Free Web NovelChapter 539: Chapter 319: Professor Zhao’s First Lecture
Many famous mathematical conjectures in the world began with special case proofs, which is to say, proofs that focus on specific numerical values or regions. Fermat’s Last Theorem started in the same way.
The content of Fermat’s Last Theorem is simple--
When the integer n is greater than 2, the equation x^n + y^n = z^n has no positive integer solutions.
The equation also contains four unknowns, x, y, and z are fixed unknowns, and special case proofs usually target the exponent n.
Switzerland’s famous mathematician Euler was the first to provide a proof for Fermat’s Last Theorem in a letter to Goldbach. He stated that he had proven Fermat’s Last Theorem for n=3, and his proof was published thirteen years later in the book "Algebraic Guidelines". The method he used was an "infinite descent" combined with a unique factor decomposition theorem for number systems, which was quoted many times by later mathematicians.
In 1816, the Paris Academy of Sciences simplified Fermat’s Last Theorem to the case where n is an odd prime number (all prime numbers other than 2), which means that Fermat’s Last Theorem can be proven as long as it is proven for odd prime values of n.
Lots of mathematicians later participated in proving Fermat’s Last Theorem and completed special cases such as "n=3", "n=5", "n=7", and so on. Kummer transformed it using "ideal prime numbers" and proved that "Fermat’s Last Theorem holds for all prime indices n less than 100".
This was a significant breakthrough for Fermat’s Last Theorem in the nineteenth century.
For the next one hundred and fifty years, there were no further breakthroughs with Fermat’s Last Theorem, until the British mathematician Wiles claimed to have proven it.
Zhao Yi, at the International Mathematicians Conference, exposed the logical error in Wiles’ proof of the theorem by using the Riemann Conjecture as a link to Wiles’ proof arguments.
Since then, Fermat’s Last Theorem became an unsolved mystery once again.
Zhao Yi had thought about Fermat’s Last Theorem for a long time before and found that it was very difficult to carry out a direct overall proof like Wiles’ proof. However, special case proofs targeting n were also difficult to promote to all prime numbers.
For instance, if they continued to push forward and proved that Fermat’s Last Theorem held for n=101.
It would indeed be progress, but the progress would be minimal.
Trying to prove for n=101 could only show that it worked for that case. Since there are infinitely many values for n, it is impossible to prove Fermat’s Last Theorem entirely.
"If we are to make separate special case proofs, why not choose the variables x, y?"
"Although x and y are indeed random numbers, there are still available values."
Zhao Yi carefully considered the Fermat’s Last Theorem equation on the draft paper, "If we could prove that x, y are both odd prime numbers, maybe we could generalize it to all numbers."
"We must first prove this process."
He began to put pen to paper, thinking, "Suppose x and y are both odd prime numbers..."
Prime numbers are magical.
All numbers can be seen as evolved based on prime numbers. For example, even numbers can be seen as the sum of two prime numbers, which is now Goldbach’s conjecture.
At the same time, any large enough odd number can be written in the form "3+ an even number", which means it can be seen as the sum of three prime numbers.
"If we can prove that x, y are odd prime numbers, we might be able to generalize it to all numbers." freeweɓnøvel.com
"The special case for 2 would be easy to discuss."
"Once this proof is perfected, we can further simplify Fermat’s Last Theorem..."
...
Although Zhao Yi had a thought to simplify Fermat’s Last Theorem, it didn’t mean the idea was correct nor that it could be proven.
Zhao Yi exhausted a lot of brain cells and found that the more he thought about the problem, the more complex it became. He understood why Wiles’ paper was so complicated that it took over a hundred pages of proofs to truly delve deep into it.
Fermat’s Last Theorem became extremely, extremely complex when examined in depth.
He figured he could return to his normal life, and there would still be time to think about it later. He shouldn’t let research get in the way.
The second week arrived.
The "Particle Boundary Theory Overview" course was scheduled for Tuesday night at the School of Sciences’ main lecture hall.
On the day of the lecture, Zhao Yi felt anxious, his mind wandering during the afternoon classes. He kept thinking about the lecture and even made minor adjustments to his prepared teaching plan with Qian Hong’s help.
After dinner, he went back to his dorm and rested for a bit. With half an hour left, he took out the teaching plan to check it again, feeling as if he were facing an exam.
Fan Lei’s reminder came from the side, "Zhao Yi, it’s almost time. Get ready!"
"Right!"
Li Renzhe chimed in, "Today’s the big day, don’t you need to wear a suit too?" freeweɓnovel.cѳm
"Let me put it on!"
Zhao Yi usually wore a sportswear outfit, which was not much different from other students. Even during presentations, he usually wore casual clothes, and this was his first time putting on a suit. He mainly considered it necessary to distinguish himself from the students since it was his first time as a teacher. It would be best if he dressed more appropriately.
With Li Renzhe and Fan Lei’s urging, Zhao Yi changed into casual suit attire. The fitted appearance made him look quite stylish.
Zhao Yi checked his reflection in the mirror, satisfied with his appearance.
Once dressed, they all went to the lecture hall together, leisurely.
On the way location.
Zhao Yi’s suit made him seem even more low-key than usual. Some people recognized him from afar, but it attracted the attention of passing female students who turned their heads in unison.
"So that’s Zhao Yi!"
"I only noticed when I looked closely. He’s dressed so stylish today! Oh right, he seems to be going to class; I noticed his class is tonight!"
"The two ordinary-looking guys next to him are his roommates..."
The voices of the girls discussing were not low, and Zhao Yi and his friends heard them from a distance.
Zhao Yi felt gratified.
Fan Lei didn’t care.
Li Renzhe glancing away sullenly said discontentedly, "They’re saying we’re so ordinary? If only I wore a suit too, I would definitely be more handsome than Zhao Yi!"
"By then, the girls would first look at Zhao Yi, but when they saw me, they wouldn’t be able to look away..."
"Thwack!"
Fan Lei slapped Li Renzhe on the back of his head forcefully, "I’ve noticed, Old Li, how shameless you’ve become since you started dating Huang Wenqian..."
"What are you doing!"
Li Renzhe jumped in surprise and mumbled a complaint while raising his fists, only to be stopped by Zhao Yi, "Let’s go, stop messing around."
"See, Zhao Yi doesn’t care about what I said, so why should you?" Li Renzhe continued walking forward while speaking to Fan Lei.
Fan Lei rolled his eyes without responding.
Zhao Yi walked with a smile on his face, seemingly not caring about what was just said, but he gradually slowed down, and when they passed the basketball court, he suggested watching the game, "Look at that tall guy, he’s playing so well!"
"He can’t even score!"
"So clumsy!"
Zhao Yi seemed immersed in the joy of watching the game.
Fan Lei and Li Renzhe checked the time and hurriedly prompted, "Zhao Yi, it’s about time. We have five minutes left. Let’s hurry up. It doesn’t matter for us as students, but today is your first time teaching."
"Alright."
Zhao Yi sighed and continued walking, but they had already reached the School of Sciences’ teaching building, and it would only take a few more minutes to get there.
When they reached the classroom door, he looked at the time and realized they still had two minutes.
"Stop!"
Zhao Yi signaled for Fan Lei to enter first, and then he took Li Renzhe aside to the window, speaking softly with a sigh, "Old Li, to be honest, I’m really nervous."
"Can you share some of your experience with me? Like... about Huang Wenqian, that sort of reluctant and doing it for the sake of pleasure... Anyway, just tell me how did you bear with it?"
"Huh?"
It took Li Renzhe a while to understand.
Zhao Yi’s words were a bit ’unpleasant’, as if his relationship with Huang Wenqian was not true love... Well, no matter what, Zhao Yi was speaking from his heart, so he should respond earnestly, and maybe he could help him?
He started, "Well, just think about the past and grit your teeth to go through with it... Anyway, that’s how it is."
"I don’t really know how to put it."
"But what are you afraid of? It’s your first time teaching, everyone knows you don’t have experience, so even if it’s not good, there’s no..."
"Alright!"
Zhao Yi lowered his head to check his watch, realizing class had already started. He immediately interrupted Li Renzhe with a smile, "Let’s go in, we don’t want to be late. It’s my first time being a teacher, and I can’t be accused of favoritism, even if you’re my roommate..."
"If you’re late, I can’t pretend not to see it." Zhao Yi ended his sentence with a tone of guilt.
Li Renzhe nodded in understanding.
They both entered the classroom together.
Zhao Yi walked up to the podium with a smile, his footsteps steady and demeanor relaxed, showing no signs of nervousness. He greeted everyone and introduced himself, "My name is Zhao Yi, Zhao from ’Zhao Qian Sun Li,’ and Yi from ’Bo Yi’ and ’Dui Yi.’"
"Life, humanity, is all about constant maneuvering and competition to make progress. I hope that every student can become a winner in the game of life!"
"Whoosh!"
A round of applause erupted from the audience.
When the applause subsided slightly, Zhao Yi started talking about the course, "This is my first time teaching and giving a lecture. You all want to earn credits, so let me begin by discussing the scoring."
"’Particle Boundary Theory Overview’ is a novel course in mathematical physics. There’s no textbook for now, but after each class, I will distribute materials for the next lecture. The exam will draw from those materials."
"The exam will account for 70% of the total score, and regular class participation will account for 30%."
"I won’t be assigning homework for this course. All you need to do is understand the content, especially for non-Science Academy students. Just understand the science theories, broaden your horizons, and expand your knowledge."
"Attendance scores are based on roll call during classes. There will be ten classes in total, and I will conduct two roll calls. Full attendance scores will be awarded for attending both."
"Today is the first time."
"By the way, I’d like to especially remind you, marking tardiness and absenteeism is troublesome. I hope that our course assistant, Teacher Qian Hong, will have an easier job." As Zhao Yi spoke, he gestured towards Qian Hong, who was seated in the front row, as if he was considering her feelings entirely.
Qian Hong promptly stood up, turned around, and greeted everyone.
"Oh, right!"
Zhao Yi added a special reminder, "Not only are tardiness and absenteeism the same, but being late by one minute or a few seconds also counts as being late."
"I remember who was late just now."
"Now, let’s start the roll call!"
"Swoosh!"
As soon as Zhao Yi finished speaking, many people looked at Li Renzhe. Since it was Zhao Yi’s first class, the majority of the students had arrived early and had seen Li Renzhe enter the classroom with Zhao Yi. They entered right on the dot, but they were definitely late.
Li Renzhe realized this as well, but he quickly calmed down and muttered to the students who turned to look at him, "What are you looking at! Zhao Yi and I are roommates, how could he deduct points from me?"
"Oh~"
The students in the front row didn’t say anything.
It made sense.
Li Renzhe was Zhao Yi’s roommate, and they had entered the classroom together. There was no way he would be considered late.
But...
Wasn’t Li Renzhe the only one who was late just now?
