Chapter 524: The proof, completed!
More and more people had been alerted about this matter by now.
The venue was already getting overcrowded with people as large numbers of mathematicians, park visitors, and media reporters descended upon the site. Wave after wave, people arrived in droves.
"Where is he?"
"How's the attempt going?"
"Which mathematics master of our country is it?"
"What the f**k! How could it be him?"
"Right, oh my god, how could it be him!"
Every batch of people who did not know about the news and saw the young figure of a person in front of all those whiteboards had the same reaction. Other than disbelief, it was still disbelief. Some mathematicians, who were always holed up by themselves and knew nothing but equations all day long might not be familiar with Zhang Ye, but how could those reporters who were always up to date with the latest news not know about Zhang Ye infamous name? Right now, they did not care about anything else, they were not bothered by why Zhang Ye would know such high mathematics. All they knew was that the solving of Dale's Conjecture was the most important!
They had already advanced a huge step now!
Could there be another big breakthrough today?
At this time, the last key figure had reached the venue. It was Fellow Wan from the Chinese Academy of Sciences!
"Teacher, you've arrived!"
The Chinese mathematicians had suddenly gathered together.
Fellow Wan did not care about the who the person attempting to solve the problem was at this moment. He went straight for the point of his visit and began discussing with Elder Rong, Professor Qu and the others in front of the whiteboards, pointing and speaking as mathematicians from each specialization suggested their own analysis on the solving of the problem.
"Are you sure?" Elder Rong asked.
Fellow Wan replied very excitedly, "I'm very sure!"
Professor Qu turned to his side and asked, "Professor Yan, how about the part that you're concerned about?"
The professor also said excitedly, "I've been analyzing this for a very long time now and there's definitely a possibility of it logically speaking. His direction of argument is definitely correct!"
Elder Rong cried out loudly, "Great!"
After having much discussion among the experts, everyone finally seemed convinced. Zhang Ye had not only taken a huge step forward in regards to Dale's Conjecture, he had even managed to prove all of his research was feasible. Although he might not be able to finally solve the conjecture, but at least the direction of study was possible. This meant that this crazily young mathematician was running at full speed towards solving Dale's Conjecture and with each step that he took, he was changing the history of Dale's Conjecture. He had set the wheels in motion regarding this conjecture and that was something to cheer for the people!
Elder Rong sighed and said, "To think that I was able to live to see this day of Dale's Conjecture being solved. I have no regrets anymore."
Wang Yiming quickly said, "Elder Rong, you're still young."
Professor Qu laughed, "If this young man is really able to solve the conjecture and make it into a theorem, it would be the best. Then there would be even less regrets."
"It's easier said than done." a professor said.
Fellow Wan who overheard this said, "If it were to be fully proven, then the global mathematics world should have a feast to celebrate this. By that time, our country's mathematics world would become famous." At this time, Fellow Wan suddenly took notice of that person and asked, "Where did you all find such a young mathematician from? Whose student is he? Why do I find him to be so unfamiliar. I don't think that I've ever seen him before?"
Elder Wan laughed out loud, "Of course you'd find him unfamiliar. That kid has never been one of us mathematicians. Old Wan, I bet that you would never guess what this person does for a living! Hahaha! When the group of us arrived earlier just now, we were stunned to see him too!"
Time was passing by very quickly.
Yes, but it was going very slowly too.
Among those who could understand what Zhang Ye was writing, some were already in a daze. It was like they were under a spell, uttering to themselves as they stared at the whiteboards. Time passed very quickly for these people as they had already lost sense of time. In fact, since Zhang Ye began his work on solving the conjecture, 5 hours had already passed.
The 28th whiteboard......
The 29th whiteboard......
In the blink of an eye, the 30th whiteboard had also been filled to the brim with writings of equations!
Zhang Ye's method of reasoning was also getting clearer and clearer, presented detailedly in front of all the mathematicians and cameras.
He continued attacking by simplifying the conjecture, suggesting a another proposition: Assuming 'Dale's Conjecture' was invalid, and there exists a group of non zero integers A, B, C, such that A^n+B^n=C^n. Then using the group to construct elliptic curve of the form, y²=x(x+A^n)(x-B^n), it is impossible for it to be a modular curve. If he could provide proof of these 2 propositions, then he would be able to show that Dale's Conjecture could not be established by proof by contradiction and in turn prove Dale's Conjecture.
The proving was progressing rapidly!
The direction of approach was getting stronger!
The Chinese mathematicians could no longer bear it and kept cheering!
"This step was solved with such great excitement!"
"It's another milestone! He's reached another important point in his calculations!"
"This person is really good!"
At this point in time, even those foreign mathematicians were starting to believe that this young Chinese mathematician could really solve Dale's Conjecture. Just the idea alone made everyone's heart beat faster. In such a setting and with such a person, it was turning out to be a really unbelievable situation!
Fellow Wan couldn't sit around any longer, "Let's go, we should not be idling around. Let's start by verifying the equations."
"There isn't enough time, there's such a large amount of calculations to be done...." said a professor.
Elder Rong said, "We don't need to calculate everything. Just do a simple check so that we know everything looks to be in order. If there isn't a big problem in there, it should be fine. The details can be worked out at a later time!"
The manpower was available and everything was in place. A large number of Chinese mathematicians immediately initiated the process and started verifying each of Zhang Ye's whiteboards. With computing equipments available to them and so many authoritative experts around, the workload that needed to be done could be considered as light.
Seeing the situation, a few foreign mathematicians also volunteered to join the Chinese in the verification process and work with them in light of such a grand moment in the history of mathematics!
They advanced very quickly!
Elder Rong said, "Equation (1) verification, complete!"
A young mathematician said, "Function C's equation is correct!"
One of Fellow Wan's disciples was furiously writing and calculating an equation in his notebook. Without even raising his head, he said, "The logical operation's calculation is reversible, it is valid!"
Xin Ya also joined in, "Passed!"
Han Henian was doing his part with the calculator!
The voices rang out one by one.
With every call, everyone became even more excited. When it comes to mathematics, there were some calculations which could be valid, but not necessarily correct. This was also the reason why many conjectures which had been proven still required a large effort and even longer time to be verified. As there might be some hidden mistakes or error which might invalidate a certain equation, the arguments and calculations following it would definitely be invalidated as well. Even if the latter part of the proof were to look perfect, it wouldn't mean a thing if the beginning part of it was wrong. In mathematics, what was important was accuracy and rigorosity. Not a single mistake would be tolerated. This was also the reason why a lot of people were afraid that Zhang Ye had a vulnerability in his proof, as that would invalidate everything he had done so far.
The Chinese were naturally worried about this, worried that Zhang Ye would fail!
Among some of the foreign mathematicians, like Louis and David from the United States, they would probably prefer to see this outcome, hoping that this person would make a mistake.
But what was astonishing was that this person attempting to solve the conjecture had a brain like a most intricate computer that could handle the calculations in the most precise and accurate manner!
With a larger team of people, the group was speedily catching up to Zhang Ye's progress and calculations.
Suddenly, when another one of the whiteboards was filled, Zhang Ye stopped writing. He looked at the remaining 11 whiteboards and did not move.
"He's stopped writing?"
"What's the matter?"
"Could it be he has no idea on how to go on anymore?"
"This is where it stops?"
Elder Rong, Fellow Wan, Professor Qu and the others' had a change in their expressions. They seemed like they had a tinge of regret, but they also understood that matters like this could not be forced. What was this conjecture to begin with? It was the great Dale's Conjecture! For this youth to even get to this step was already enough to cause a stir in the mathematics world. They couldn't ask for more than this.
Xin Ya had gotten a little anxious and asked, "Teacher Zhang?"
A female mathematician from the United Kingdom looked admirably and surprisingly at Zhang Ye. She got the translator to help her say to him, "You've already done something that no one else thought possible!"
Some mathematicians were sighing, thinking that this conjecture was really more difficult to prove than they had expected.
There were also some reporters who were busy trying to capture the last shots of this event, knowing that all the excitement was probably coming to an end now.
But at this moment, Zhang Ye said something that left everyone dumbfounded. He patted Huang Lingling on her shoulder and said, "Which one of the remaining whiteboards do you like?"
Huang Lingling just blinked in surprised, "Eh?"
Zhang Ye smiled, "Help Big Bro to choose one."
"Oh, that...that one then." Huang Lingling did not understand his request, but just pointed out to the second whiteboard at the other side anyway.
Zhang Ye nodded and then walked over to bring the whiteboard back.
Her brother, Huang Leilei subconsciously asked, "What about the other whiteboards?"
Zhang Ye was just starting to write on the blank whiteboard as he uttered, "The others? All of them can be taken away!"
Han Henian asked, "Take them away?"
Wang Yiming was startled, "What do you mean?"
Xin Ya also hurriedly asked, "Teacher Zhang, do you mean...."
The rest of the sentence was meaningless as everyone had already understood. Then, it set off an uproar as the regretful atmosphere earlier once again reignited with a cheer of hope!
Professor Qu was surprised, "It's not because he couldn't calculate any further, but because he had already finished his calculations!?"
At this key moment, Fellow Wan was no longer able to suppress himself as he raised his shaking hands, "It's down to the last board?"
Elder Rong took a deep breath, "He's really gone and done it?"
After the commotion died down, everyone was suddenly quiet again. It was as though everyone present had become frozen. Only the sound of the marker screeching as it left its ink on the whiteboard could be heard!
Under the close attention of everyone, Zhang Ye's hand seemed like it was dancing across the whiteboard. A sudden flick of his wrist and an elegant stop. Thereafter, with a few more strokes, he finished writing all that was needed.
And with this, Dale's Theorem was born!
-- by Zhang Ye.
In this exact second, everyone at the event venue broke into a frenzied excitement!!
*QED: Q.E.D. (also written QED) is an initialism of the Latin phrase quod erat demonstrandum, meaning "what was to be demonstrated", or, less formally, "thus it has been demonstrated". The phrase is traditionally placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been exactly restated as the conclusion of the demonstration.
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Thanks to CKtalon for his work on Dale's conjecture!