The first sunny day after the snowfall, warm sunlight falling upon the body, bringing a pleasant feeling.
Thud, thud, thud — the heavy footsteps of the Steel Golem echoed down the corridor. It pushed open the door, its eyes flickering with crimson light, its voice as cold and metallic as its body: "Master, I have obtained six similar papers previously submitted by the paper's author, along with the review committee members' evaluation comments."
This was one of the perks of being a member of the Archanist Review Committee — one could access papers and review results without spending Archanist Points. Otherwise, it would be ridiculous for a committee member reviewing a paper to have to spend their own Archanist Points to obtain similar papers for comparison. That was no way to approach arcanist research.
Lucian took the thick stack of papers, waved the Steel Golem over to guard the doorway, and began flipping through them himself. He could clearly see the author Levsky's deepening and refinement of research into "Anti-Tower Geometry." By the most recent paper, Levsky had constructed an entirely new geometric system — one built upon the Tower Geometry's five axioms, four postulates, and the foundational assumption that "through a point outside a given line, at least two lines can be drawn parallel to that line."
"I didn't expect someone to have independently proven and derived Lobachevskian geometry on their own..." Lucian murmured to himself.
This geometric system was the first non-Euclidean geometry to appear on Earth, proposed by Lobachevsky. When he made the assumption of "at least two parallel lines" and deduced an entirely new geometric system through rigorous reasoning, he was still a widely recognized young mathematician. But after presenting his findings, what awaited him was a lifetime of indifference, contempt, slander, and abuse — dismissed or condemned by one authoritative mathematician after another. Even Gauss, the "King of Mathematics," who privately acknowledged the validity of Lobachevskian geometry, chose to remain silent, fearing the opposition and displeasure of the entire academic establishment.
In such bleak circumstances, Lobachevsky never gave up. He continued to fight for the survival and development of his new geometric vision, even completing a work on geometry in the year before his death. Sadly, he never lived to see the dawn. He died in depression, anguish, and blindness, and it was not until over a decade after his passing that his work finally gained the attention and study of the academic world — when other mathematicians proved the realization of Lobachevskian geometry on certain curved surfaces — earning him belated but towering recognition.
Such research might seem to hold no significance for the current development of arcanism, nor could it enhance one's magical power. But in truth, as arcanism and magic continue to delve deeper — stepping into the domains of spacetime, the cosmos, and beyond — the current mathematical tools would face a dead end, unable to accurately describe or help solve practical problems. That was precisely when mathematics needed to advance and provide new tools.
For instance, on Earth, another non-Euclidean geometric system based on the foundational postulate that "through a point outside a given line, no line can be drawn parallel to that line" — Riemannian geometry — served as the mathematical foundation for Einstein's great General Theory of Relativity in describing spacetime. And Lobachevskian geometry found application in humanity's study of the cosmos.
If Tower Geometry — Euclidean geometry — was humanity's intuitive understanding of the world based on empirical experience, then the two non-Euclidean geometries approached objective truth. In reality, the three geometric systems differed only in their curvature.
Lucian sighed. Compared to the magical world, where improved understanding of reality could directly enhance one's power level, the current field of mathematics — used purely as a tool — was far harsher and more conservative toward rebellious, paradigm-breaking theories. Just like the evaluation comments these committee members had given:
"A ridiculous line of reasoning that arrives at an absurd conclusion. I believe the author should look up from his desk and out the window, observe the real world… My opinion: this paper cannot pass review."
"…This is a paper riddled with errors and devoid of any value. It cannot pass review."
"…In my view, the best course of action for this sort of fantastical nonsense that no one can comprehend is to toss it into the fireplace — that would serve its only possible use. Obviously, it cannot pass review."
……
As he read, Lucian shook his head. He himself had received lukewarm evaluations on his own papers before, but the standards and the tone of those reviews had all been within the realm of reason — reflecting reviewers who couldn't yet fully understand a paper or couldn't verify its claims. These review results were nothing like that. They either launched direct personal attacks and slander, or twisted the paper's content to lodge accusations. Not a single one addressed the paper on its own merits — its foundational postulates, its deductive reasoning, or its logical consistency. It was a grave dereliction of the review committee members' duties.
After requesting leave from Fernando for the evening, Lucian read through Levsky's new paper from beginning to end, performed his own independent deductions and reasoning, then picked up his Feather Pen and composed his first evaluation result as a committee member.
"A bold hypothesis, rigorous deduction…"
……
The evening sky over Allence was stained with the afterglow of the setting sun and the splendor of evening clouds, lending the city an extraordinary beauty.
Inside a towering Magic Tower, a white-browed elder wearing the special gray pointed hat of the "Tower" faction was frowning over a mathematical calculation. Several intricate and complex Magic Circles, occupying most of his desk, periodically lit up to assist him in his computations.
Knock, knock, knock — his assistant knocked on the study door.
The elder, who appeared to be in his sixties or seventies and wore the emblems of an Eighth-Rank Archanist and Seventh-Ring Mage on his chest, was in a foul mood at having his concentration broken. "Enter," he said irritably.
His assistant was a beautiful, serious young lady dressed in a conservative Holm-style gown, carrying a stack of documents. "Master, your Secret-Method Puppet has delivered today's batch of papers for your review and assignment."
The elder rubbed his brow. "Let me see them." If they weren't important or particularly challenging, he would have his students handle the reviews.
The composed, expressionless young lady walked forward with measured steps and placed several papers on the elder's desk.
The elder picked them up and began scanning the titles. Suddenly, he slammed his fist on the desk with a resounding bang: "Levsky has submitted his imaginary geometry again! Are the stewards of the Mage Management Division sleepwalking? How could they just let him submit this? Is our time as review committee members worth nothing? I'll have to petition the committee to ban further submissions of this paper!"
"
……
At the same hour, inside a villa in Allence that boasted possessing the world's most complete collection of flower varieties.
A graceful, elegant lady with her hair pinned up flung the paper in her hand violently to the floor: "Levsky still hasn't given up? He's simply squandering his own talent and his life! What possible value is there in submitting a paper that is obviously wrong at first glance?"
After a moment's thought, she picked the paper back up, drew out a specially shaped and beautiful Feather Pen, and began composing her review. With a few swift strokes, she finished in under two minutes.