Chapter 695: Test

On the top floor of the Tower that rose into the clouds…

Before Bergner, one copy of ‘Basics of Mathematics’ was opened. Long before the special issue of ‘Nature’ was published, he had already learnt the news and asked for a copy of the manuscript from Levski.

“I have to say that, although there are no groundbreaking insights and mathematical achievements in Evans’ book, he has delicately integrated the scattered studies in mathematics so far by proposing certain new concepts and redefining certain old concepts. A complete system with clear branches, a strict architecture and a solid foundation has been established…”

“…His in-depth illustration of the system has completely driven away the mist around mathematics, so that the whole palace of mathematics is finally bathing under the brilliant sun and showing the glorious gold…”

Although Bergner had already made similar remarks when he read it for the first time, he couldn’t help but compliment it again and again every time he read it. Ever since calculus was created and defined, nobody had ever made such great contributions to mathematics with a single book.

“…The age of calculus has passed; this is modern mathematics…”

Bergner envisioned that new branches were taking shape in the palace of mathematics, and they all originated from this ‘Basics of Mathematics’!

For him, the greatest significance of the book lied in two aspects. Firstly, the geometrical axiom system that Lucien completed filled him with infinite passion about the related mathematical questions. He felt that everything in the world could be axiomatized into a rigorous, self-consistent and flawless system.

Secondly, Lucien’s studies on topology, group and set theory gave him inspiration. It seemed that they were not pure, independent and abstract mathematical achievements but could be directly applied to solve many problems in current arcana studies, like the studies of crystals or the cutting edge of the microworld.

“…This is without a doubt the most remarkable book in mathematics over the past hundred years. It will be worshiped by the future arcanists in the temple of mathematics right next to ‘Mathematical Principles of Magical Philosophy’. However, it would be perfect if the ten questions in the appendix did not exist…” There was a vague, bitter smile on Bergner’s face. The book on him had been turned to ‘Current conundrums in mathematical studies’.

For a legendary sorcerer adept at mathematics, he could not resist those questions at all. After browsing through the main part, he devoted himself to the consideration and calculation of the questions.

However, a week had passed since he got ‘Basics of Mathematics’, but no progress had been made. He failed to solve any of the questions, which rather frustrated him who had always been proud of his expertise in mathematics, particularly when some of the questions seemed easy to prove but were actually full of difficulties.

Of course, none of those mattered compared to the barber paradox in the end, which stunned Bergner for a whole hour.

“Until determinism is completely denied, there can’t be a more painful and humiliating question. When we cheer for the final establishment of the temple of mathematics, its foundation has collapsed. It seems that mathematics itself will be denied as long as we apply the set theory and acknowledge the concepts in the past.”

Bergner heaved a long sigh. He almost couldn’t stop himself from destroying Basics of Mathematics and killing every barber the moment he saw the barber paradox, because he knew that infinite disasters would be caused!

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He moved his eyes down and saw Lucien’s conclusion after the paradox. “Similar paradoxes can be frustrating, but it only means that our studies are not meticulous, and that our understanding about mathematics is more or less wrong. Therefore, instead of feeling desperate and lost, we should dig deeper into the set theory. There is one and only one solution to all mathematical questions, which is to continue studying mathematics itself.”

“…Evans’ arcana attitude is what supported him to make so many accomplishments.” Bergner praised him and turned back to the set theory, starting to rethink. It was obvious that a set paradox could only be resolved with the set theory.

……

“…I am your old friend Nightingale. Coming next is ‘Arcana News’…”

It was still the holiday in the generic school. Longman could only learn the latest development of arcana through programs such as ‘Arcana Voice’ and ‘News of the World’.

“…Mr. Evans has finished his masterpiece, ‘Basics of Mathematics’. It has solved many problems in mathematics and cleared the obstacles that block the way forward. However, the most eye-catching part of the book is not the main part but the ten conundrums proposed in the end. They have fascinated all the arcanists…”

“…It is obvious that the conundrums which even puzzled Mr. Evans are truly extraordinary. Up until now, no arcanists have announced that they know how to solve them. Even Mr. President and Mr. Brook openly admitted that it was not easy to solve those seemingly easy questions…”

“…It appears that whoever solves the ten questions will be given abundant arcana credits and respected as an authority of mathematics. Those questions are as follows…”

The boy Longman’s eyes were widened after he heard that the questions puzzled Mr. Evans. Apart from disbelief, he suddenly had the urge to try. If he could solve the questions that even Mr. Evans couldn’t…

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The conundrums that Lucien selected were highly representative, but they all looked simple on the surface. Therefore, even Longman could understand them. He took out his pen and paper and calculated.

“…Mr. Evans told us that, while those questions are not concerned with actual arcana studies, and solving them will not bring any substantial results, studying them will itself boost the development of mathematics, and the development of mathematics will support the arcana studies… The same logic applies to the other mathematics domains. In this pure world, one should not blindly pursue applicativeness…”

Very soon, Longman couldn’t calculate any further, but his heart was burning with fire after hearing those words, and his cheeks were flushing. “Mathematics is so important? Also, it doesn’t seem to need the support of magic… Although I’m not gifted at spiritual power, it doesn’t mean that I don’t have talents in mathematics…”

“I will certainly be an arcanist! An arcanist that is good at mathematics!”

……

After reading Basics of Mathematics, most arcanists tried solving the conundrums that Lucien proposed curiously and hopefully. Just because Mr. Evans cannot resolve them doesn’t mean we can’t! If they could solve one of them, they would earn unimaginable glory and benefits!

As a result, Iristine and Nodanielle often saw lost, unsteady arcanists who seemed to be dwelling in their own world when the two of them traveled in Allyn recently.

However, as time went by, such arcanists were fewer and fewer, and stricken faces were more and more. The copies of Basics of Mathematics in their hands were often marked with different symbols. Some represented demons, some nightmares, and some were mazes without exits. In the end, even though the ten questions had been placed on the permanent screen in the Task Zone, the trend about them came to an inevitable end.

Among them, the Tower arcanists felt most complicated. On one hand, such questions were truly their interest; on the other hand, they had been so gravely stricken by the paradox that they felt the confusion and desperation when determinism was shaken again. Also, while the uncertainties hadn’t been proved by any important experiment, the paradox had shown self-contradiction in the most clear way. There was no way to evade it.

“If Havin were alive, he would’ve done the same after he saw this paradox…” Samantha looked out of the window gloomily.

Rachel’s lips twitched. “To think that you burnt ‘Basics of Mathematics’ for him… Do you want him to have nightmares even after he is dead… You must know that the book has been publicly acknowledged as ‘book of demons’. For the arcanists who are not good at mathematics, the number theory and the knowledge on set and group are more dreadful than demons, but for us, the questions and paradoxes at the end are most horrible of all…”

“In any case, mathematics will continue, and we will find a way to resolve the problems…” Samantha encouraged herself.

Therefore, the other arcanists discovered that the Tower arcanists and the other arcanists who were good at mathematics fell silent. In their silence, an outburst was brewing.

……

In Atom Institution…

Lucien, Natasha, Lazar, Annick and some other people were gathered in Heidi’s personal laboratory to observe the first prototype of artificial intelligence that she and Chelly assembled.

At the center of the room, countless enormous glass tubes were connected to each other delicately. At their center were simple magic patterns and relatively complicated alchemical parts. Also, there was a curtain standing on the top, rippling like a curtain of water.

“This is huge…” Iristine had been invited to observe it. Although she had guessed its final shape based on her daily observation, the size of the artificial intelligence was still much greater than she thought.

The prototype occupied the better part of the room and equaled to almost ten golems.

Lucien nodded. Thanks to magic, this was much smaller than the first computer on Earth. “Well done. Turn it on and demonstrate it.”

Nervously, Heidi pressed the switch of power. The glass tubes glittered one after another, emitting in red or green colors and changing nonstop. It made the room look like the field of a ball. Since different colors had been developed for magic crystal lamps, there were already balls which attempted to control the change of lights.

“Input the data…” Thanks to the assistance of magic, Heidi did not make things like punched tape but simply inputted with voice and keys.

After she inputted a rather complicated formula, the red and green lights glittered even more intensely, and the electric noises could be heard. In the end, the result was printed on the ‘curtain’.

“The result is correct.” Sprint interjected. “But I have already got the answer a few seconds ago with the ancillary computation circles.”

So, what’s the point?

Heidi secretly snorted and looked at her teacher, hoping to be praised. That was only the first prototype of artificial intelligence, and there was still plenty of room for improvement!