration. The currently accepted foundation of geometry rested on the five axioms and five postulates put forward by Mentas, the legendary mage of the ancient Magic Empire, in his *Treatise on Geometry* — known as Mentasian Geometry. And because Mentas was also the founder of the Tower, it was additionally called Tower Geometry.
The fifth postulate (its equivalent proposition being "through a point outside a given line, there exists one and only one line parallel to the given line") was far too cumbersome for a postulate — it read more like a theorem that needed to be proven, and it had attracted considerable interest among mages. Especially after the founding of the Arcane Council, when achievements in mathematics and logic had become increasingly prominent, more and more mages had joined the effort, constantly attempting various methods to prove this postulate. All of them had met with failure, unable to produce a convincing logical derivation.
In Eric's eyes, Levsky was simply one of them. Levsky had first assumed that "through a point outside a given line, at least two lines can be drawn parallel to the given line," and then attempted to prove that assumption wrong — thereby using proof by contradiction to establish the correctness of Tower Geometry's fifth postulate. But the result had been entirely unexpected: combining that assumption with Mentasian Geometry's five axioms and four postulates, he had arrived at a geometric system that was logically flawless yet utterly bizarre, absurd, and contrary to "reality." It had been met with unanimous cold indifference by the Tower's Archai.
After Levsky submitted his paper without being blocked, it received savage criticism and vicious ridicule, and it predictably failed to pass the review.
"Eric, have you actually read my paper carefully? Have you read through the entire chain of reasoning? Are there any errors in its premises, its postulates, its logical derivations? Why won't you people even try to understand it?" Levsky trembled all over with agitation. Years upon years of setbacks had not broken him. Over the past decade and more, no matter how much ridicule he endured, how biting the sarcasm, how impoverished his life became, how his Arcane Magic research stalled and his strength plateaued — none of it had made him abandon his theory.
Eric raised a hand in a calming gesture. "Yes, the application of proof by contradiction and the logical derivation contain no errors. But Levsky, open your eyes and look at our world — look at this table, this room, these Arcane Magic structural diagrams. They don't match the geometry you've imagined! They truly, actually exist. So tell me — which should we believe? Didn't you spend your own money to print copies and distribute them to other Archai? Did you win their approval?"
"I didn't." Levsky slumped, lowering his head in dejection. He had once believed that it was the review committee members and the Tower Archai who were too rigid and conservative — that they had "killed" his paper. So he had decided to spread his geometric system to younger mages who hadn't yet absorbed too many entrenched theories, as well as to mathematical authorities like Council Speaker Douglas, Her Excellency Hathaway, and His Excellency Paris. But he had still been met with merciless laughter and rejection from young Archai. What a joke — your propositions flatly contradict common sense. Go ahead and try drawing two parallel lines through a point outside a line!
As for the mathematical authorities, they had maintained the same silence.
"But I've refined it further," Levsky pressed on, his tone slightly less resolute than before — though the waver vanished quickly. "It should pass this time. Eric, I'm begging you."
Eric sighed with a mixture of sympathy and exasperation. "But Levsky, over the past decade-plus, you've already submitted it several times. Every single time it failed to pass review. And the committee has a rule — papers cannot be submitted repeatedly, to avoid wasting the members' time. Look at you: you're already over forty, still a low-tier mage. Have you spent any time studying Archana or improving your magical strength? If you keep going like this, it won't work…"
"This is the most refined version of the proof and explanation, Eric. Please, submit the paper to Council Member Evans. For the next few years, I'll dedicate myself to studying Arcane Magic." Levsky's gaze was pleading, brimming with hope.
Eric's expressionless face twitched. "Levsky, Council Member Evans only reviews subversive papers — the kind that overturn a mage's understanding of the Cognitive World, the kind that make your head explode. Yours is purely a mathematical paper. Even if it contradicts common sense, it has nothing to do with the Cognitive World and won't produce serious consequences. So, in principle, it cannot be submitted to Council Member Evans."
The Cognitive World was built upon a mage's deep understanding and exploration of the real world. Mathematics was merely a tool — it didn't affect the stability of the Cognitive World.
Before Levsky could persist further, Eric sighed once more. "Tell you what — I'll mark your paper with both 'subversive' and 'mathematical' on the cover. That way, in addition to sending it to the two mathematical authorities on the committee for review, I can also send a copy to Council Member Evans."
He understood. The committee members responsible for reviews had barely changed in years — they had long since grown to despise Levsky's paper. If not for the fact that Evans, a newly appointed committee member, reviewed subversive papers, Levsky might not have been so determined to insist on submitting.
A sliver of hope was still hope!
"Thank you, Eric…" Levsky didn't know what else to say.
Eric waved a hand. "Go home and wait for the review results. I hope your life can get back on track soon."
Levsky nodded solemnly, torn between anxiety and anticipation. Would Council Member Evans view his paper fairly?
…………
Fifteenth floor of the Arcane Tower. A spacious, bright room.
The Magic Circle, which periodically flickered with milky-white light, extended arms from both sides, distributing the papers one by one.
"Mathematical? Subversive? Forward to Mr. Neusika, Ms. Milina, and Mr. Evans." The voice, tinged with a metallic quality, paused briefly before making its selection.