Throne of Magical Arcana

Under the help of the tower guard, the sorcerers who arrived early opened the closed gate, revealing what was inside the room to Samantha and Rachel clearly.

It was a clean and tidy library, where every book had been placed in order. The paper on the desk had been divided into several piles in an organized way, even including the scribbles. Every detail and every corner suggested the strict if not obsessive-compulsive personality of its owner, Havin.

Havin was seated in the chair behind the desk, with a layer of clear ice frozen on his body. The ice was not melted even in the scorching July. Instead, it turned the air around into frost.

Havin sat straight in the ice. He was wearing the standard attire of the Tower sorcerers. Together with the badges on his chest, he dressed so formally as if he were going to the award ceremony of ‘Evans Prize in Arcana’ or ‘Arcana Scepter’.

His face was pale, frozen with vague hopelessness and relief. There was a cup of wine in his hands, as if he would stand up and greet everyone any moment, if it weren’t for his hollow and lifeless eyes.

“This is truly the way of death that Havin would choose. Clean and graceful…” Said Rachel to Samantha in a low voice.

Both of them knew Havin. As the arcanists in the Tower who had hope to advance to the sixth circle, they had been both competing with and encouraging each other. The two of them knew Havin rather well. However, while the two of them had become senior-rank arcanists and sorcerers, Havin ended his life with an ice spell. It was truly two examples of the age.

Thinking about her frustration recently, Samantha said in deep thought. “As a matter of fact, Havin would’ve advanced in another ten years… One shouldn’t give up easily however desperate they are. If I were him, I would live on and live well to see how the world of arcana would develop, and if our defeat was worthwhile…”

“Havin had severe obsessive-compulsive disorder and depression in the first place. I’d been meaning to help him with corresponding spells. It’s a shame…” Rachel mentioned the concepts that were proposed recently.

In the past, such psychological problems could be dealt with magic, such as Mechanized Mind and other spells, but their effect was short. No sorcerers could completely resolve the problems unless they were willing to abandon their normal feelings. Therefore, it was not rare for the ancient sorcerers to go extreme or crazy!

As her good friend, Samantha was not ignorant of the development of psychology. She nodded, “Other than the help of magic, daily comfort is also required. However, psychological therapies always lack a fundamental theory. The research results cannot be gathered into a complete system.”

As they talked, they walked into Havin’s room. As Havin’s friends and senior-rank sorcerers, they were acknowledged that they were suitable to deal with the issue.

Thanks to Havin’s ‘good habit’, Rachel and Samantha didn’t spend much time searching when they found an unsealed letter on the desk.

The paper inside the envelope carried the aroma of books. It had been folded squarely.

After careful examination, Rachel opened the letter and read its contents:

“…The debate recently exhausted me. I cannot imagine that the foundation of the whole school of astrology would be disrupted, or the certainties of the material world would be lost… I kept arguing with other people, but things were developing the exact opposite way…”

“…I’m deeply lost when I recall the rapid development of arcana in the past years. What we fear and resist today is the product of the theories that delighted and satisfied us previously. How absurd…”

“…My brain is haunted by the irresolvable and even self-contradictory problems without one moment of peace, but my consideration cannot answer any dilemma. I’m tired, and I want to end such a life…”

“…I’ve made a cowardly decision. I don’t think I can catch up with the development of arcana, and nor I can live with it. I hope that I can return to the golden age of determinism in my dream…”

Reading the letter that was brimming with exhaustion, desperation and confusion, Rachel suddenly felt sympathetic. In fact, most of the arcanists in the Congress shared similar feelings.

“Havin…” She meant to say something, but it eventually became a sigh.

All the sorcerers who came fell into silence, as if they were mourning for both Havin and themselves.

Samantha moved her eyes back from Havin and looked out of the window. The sunlight at the noon of July was so brilliant and dazzling.

Time went by one second after another. Rachel cleared her throat and planned to arrange the funeral, when a Tower sorcerer came from the lift with a thick book in his hands. “‘Nature’ has published a special issue, ‘Basics of Mathematics’!”

He sounded so delighted as if a quick glance had already shown him a strict temple of mathematics.

“Basics of Mathematics?” Asked Samantha subconsciously.

The Tower sorcerer replied joyfully in a loud voice. “Yes. It contains Mr. Evans’ answers to many mathematical problems. Through the answers, he has constructed a broad and valid mathematical system!”

He could only describe it in general, because he hadn’t read it carefully yet. Suddenly, he noticed the situation in the library. “What… What happened to Havin?”

The other sorcerers told him what happened and Havin’s last words to him. He said regretfully, “I should’ve come earlier. If Havin had seen ‘Basics of Mathematics’, his passion in mathematics would’ve been rekindled. I was similarly confused and frustrated before, but those feelings cannot extinguish my enthusiasm for mathematics now. It turns out that there are still so many things we can work on!”

After hearing his declaration, Samantha and Rachel couldn’t help but ask for the copies of the book that he bought for other people. They read the books in Havin’s library.

Although they did not have the time to read the specific deductions, Lucien’s proposition and redefinition of certain mathematical concepts in the fields of numbers, set, group, field and topology already refreshed them. It felt that the scattered, random studies in the past had been gathered into an unbreakable whole.

The content in the book was not beyond their knowledge. It was based on the current mathematical studies and dived deeper into them. The new concepts it proposed were not incomprehensible. Not only were they deduced strictly and logically, but they also met the difficulties that the Tower arcanists had.

Browsing through the book, Samantha and Rachel envisioned a particularly broad world in the realm of mathematics!

“Before, Mr. Evans always said that mathematics must not depend on arcana, that it should not only be used to provide answers for their problems, and that it should be an independent theory based on deductions and reasoning.” Rachel suddenly said with mixed feelings. “I remember what he said clearly and feel that it is very reasonable, but I tend to neglect a lot of questions in the actual research. Now, I have fully understood what Mr. Evans meant.”

Her previous grief and confusion were gone. She seemed to have been reinvigorated.

Samantha also said in deep thought. “Before, when we applied unsystematic mathematical knowledge to solve problems, although we achieved our purpose in the end, the process always felt obscure and difficult, as if certain invisible walls thwarted our efforts. Now, those walls are gone…”

“Yes, Mr. Evans has also further illustrated axiomatization and given a complete axiom system of Tower Geometry.” An arcanist mentioned what was in the latter half of the book. Although Lucien had come up with the notion of axiomatization a long time ago, and the arcanists had certain studies and applications in their work, he still vaguely felt that the fundamental opinion of mathematics seemed to have changed after he saw the axiom system of Tower Geometry.”

In the heated discussion, Samantha suddenly rose. She copied the book in her hand and put it before Havin. Then, she ignited it.

“Your afterworld will be full of color with the company of Basics of Mathematics.” She said in a low voice.

The other arcanists also felt quiet, feeling lucky that Basics of Mathematics was published at such a moment.

After Havin’s body was moved away, Samantha, Rachel and the other arcanists left the room one after another. In the meantime, those arcanists seized the time to read the book. “‘Current conundrums in mathematical studies’?”

“…Is it possible to write any even number greater than 2 as the summation of two prime numbers?…” He was stunned after he read the question.

“The four-color theorem?” Another arcanist turned to the next page.

Hearing their words, Samantha and Rachel looked at each other and hurried to read the content behind.

After a while, all the arcanists were standing in the hallway like statues. They mumbled nonstop, looking now lost and now crazy.

After a long time, Samantha and Rachel were suddenly woken up by footsteps. They saw the shock in each other’s eyes.

Rachel said in amusement. “Those questions are really terrible. They seem easy but turn out to be extremely difficult if you think deeper…”

“That’s why even Mr. Evans is puzzled.” Samantha put on a rare smile.

“The last question, the barber paradox?” Rachel reached the end of the book, “A barber in a town, after a certain incident, announced that ‘I shave those and only those who do not shave themselves’. Then, should he shave himself? What’s the source of the paradox?”

“Well…” Samantha thought for a moment, and the book in her hands hit the floor.

Dum, dum, dum. The other arcanists who heard Rachel’s words dropped their book in shock, too.

It was a famous paradox about the set theory. At present, it meant that the set theory had been shaken, and since the set theory was the foundation of mathematics, one might say that the paradox made people doubt the legitimacy of the fundamental structure of the whole mathematics!

“We have to face the horror and desperation brought by the perfection of the set theory when we were just overjoyed by it…” One of the arcanists said what was similar to Havin’s last words.

……

Iristine and Nodanielle roamed inside the city of Allyn. They saw that many arcanists were working hard in the shadow of trees.

“They are truly hardworking. No wonder the Congress of Magic has been developing so fast.” Observed Iristine in mixed feelings. Then, she looked at one of the young sorcerers curiously. “What’s the book he’s reading?”

“Basics… of… Mathematics…” Thanks to her exceptional sight, Nodanielle identified the words one after another.

“Mathematics…” Iristine nodded her head and was about to leave, when Nodanielle added in confusion, “Those few words have been scrapped, and there are some handwritten words below it…”

Iristine was even more curious. “What are they?”

Nodanielle identified them carefully again. “Book… of… Demons…”

“Book of Demons?” Repeated Iristine in confusion.