Free Web NovelChapter 133: Chapter 126: Have I Actually Proved the Collatz Conjecture?
When Zhao Yi heard how formidable Luo Zhijin described "He Sect" to be, he assumed it was some large "sect", when in reality it was small and was referred to as ’He Sect’ for entertainment purposes.
He Mingcheng spent his whole life conducting research, and it would be impossible for him to devote much time to mentoring students.
He only took on a student every few years when a promising one caught his eye, and his mentorship was limited to offering advice on what they should study.
For instance, Yuan Zhongchen.
When Yuan Zhongchen was a freshman at Yanhua University, he met He Mingcheng in the library. After a brief chat, He Mingcheng discovered that Zhongchen’s ideas were very unique and realized he had found a ’kindred spirit,’ so he guided Yuan Zhongchen on what he needed to learn.
Upon graduation, Yuan Zhongchen, left Yanhua University.
He Mingcheng considers him to be his best student, even though he only mentored Yuan Zhongchen for three years. His mentorship consisted only of advising him on what to read and helping answer his questions. He did not demand Yuan Zhongchen to do anything specific after graduation.
’He Sect’ became renowned thanks to its students.
Seven years ago, one of He Mingcheng’s students, Ying Huaguo, won an international award for his research. During the award ceremony, he stated, "I wish to thank my mentor, He Mingcheng! Although I obtained my PhD in the United States, He Mingcheng is the teacher I respect the most. I will forever be a ’disciple of the He Sect’."
That was how the title ’disciple of the He Sect’ was born.
While others may refer to He Mingcheng’s students as ’He Sect disciples,’ altogether they would not number more than ten. Despite their number, their impact wasn’t insignificant.
By ’capable,’ they were nothing more than researchers, professors, and doctoral advisors.
One should not even think about the academician level.
He Mingcheng devoted his life to research and yet none of his students achieved the rank of academician.
This had little to do with Zhao Yi.
When Zhao Yi returned to his hotel that night, he meticulously went through the process of proving his thesis. He was going to present on stage the next day to an audience of experts, which made him a little nervous.
It felt like...
he was about to defend and have his graduation project and thesis strictly reviewed!
Zhao Yi woke up early the next day.
He went through his thesis once more in the morning, and after carefully verifying that there were no issues, he allowed himself some time to relax.
The presentation was scheduled for two in the afternoon.
By noon, many people had arrived at Yanhua University. The graduate building was crowded with numerous top computer experts, as well as some professors from mathematics, physics, and other subjects. The attraction of an algorithm, after all, was its universal applicability.
If it were a highly specialized computer algorithm, only industry insiders would be interested. Others might struggle to understand it and fail to see its usefulness.
’Effective and Irrelevant Carry Filtering’ was different.
The ’filtering method’ was derived from attempts to solve Rubik’s cube problems, a topic that didn’t require an expert. Even a middle school student - or even an elementary school student - would understand the general idea.
When such a seemingly simple problem becomes a world class challenge, it is bound to attract a lot of attention.
Thus, the attendees were a diverse bunch. ƒreeωebnovel.ƈom
By about 1 p.m., Zhao Yi arrived at the graduate building. To avoid unnecessary distractions, he was led by Xu Chao into a small room within the conference room where he focused on preparing for his presentation.
Two o’clock.
The conference room was packed.
Zhao Yi promptly entered the room, immediately attracting the camera’s focus. With a casual smile on his face, he approached the computer, opened the prepared PPT, and began his presentation according to the planned content.
This was essentially no different from delivering a scripted speech. It was merely about detailing the already developed proof process.
It should have proceeded smoothly until the end, but the mid-presentation Q&A went awry.
A professor named Li Yilai kept asking tricky and bizarre questions, incessantly inquiring about steps involving college mathematics and theorems.
Zhao Yi answered effortlessly.
With knowledge of proof theorems and results, the "Connection Law" helped him easily solve the process. His confident presentation on stage irritated Li Yilai all the more.
But Li Yilai’s nitpicking had a reason.
His research project involved a ’data mining’ algorithm. But despite a few years of effort, he had made little progress. Finally, he had some advancements and planned to publish a paper related to optimization algorithms to apply for some research funding.
The paper was complete.
In his paper on optimization algorithms, he used examples related to Rubik’s cube computations and stated that his algorithm could greatly simplify computations. With further research, he believed he could find the most concise algorithm to solve the Rubik’s cube.
Then the Rubik’s cube calculator appeared.
Li Yilai felt like he had been slapped on the face. He was so angry that he almost smashed his computer, but thinking of how expensive it was without research funding, he ended up sparing it.
Of course.
The main point was that all his hard work was in vain.
The most feared scenario in the research field was for two projects to be headed in the same direction. If they were, then one party’s research would end up being useless.
Defeated by a high school student, one can only imagine Li Yilai’s frustration. He couldn’t vent his frustration and was even thankful his paper wasn’t published. Otherwise, it would have turned into a laughingstock.
Now, looking at the young high school student on stage, while the others wore a face of ’fearing the youth,’ all Li Yilai felt was an urge to spit blood in frustration.
’Effective and Irrelevant Carry Filtering’ isn’t something that can be proven simply. A pause was needed midway through the proof for the audience to digest and understand, and to provide an opportunity for questions.
Li Yilai kept asking questions.
Li Yilai is a professional algorithm researcher and is quite capable. After asking several questions, he suddenly frowned and raised his hand again to ask another question.
The others were getting annoyed--
"Does this Li Yilai have no shame?"
"Why is he making things difficult for a student? The things he’s asking are obvious, he shouldn’t be asking them in the first place."
"Totally shameless!"
Professor He Mingcheng, sitting in the center of the front row, was not only listening carefully but also taking notes. Noticing that Li Yilai kept interrupting with rather silly questions, he couldn’t help but furrow his brow.
Nevertheless, Li Yilai spoke up, pointing out a real issue, "Zhao Yi, I noticed your proofing process. You stated that all possible situations, after being analyzed and determined, will be reduced to the number one, leaving only one possibility."
"This process is not meticulous; you used a few algebraic theorems, but the final conclusion was reached effortlessly."
"If your proving process is correct, wouldn’t it mean you have proved the Collatz conjecture?"
After finishing his speech, Li Yilai sat down rather smugly.
The venue fell silent immediately.
Everyone began to discuss the process. Due to its complexity and roundabout nature, and because a part of Zhao Yi’s demonstration and explanation used a computer model, others didn’t pay attention to it.
Once Li Yilai pointed it out, everyone noticed it right away.
The Collatz conjecture, also known as the Hail Conjecture, is a mathematical conjecture which states that a positive integer x, if odd, will eventually return to 1 after being multiplied by 3 and added 1, or if even, will return to 1 after the even factor, 2^n, is removed and this process repeats.
Many people have claimed to prove the Collatz conjecture and have published a series of papers. However, to this day, no proofing process has been ’universally recognized’ as meticulously as it should be.
So the conjecture remains a conjecture and is not a theorem that can be directly applied.
In Zhao Yi’s proofing process, it seemed very meticulous when demonstrated and explained by computer, but it involved the content of the Collatz conjecture.
This doesn’t necessarily mean he is wrong.
What Li Yilai discussed in his proofing steps was in the case of infinitely large numbers, each possibility is analyzed and determined, and when applied to a Rubik’s cube, there are at most 27 possible moves.
According to the research breakthrough of mathematicians in Japan and the United States, all positive integers less than 7*10^11 conform to the rule of the Collatz conjecture. Any number greater than this is approximately theoretical and would be hard to analyze and determine using a computer.
Moreover, computer science and mathematics are different.
In mathematics, the most meticulous proof is required, even for theoretical numbers. However, the ultimate goal of computer algorithms is to output the correct results.
Even if there are minor flaws, ’Effective and Irrelevant Carry Filtering’ is already a perfected algorithm in the field of computer algorithms and can be directly applied.
Questioning it using a mathematical mindset can be seen as ’looking for a bone in an egg’.
The audience was buzzing with debate.
Most people admitted that the problem Li Yilai pointed out indeed existed. But Zhao Yi’s proofing process was flawless under the current computing power, and the most important thing for computer algorithms is that they can output results, which is more important than the theory in practice.
If the outcome is right, the algorithm can be applied.
That was enough.
On the stage.
Zhao Yi was staring at the process on the screen, continuously pondering about what Li Yilai had questioned.
Collatz Conjecture?
It does seem so!
If the proof is correct, wouldn’t that signify that the Collatz conjecture is correct too? Otherwise, it would not be correct.
But it must be precisely 100% correct!
Zhao Yi had a lot of confidence. "Connection Law" wouldn’t deceive people. He completely understood the proofing process, while the Collatz conjecture was just a conjecture, not an inherent formula or theorem, and certainly not a ’pre-condition’ used by "Connection Law".
So...
Zhao Yi pondered quietly for about five minutes.
The crowd below the stage thought he had been affected. Professor Luo Zhijin came over to comfort him, telling him that computer science and mathematics are different and not to care about Li Yilai’s ’nit-picking’ nonsense.
At this moment, Zhao Yi lifted his head, looked at Li Yilai seriously, then stood up, walked over to Li Yilai.
Everyone cleared a path for him.
"Hold him back!" someone suddenly shouted, "Don’t let him hit anyone! You never know with these young people nowadays!"
"Hurry up!"
"Professor Li, watch out!"
Li Yilai was startled by the outcry and took a step back, but there was no way back since he was seated. He was over fifty and his body was not strong enough to withstand a punch from a young man.
Finally, Zhao Yi made a move.
Excitingly, he grabbed Li Yilai’s hand and said earnestly, "Thank you! Professor Li! Thank you! I really appreciate it."
"Huh?"
Li Yilai was a bit stunned.
Zhao Yi took a deep breath and said, "If it weren’t for your reminder, I wouldn’t have realized that I had actually proved the Collatz conjecture!"
