Tike stood in place, pondering for a full three hours, his mind spinning at super speed, contemplating the resolution of these two paradoxes. Yet, he found no leads, finally turning to Leibniz with a helpless expression.
"Please forgive me, Master Leibniz. This question is too profound; I fear I can't provide you with any answer in the short term."
Alva, Ellison, and the others felt some reluctance but had to admit the same.
These two paradoxes truly befuddled the entire realm of arcane mathematics. Based on the most common motion of objects, they were simple and straightforward yet profoundly thought-provoking.
(TL/n - Magic Web is split into multiple realms such as Beyond Space-Time, Arcane Mathematics etc. for different gatherings.)
Leibniz didn't respond verbally but secretly communicated with the AI.
His prior speculation was incredibly accurate. Under rapid thinking and the brain's rapid rotation, the AI's decryption of spiritual power frequencies was almost ten times its usual speed. The assembled formal wizards felt uneasy at Leibniz's silent response, mostly resigned to the situation.
Even these mathematical masters couldn't provide precise answers to such paradoxes. Hoping they could solve it might have been asking too much.
Leibniz, of course, didn't expect them to crack it. Once confirming his speculation, he immediately put on a more amiable expression. "In fact, regarding the resolution of these two paradoxes, I've gained some insight."
Tike and the others immediately breathed a sigh of relief, then looked to Leibniz, intensely curious about his methods to resolve these paradoxes.
"The key to these two questions lies in whether values can be infinitely subdivided, whether two values infinitely close are equal, and how we should calculate them. This problem has confounded every discipline in the past. Thus, I believe arcane mathematics needs a revolution to redefine this world." Leibniz solemnly proclaimed.
"I'll name it—Calculus."
Tike felt a surge of spirit. They hadn't expected that, for the sake of a gamble's outcome, this master of arcane mathematics would prepare to establish a new branch within their field. And they never anticipated they would have the chance to be a part of it, becoming one of the founders of this field.
***
At night, after spending a full ten hours in the Magic Web, Tike finally emerged from the ocean of thoughts, rubbing his throbbing forehead, with only one thought left in his mind.
"Difficult... It's so darn difficult."
Compared to calculus, Tike felt that all the arcane math he had encountered before was child's play. His mind was dizzy from concepts like tangents, functions, and limits, to the extent that upon seeing some approximate curves, one thought surfaced in his mind:
"Can this thing even be integrated?"
What surprised Tike even more was that his magical power had actually grown and improved to a certain extent. Ever since Iyeta Harbor, he had heard that many apprentices could enhance their magical and spiritual growth by studying arcane mathematics, even better than the effects of meditation.
However, for a formal wizard like him, the effect was minimal. Initially, Tike had some regrets, only now realizing it wasn't that this method wasn't useful for them, but those arcane math problems they'd encountered before were just too easy for them to exercise their computational abilities.
Not only Tike but also Alva and others were pleasantly surprised. Most of these third-tier wizards were not young anymore; for most, the growth of their magical powers had long stagnated, with slim chances of further advancement.
Now, research and exploration into the field of calculus have brought new hope to Alva and the rest.
Despite losing a few hundred hairs in just half a day, faced with the dual temptation of increased magical power and becoming a foundational member of a new school of thought, nobody would retreat due to these slight difficulties.
While Tike and others were immersed in their studies and research of calculus, oblivious to the outside world, the situation within the Wizard Council was different.
In recent days, the Cult of Apocalypse has become increasingly active. Some city guards assigned to monitor and track certain cult followers had inexplicably disappeared, causing a mixture of anger and fear among the council members.
"We can't tolerate this any longer. I suggest taking action immediately and clearing out the entire Cult of Apocalypse." Raphael slammed the table, angrily shouting.
"Are you planning to start a war within Greenville City, Raphael?" Another council member stood up, vehemently retorting.
This involved hundreds of wizards; these weren't unarmed civilians. Once a full-scale war broke out, the losses would be hard to predict.
Moreover, they still didn't know which wizards were being manipulated and who the instigators behind this turmoil were.
Several cult members captured previously had only spouted about the "end times" and "elemental spirits." They couldn't extract any useful information, leaving them unable to confirm the link between the recent attacks on council members and this peculiar cult.
"Otherwise, are we just going to sit here and watch things get out of control?" Raphael roared.
"Regardless, we must investigate thoroughly first. We can't recklessly attack so many wizards without cause." The council member insisted. The resources required to train a formal wizard were unpredictable; Greenville couldn't afford the cost of clearing out hundreds of wizards in one fell swoop—it would be self-destructive.
The Sky Mirror quickly turned into chaos inside, with many council members arguing, worrying, or getting angry. Several grand wizards looked pityingly at Ogest, the acting speaker.
Before, when Harof made Ogest responsible for council affairs, they were somewhat envious and even resentful. But now, it was just relief because this was a complete mess, and who wanted to take over and bear the consequences.