Though the voice was soft, it struck Nesica, Mirina, and the others like a thunderclap, deafening in its resonance.
Having studied mathematical knowledge and earned the Arcane Scepter Award, they could not help but feel a certain pride in mathematics. Yet in practice, mathematics was merely a tool for arcane exploration and spell analysis—an appendage to those greater pursuits. Few arcanists were willing to devote their entire lives to this field of unparalleled beauty. For most arcanists, good enough was all that was needed.
Among the arcanists within the Tower who harbored an affinity for the mathematical domain, thoughts similar to Lucian's words had surfaced in their minds at one time or another. But those were merely fleeting moments of vanity, occasional flashes of insight, offhand complaints. Never had anyone—like Lucian Evans—under the weight of such a stunning proof, used such a forceful argument to articulate mathematics' superiority over intuition and lived experience, elevating the importance of mathematics to a status they had never dared to hope for.
Even though they knew full well that Lucian was adding weight to the scale in favor of
Levski himself trembled with emotion. Yes—mathematics does not deceive. That was precisely why he had written his *Rigorous Proof of the Principles of Geometry and the Parallel Postulate*. In this seemingly boundless sea, in this ocean where storms never ceased, it was by clinging to mathematics with all his being, relying on it completely, refusing to be "deceived" by the outside world, that he had weathered the tempests and crossed the vast expanse—never capsized by the waves, never sunk by despair.
Fernando still did not praise his student. He merely gave a slight nod. The deeper implications of those words were worth far more exploration than their surface content.
Lucian withdrew his right hand, collecting the paper that had been circulating around the entire conference hall. He placed another thick stack of papers—freshly taken from his storage pouch—onto the magic circle and said with a gentle smile: "Next, let us try a different path, and see if we might find some unusual scenery along the way."
With a mathematical model and with the proof that Levski geometry and Tower geometry were compatible, Mirina and the other committee members, though still deeply resistant—for no one liked to deny themselves, to admit they had made a mistake, and a mistake that had persisted for over a decade—were nevertheless compelled to give preliminary acceptance to this new geometric system. At this point, to overturn Levski geometry would necessarily mean overturning Tower geometry as well, which ran completely counter to their original intention.
Moreover, having been struck to the soul by Lucian's words, their emotions were now complex but relatively stable. They looked at the papers with no particular prejudice.
"*Another Postulate Regarding the Parallel Postulate*?" With her hair pinned up in an elegant arrangement, the dignified Mirina read the title softly, vaguely guessing what was to come.
"Another postulate..." Levski felt as though the fog before his eyes had been swept away, revealing a problem he had overlooked throughout more than a decade of perseverance.
Lucian, as though lecturing at the magic academy, pointed his finger at the projected paper, letting its contents display line by line: "Mr. Levski assumed that 'through a point not on a given line, at least two lines can be drawn parallel to the given line,' and from this, together with the existing axioms and postulates, deduced a new geometric system that is logically rigorous and self-consistent. But what if we make a different assumption? The third assumption that, together with Levski geometry and Tower geometry, forms a complete set: 'through a point not on a given line, no line can be drawn parallel to the given line.'"
"Next, let us conduct a deductive reasoning, and see what emerges."
Levski drew a soft breath, his emotions stirred once more, as though he had grasped something. Nesica, Mirina, and the other committee members looked gravely at the paper Lucian had projected.
Page after page turned, argument after argument was presented. Since he was addressing authorities in the mathematical field, Lucian explained at great speed, glossing over many points. Yet the expressions of Nesica and the others grew increasingly serious, increasingly perplexed. At some point, Mapei blurted out, murmuring to herself: "It has actually deduced propositions that differ from Levski geometry but are equally strange and bizarre..."
"What on earth is going on..." Her voice prompted a response from Salguero.
"Could it be yet another new geometric system fundamentally different from Tower geometry?" Mirina was utterly lost. Just a few hours ago, she had been firmly convinced that no geometric system fundamentally different from Tower geometry could exist. Yet in less than a day, that belief seemed to have been ruthlessly shattered—twice over, no less.
She was bewildered but also relieved. Fortunately, this concerned only the domain of mathematics and did not involve the composition of the perceived world—otherwise, her head would have burst with a bang. As expected of Lucian Evans, who was secretly known by the epithets "Skull-Crusher" and "Brain-Eater."
Levski was not perplexed. Instead, he sank into deep contemplation. Why did this happen? Why did starting from different negations of the fifth postulate, and from the fifth postulate itself, yield separate geometric systems—each complete, independent, and logically rigorous? Why was this so? Was there any connection to the real world?
Under the influence of Chairman
"Quite interesting..." Fernando nodded gently.
Time flew. Lucian's paper reached its final section, where he used a model similar to a spherical surface to prove the realizability of everything that had come before.
Nesica let out a deep sigh: "Indeed, it is yet another new geometric system—Evans geometry."
"Mathematics truly does not deceive..."
It was precisely because of arrogance and prejudice that he had missed the opportunity to name an entire geometric system after himself. If only he had accepted Levski's assumption, then Lucian Evans's assumption would have been easy to conceive.