Free Web NovelChapter 134: Chapter 127: Is this... Eunuch?
One day in 1976, the front-page headline of the "Washington Post" reported a piece of mathematical news.
The story unfolded as follows: In the mid-70s, campuses of prestigious universities in the United States saw people engrossed in a mathematical game as if they were possessed, working day and night, forsaking rest and meals. The game was incredibly simple: Write down any natural number N (N ≠ 0) and transform it according to the following rules:
If N is an odd number, the next step is 3N + 1.
If N is an even number, the next step is N/2.
Not only students, but even teachers, researchers, professors, and scholars joined the frenzy.
Why did this game have such enduring appeal? Because people discovered that no matter what non-zero natural number N was, it ultimately couldn’t escape the descent into 1. To be precise, it couldn’t escape falling into a 4-2-1 cycle, forever destined to this fate.
Everyone could start from any positive integers, and continuously perform the following computations: If it’s an odd number, multiply it by 3 and add 1; if it’s an even number, divide it by 2.
Keep performing these operations until obtaining 1 for the first time, marking the result as the end.
Would every positive integer, when manipulated according to these rules, eventually lead to 1? This question is known as the Syracuse Conjecture, the Hail Conjecture, or the Collatz Conjecture. Including what later came to be the Collatz Problem, they all were intriguing ’3X+1’ issues in the world of mathematics.
Internationally, the ’3X+1’ problem is often called the Syracuse Conjecture or the Hail Conjecture, while domestically in China it’s called the ’Collatz Conjecture’ because a person named Collatz introduced it to the country.
This problem might sound straightforward, but proving it is a mighty challenge.
Over the decades, numerous top mathematicians have invested a huge amount of energy in it, but none have been able to produce a rigorous proof.
So, the conjecture remains a conjecture.
...
When Li Yilai stated that Zhou Yi’s process incorporated a portion of the Collatz Conjecture, it made those at the conference believe that there was a theoretical flaw in the ’Effective and Carry-free Method.’
Unless the Collatz Conjecture can be proven one day, there will always be a ’potential’ flaw in the ’Effective and Carry-free Method.’
So, mathematical theory truly forms the foundation of all sciences.
What the audience did not expect was Zhou Yi’s reaction. He excitedly thanked Professor Li Yilai, even stating that ’he had not realized he had proven the Collatz Conjecture.’?
This unexpected twist in the situation left everyone speechless.
Amongst the murmurs of the crowd, Zhao Yi thanked Professor Li Yilai, then, with excitement coloring his face, he returned to the stage. He did not continue the discussion about the Collatz Conjecture but instead carried on with the ’Effective and Carry-free Method.’
The end of the talk was near.
The proof step involving the ’Collatz Conjecture’ was the crux of the ’Effective and Carry-free Method.’ Once the process was explained, the remaining part became easier to understand.
"... Thus, we can affirm that this step is detrimental to the overall progress, and we can choose to leave it out!"
"That’s my Effective and Carry-free Method!"
"The above is my proof!"
"Thank you all!"
Upon completing his final sentence, Zhao Yi took two steps backward, and bowed politely. Then, the room erupted in thunderous applause.
The presentation was a great success.
Despite the uncertainty regarding whether the ’Collatz Conjecture’ has been proven, even if it hasn’t, ’Effective and Carry-free Method’ can certainly be applied in practice, as computer performance doesn’t reach a theoretically possible ’counterexample number.’
This feature is of utmost importance in the computing industry.
Computer algorithms do not need to be ’perfectly accurate.’ Much like how any software will have its flaws, the purpose of a computer algorithm is to be used in practice, not to be theoretically perfect.
A newly manufactured car cannot be guaranteed to be without faults 100% of the time; an artificial intelligence translator doesn’t need to have perfect translation capabilities, an accuracy rate of over 90% is already considered quite successful.
The foundation of computing, algorithms call for a higher level of accuracy, yet theoretically ’inaccurate’ potential only means 100% accuracy.
So, the ’Effective and Carry-free Method’ is already a near-perfect algorithm.
The presentation ended.
Nobody in the conference room left their seats; they were all curiously watching Zhao Yi as he stepped down from the stage. They were all wondering about the issue he had brought up, "Has he really proven the Collatz Conjecture?"
They craved an answer.
Zhou Yi, of course, was aware of what was on everyone’s mind. But he couldn’t lay out the proof of a mathematical conjecture during a presentation on his ’Effective and Carry-free Method.’ The very reason he had become so excited implied that the proof of a mathematical conjecture carries tremendous significance.
The "Effective and Carry-free Method" that he had presented was merely a computer algorithm. As sophisticated as the process might be, as broad as its application might reach, most ordinary folks wouldn’t really care.
But mathematical conjectures are different.
If one could prove a mathematical conjecture, his name might even appear in math textbooks at the primary and secondary school levels.
A chance to be remembered in history!
The research building at Yanhua University, where the presentation was taking place, was certainly not the appropriate venue to demonstrate a mathematical conjecture, let alone the fact that he hadn’t yet composed any related papers or made any direct submissions.
What if...
Some shameless person, having observed the entire process, swiftly organized the evidence and submitted it, thereby jeopardizing the copyright of the proof?
The probability of such an occurrence wasn’t small. After all, the proof of a mathematical conjecture carries tremendous significance.
As Zhao Yi acknowledged the gazes of the crowd, he thought for a moment, then returned to the stage and announced, "Now, I am going to present to everyone the thought process behind the proof of the Collatz Conjecture!"
All of a sudden.
Everyone perked up.
Some people thought Zhao Yi was bragging, but whether he was or not, you needed to hear it to be sure.
The venue fell silent.
"A mathematical problem may have many proof methods, my method uses the binary thinking of computers."
Zhao Yi wrote a number on the blackboard--
11011.
This is the binary digit for 27.
In the Collatz Conjecture, 27 is considered a formidable number. Unassuming in appearance, terms of the conjecture dictate that it requires 77 steps to reach the peak of 9232, and another 32 steps to descend back to 1. The entire transformation process requires 111 steps in total. The peak value of 9232 is more than 342 times the original number 27.
Zhao Yi then began to calculate 27 in the form of ’3X+1’ computation. What was remarkable was that every number he wrote was expressed in binary. He continuously wrote more than a hundred binary numbers, filling the entire blackboard.
The audience below had a headache just looking at it. The blackboard was filled with 1s and 0s, making it look like a drawing.
But in the entire calculation process, one thing was clear to all; Zhao Yi is truly a binary super genius. Even for four-digit numbers in the thousands, he could instantly write down the corresponding binary number.
Once Zhao Yi had finished his calculation, he smiled at the audience below and said, "My approach to proving the Collatz Conjecture is to demonstrate it using binary numbers. Due to time constraints, I won’t keep you here too long."
"That’s it for today’s lecture!"
"Thank you all!"
...
The people in the venue were a bit taken aback.
They thought Zhao Yi was going to prove the Collatz Conjecture on the spot, but he seemed to stop just as he was getting started. Was this it?
Many people felt like they were about to spit blood from frustration!
Only then did someone recall that Zhao Yi had mentioned ’an approach to a proof,’ not the entire proofing process.
If Zhao Yi had actually proven the Collatz Conjecture, offering a glimpse of his proofing thought process at this inconsequential symposium was already quite generous. Anyone else would have kept their mouth shut until their paper had been published and recognized by the World Mathematical Society, and only then would they start giving lectures - and they would choose a much larger stage to do so.
Zhao Yi received a warm welcome as he left the stage.
"Professor Zhao!"
"Professor Li!"
"Professor Wang..."
Several rows were occupied by ’professor seats.’ Luo Zhijin introduced everyone in turn, acting as if he was ’one of Zhao Yi’s people.’
Professor He seemed quite pleased. The elderly professor stood up, shaky on his feet, to announce publicly that Zhao Yi was his disciple, which earned him a lot of congratulations.
There were also... envies.
Any scholar would want to have good students. It adds face to the teacher when their students can achieve something. Zhao Yi couldn’t even be considered twenty years old, but he had already invented a completely new computer algorithm. He was definitely a super genius in the field of computer science.
Everyone wanted such a genius to be their student.
Luo Zhijin was also standing by with a smile. In reality, he was savvier than Professor He.
The process of Zhao becoming the disciple of Professor He indeed had a playful side. However, if it happened to be soft-heartedness towards the old man’s age, reluctant to refuse him bluntly...
What’s the meaning of being a student or a teacher? fгee𝑤ebɳoveɭ.cøm
This is not ancient times anymore!
Luo Zhijin couldn’t care less whether half-hearted Zhao Yi became Professor He’s disciple or not. ’Disciple of He Sect’ sounded powerful, but it’s just a title after all.
Professor He is really getting on in years. He has some weight in the academic world, but the old professor doesn’t like worldly matters. He doesn’t care about the students he brought up either. Most of his students don’t know each other and can merely claim to be part of He Sect. The level of their connection is difficult to say.
What Luo Zhijin cared more about was whether Zhao Yi would choose Yanhua University.
Professor He’s method of accepting disciples was questionable.
There were so many professors and experts at the site, if one of them started to try and recruit Zhao Yi, he might just choose another university. At first, Luo Zhijin merely hoped for Zhao Yi to choose Yanhua University. Now, however, he had turned that ’hope’ into a ’must.’
Zhao Yi MUST choose Yanhua University!
Such a whiz kid who hasn’t even started university is already able to independently create a new computer algorithm, and ’potentially’ prove the Collatz Conjecture. Missing this one chance would be unbearable, one wouldn’t encounter another in the next few decades.
This is an opportunity that must be seized!
Taking advantage of an intermission, Luo Zhijin found Xu Chao and Qian Hong and urgently instructed, "Pay attention to prevent Zhao Yi from getting drawn away by the others following."
"Stick with Zhao Yi, help him fend off the crowd. When you get a chance, lead him away and take him to tour our lab."
"Once he’s led away, it’ll be hard to bring him back."
"Do you understand?"
"!!"
