Reilia pulled out two copies from the thick stack of journals she was holding: "The hot topic of discussion this month is your "Fundamentals of Mathematics and Physics", and the most concerned is the barber's paradox, which is known as the great crisis in the field of mathematics and physics. ”

Although under Lucian's tutelage, she is also good at mathematics and physics, but in essence, she is also an arcane in the field of elements and alchemy, and she applies mathematics more than research, so when it comes to the "great crisis in the field of mathematics and physics", she does not have the anxious and confused appearance of the tower arcanist, but has a little more excitement to see the excitement and not be afraid of big things.

Lucien took over "Arcane" and "Nature", and found that His Excellency the Speaker, Teacher, Granny Hathaway and other great arcanists had written papers specifically on "Foundations of Mathematics", on the one hand, they fully affirmed the important role of "Foundations of Mathematics" in the development of mathematics and physics, and did different degrees of research on the many branches of mathematics and physics that were formed as a result, and on the other hand, they all invariably pointed out that the solution of the barber's paradox must depend on the development of set theory itself and on the strict definition of it.

Although the Council of Magic did not have a fully formed system of set theory before Lucien wrote The Foundations of Mathematics, many arcanists who were good at mathematics had realized that starting from set theory and combining it with other concepts could build an entire mathematical palace, which was the cornerstone of all mathematical achievements, so not only did the Grand Arcanists want to strictly define and avoid paradoxes while retaining all the valuable content of the current set theory, but the papers of other tower arcanists also reflected this view.

However, their papers show different tendencies, and some of the arcanists start from the equating of mathematics with logic. Represented by Douglas and Hathaway, and some Arcanists believe that mathematics can be a completely formal system of symbols, without any real content, as long as they do not contradict themselves, this radical view is represented by Fernando, Lucian's concept of axiomatic systems also belongs to this category, in addition to other tendencies, there are other tendencies.

Of course, these tendencies belong to their own worldly outlook and values. It's hard to tell who's right. Whoever is sure of the mistake can promote the development of the field of mathematics and physics, but there is more or less promotion.

"It seems that the Arcanists are not intimidated by the barber's paradox, but are motivated to study how to solve this problem. Lucien chuckled.

Heidi, Cherie and the others quietly glanced at the teacher. Say as if the barber's paradox was not something you proposed.

Flipped through it. Lucien saw again the soothsayer Begner's thesis on the "Goldbach conjecture". He admits that there is no way to prove it for the time being, but thinks that he can get closer and prove that even numbers can be expressed as the product of M prime numbers plus the product of N prime numbers. That is, "M+N" is proved first, and when both M and N are reduced to 1, the problem is solved.

"Teacher, your conjecture is jokingly called proof '1+1', which is very interesting, but Lord Begner has not even proved '9+9', and there is still a long way to go to solve it. Heidi grinned and said, "Teacher, you can't have solved this conjecture and then throw it out to see everyone's thoughts, right?"

"I really haven't solved the ......," Lucien shook his head amusedly, as if he could imagine that in the future, "M+N" papers would be indispensable in the journal Nature, and maybe someone would be able to go to "1+2" in a few decades......

After exchanging the latest periodicals, Lucien was about to enter his office, when Heidi suddenly smiled and said, "Teacher, I heard that there is a Rentat festival in the kingdom soon, and the opening ceremony is your opera "Valkyrie"?"

"If nothing else, it should be like this. Lucien did not deny it.

"Oh, I'm looking forward to it!" said Heidi, Leilia and other students and assistants with sparkling eyes, over the years, most of the teacher's energy has been focused on the study of arcane and magic, and in the field of music, in addition to the classic and alternative violin concerto, there are only some simple and short piano pieces and light music, which really makes those of them who also like big musicians disappointed, and this opera is said to have been written by the teacher for several years, and it must be very perfect, with many classic melodies and arias.

Sprint pursed his lips quietly, unable to understand their attitude, he listened to the music if it was there, and it didn't matter if it wasn't there, as for being so excited?

Amid the chatter of Reilia and Heidi, Lucien walked into his office and looked at the paper in front of him in a daze.

After a while, he picked up a quill, dipped it in magic ink, and wrote a title: "Determinism, Self-Awareness, and the Roots of Magic."

Although the title of this paper looks similar to Schrödinger's famous "Determinism and Free Will", the content in it is only a few similarities, Lucian, after analyzing the contradictions of determinism itself, leads to self-consciousness, and then brings the problem to the relationship between the "observer effect" and the "source of magic", which is also not theoretically proven, but belongs to the possible model of "vacuum sea of negative energy states".

“...... It is precisely because of the effect of consciousness on microscopic particles that our material foundation is not 'solid' enough, so that various changes can occur under the action of mental power and corresponding magic patterns, resulting in strange and changeable magic, for example, our partial metamorphosis can be described as a reorganization of the body at the level of microscopic particles...... Therefore, magic without a constant effect has a duration, a phenomenon that we used to interpret as being rejected by 'nature', but now it seems that it is better to describe it as being influenced by other 'observers', resulting in a collapse ......"

"The mutation of the bloodline may come from this 'instability' at the microscopic level, such as quantum jump ......"

“...... Of course, a lot of magic requires a huge amount of energy, which is beyond the reach of our mental power, so the question is, where does this energy come from?"

“...... In some transfiguration, there is a decrease and increase in matter before and after the transformation, and the decrease is understandable, that part of the matter does not disappear, but is stored in the temporary space-time created by magic, and as soon as the continuous effect of the spell arrives, it naturally returns to itself, but what about the increase of matter? Can matter be created out of thin air? And according to the conservation of mass and energy, the energy required is extremely terrifying, so where do they come from?"

"I'm guessing that when using this transfiguration, what we get from the outside world is not energy, but the base matter, but where do they come from?"

“...... Perhaps the existence of the 'real world' can solve our doubts, but in what form does it exist? Does it exist in every corner of the universe so that the vacuum in the absolute sense does not hold? What is its essence? What is the elemental matter that can provide the basis for the earth?"

"Can meditation be described as a process of increasing self-awareness? The growth of a magician is a process of becoming a weak observer to a strong observer......

After writing this paper, Lucien picked up the paper and blew a breath: "It is enough to let people see that I got the inspiration from the 'vacuum sea of negative energy states', well, we have to keep the logical self-consistency of the paper itself......"

After muttering, Lucien put down the pen and paper, and looked at the paper again in a daze: "How to explain the problem of Transfiguration, and what is its real principle......"

In the afternoon, after casually submitting the paper to the Wizard Management Department, Lucien returned to the "Atomic Universe" and saw Natasha sitting on the couch in a daze.

Is today the day of the husband and wife in a daze?Lucien smiled secretly and shook his palm: "What's wrong?"

Natasha, who was dressed in a purple court dress, woke up and said with a sneer: "It's getting closer and closer to the Rentat Music Festival, so I miss Aalto a little." ”

"I can see that sometimes I think back to Aalto's life. Lucien smiled and pulled Natasha up, "In that case, if you think of it, you can do it, let's go to Aalto now." ”

"Huh?" Natasha was stunned for a moment, when did Lucien become a doer and not plan in advance?

But she quickly came to her senses and smiled brightly and said, "Okay, we'll have dinner at Aalto." ”

This kind of "walking" thing doesn't seem to need to be planned!(To be continued......

PS: The first update, a few hundred words to make up for the next chapter~

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