On the top floor of the Tower that rose to the sky …
Bergner, the Prophet, had a copy of "Basics of Mathematics" in front of him. Long before the special issue of "Nature" was released, he had already received the news and asked for a copy of the manuscript from Levski.
"I have to admit that, although Evans' book does not contain any groundbreaking insights and mathematical results, he has cleverly integrated the scattered research results in the field of mathematics into a whole by proposing some new concepts and redefining some of them. A complete system with clear branches, a rigorous structure, and a solid foundation has been established …"
"… His deep elucidation of the system has completely dispelled the mist around mathematics, allowing the entire Palace of Mathematics to finally bathe in the brilliant sunlight and reveal the glorious gold …"
Even though Bergner had already expressed similar feelings when he read the book for the first time, he still couldn't help but be amazed every time he read it. Ever since the age of calculus was established and the corresponding concepts were defined, this was the first time that someone had made such a great contribution to mathematics through a book.
"… The age of calculus is over. This is modern mathematics …"
Bergner seemed to have seen new branches taking shape in the Palace of Mathematics, and their origins and concepts were exactly from "Basics of Mathematics"!
For him, there were two aspects that were most important. Firstly, Lucien's completion of the axiomatic system of Tower Geometry filled him with infinite passion for mathematics in similar aspects, as if everything in the world could be axiomatized into a rigorous, self-consistent, and flawless system.
Secondly, Lucien's deep studies on topology, group, and set theory gave him some inspirations. They seemed not to be simple, independent, and abstract mathematical results but also studies that could be directly applied to solve many problems in arcana studies, such as crystallography and the cutting-edge fields of the microscopic world.
"… This is definitely the most groundbreaking book in mathematics in the past hundred years. It will definitely be worshipped by the future arcanists in the temple of mathematics together with 'Mathematical Principles of Magical Philosophy'. It's a pity that the ten questions in the appendix at the end of the book were not there …" With a vague bitter smile on his face, Bergner, the Prophet, opened "Conundrums in Mathematics" in front of him.
For a legendary sorcerer who was good at mathematics, he couldn't resist the tricky questions at all. After flipping through the first part, he was deep in thought and calculation.
However, ever since he received "Foundations of Mathematics", he had been thinking about it for a whole week, but he had not made any progress. He could not even solve a single question. This made him, who was proud of his knowledge in the field of mathematics, feel quite frustrated. In particular, some of the questions seemed simple and easy to solve, but in reality, the process was full of unimaginable difficulties.
Of course, that was not a big deal. What was more terrifying was the barber's paradox. Bergner was in a daze for an hour.
"Before determinism was completely denied, nothing could be more painful and embarrassing for the arcanists of the Tower. When they were celebrating the final completion of the Palace of Mathematics, its foundation suddenly collapsed, as if mathematics itself would be denied as long as the set theory was applied and the concepts in the past were admitted."
Bergner heaved a long sigh. The moment he saw the barber's paradox, he almost couldn't help but destroy "Foundations of Mathematics" with magic and kill every barber. Infinite disasters seemed to be coming because of it!
He moved his eyes down and saw what Lucien wrote after the paradox. "Such paradoxes can frustrate us, but it only means that our studies are not rigorous enough and that our understanding of mathematics in the past has deviated to some extent. Therefore, instead of being desperate and lost, we should study the set theory more deeply. There is only one solution to the problems in mathematics, which is to continue studying mathematics itself."
"… Evans's attitude towards arcana is the foundation that supported him to achieve so much." Bergner complimented and turned back to the set theory section, reconsidering and studying it. The paradoxes in set could only be solved from the set theory.
… …
"… I'm your old friend 'Nightingale'. Now, it's time for 'Arcana News' …"
The generic school was still on vacation. Longman could only learn the latest development of arcana through programs such as' Arcana Voice 'and' News of the World '.
"… Mr. Evans has completed 'Foundations of Mathematics', a masterpiece. He has resolved the puzzles in the field of mathematics and cleared the obstacles to progress. The most eye-catching part of the book is not the content at the beginning but the ten puzzles at the end. They have piqued the arcanists' interest …"
"… I have to admit that the puzzles that baffle Mr. Evans are indeed unusual. So far, no arcanist has claimed that they have found the solution. Even Mr. President and Mr. Brook have admitted in public that it is not so easy to solve the seemingly simple problems …"
"… It seems that whoever solves the ten problems will receive abundant arcana credits and become a well-acknowledged authority in mathematics. The problems are respectively …"
The little boy, Longman, widened his eyes when he heard the question that could baffle Mr. Evans. He couldn't believe it, but he was also eager to try it. If he could solve the problem that even Mr. Evans couldn't solve …
The puzzles that Lucien picked were representative, but they all looked simple on the surface. Therefore, Longman could understand them even though he was weak. He took out a pen and paper and tried to calculate.
"… Mr. Evans told us that, although those problems have nothing to do with actual arcana studies, and solving them will not bring any substantial gains, the studies on them will promote the development of mathematics, and the development of mathematics will support the studies on arcana … The same logic applies to other mathematical fields. In this pure world, we should not blindly pursue applicability …"
Longman soon couldn't calculate anymore, but his heart was burning with fury after hearing that. His cheeks were flushed. "Mathematics is so important? Also, it doesn't seem to need the support of magic … Although I'm not talented in spiritual power, it doesn't mean that I'm not talented in mathematics … "
"I must become an arcanist! An arcanist who is good at mathematics! "
… …
Because of the common features of human nature, after reading "Basics of Mathematics", most of the arcanists tried to solve the puzzles that Lucien proposed out of curiosity and expectation. Mr. Evans couldn't solve them, but it didn't mean that they couldn't! If they could solve one of the puzzles, they would reap unimaginable glory and benefits!
Therefore, during this period, Iristine and Nodanielle, who were walking in Allyn, often saw confused and unsteady arcanists who seemed to be dwelling in their own world.
However, as time went by, there were fewer and fewer such arcanists. Most of them were frustrated faces. The "Basics of Mathematics" in their hands were often marked with different symbols. Some represented demons, some represented nightmares, and some represented mazes with no exits. All in all, even though the ten questions were hung on the permanent display in the Quest Zone, the tide about them inevitably came to an end.
Among them, the arcanists of Tower had the most complicated feelings. On one hand, they were indeed interested in solving similar problems, and on the other hand, they were deeply struck by the paradox and felt the hesitation, confusion, and desperation when determinism was shaken again. Also, the uncertainties hadn't been confirmed by important experiments, but the paradox had presented the contradictions in a simple and clear way. They had to face it seriously.
"If Havin were still alive, he would've probably chosen the same path after seeing the paradox …" Samantha looked out of the window gloomily.
Rachel's lips twitched. "You even burned 'Basics of Mathematics' to him … Are you going to make him have nightmares after he dies? It must be noted that the book is acknowledged as' Book of Demons'. For the arcanists who are not good at mathematics, the number theory, set, group, and other knowledge in the first part are even more dreadful than demons. They almost tear the book apart. For the arcanists like us, the problems and paradoxes in the latter part are even more horrifying than the Will of Abyss …"
"In any case, mathematics will go on. We will certainly find a solution …" Samantha encouraged herself.
Therefore, the other sorcerers discovered that the arcanists of Tower and the arcanists who were good at mathematics were rather silent, brewing an outbreak in silence.
… …
Inside the Atom Institution …
Lucien, Natasha, Lazar, Annick, and the rest of them gathered in Heidi's personal laboratory, watching the first artificial intelligence that she and Chelly assembled.
In the center of the room, countless huge glass tubes were connected in an ingenious manner. Among them were simple magic patterns and relatively complex alchemy devices. A curtain made of a special material stood at the top of the tube. It looked like a water curtain.
"It's so huge …" Iristine was invited to visit. Although she had guessed the final shape from her daily observation, the size of the artificial intelligence was still beyond her imagination.
The artificial intelligence temporarily occupied half of the room, which equaled to almost ten golems.
Lucien nodded. With the help of magic, it was much smaller than the first computer on Earth. "Not bad. Let's turn it on and demonstrate."
Heidi pressed the power switch nervously. The glass tubes were illuminated one after another, flashing red and green lights. The lights changed nonstop, making the whole room look like a ball. Because the series of magic crystal lamps in different colors had been developed, some balls were already experimenting with the changes of lights.
"Input the data …" With the help of magic, Heidi did not make items such as perforated tape but simply inputted with her voice and keys.
After choosing a rather complicated calculation, the red and green lights flashed even more intensely, and the sizzling noises of electric currents were very obvious. Then, the result was displayed on the 'curtain'.
"The data is correct." Spring interjected, "But I got the answer through the ancillary computation circles a few seconds ago."
So, what could it do?
Heidi snorted and looked at her teacher, hoping to be praised. It was only the first artificial intelligence. There was still a lot of room for improvement!
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