694 Book of Demons (2/2)

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.