At the venue.
Exclamations could be heard one after another!
Those who were here today were all top mathematicians in their own countries. Some of them were even famous masters of the mathematics world. However, when they saw Dale's Conjecture, which had stumped the entire mathematics world for decades, turning a new page in this Chinese youngster's hands, their hearts were in turmoil. There were even a few foreign mathematicians in their 60s and 70s who were acting like children at this moment. As Zhang Ye made a few of the most crucial deductions and deductions, they started to cry out in surprise!
"Fifth power?"
"N value superposition?"
"This is too crucial! This step is too crucial! "
"So his derivation of the formula was all for this step!"
"This is the thought process of a genius!"
"This step of deduction is simply too beautiful!"
"Art, this is the unparalleled art of mathematics!"
It was as if the Eight-Nation Allied Army had entered the city. The entire venue was filled with voices from all over the place in languages that no one could understand! Zhang Ye's artistic handwriting, coupled with his incredible calculations, had won over many of the foreigners from the mathematics world!
Of course, this also included the Chinese mathematicians.
The Chinese mathematicians who had been at loggerheads with Zhang Ye and had even verbally belittled him were now in a difficult position.
The young mathematicians did not say a word.
Han Henian also did not say a word.
Wang Yiming and Xin Ya looked at each other. They both knew that today's matter was going to be big!
Over there, an old professor looked at Zhang Ye hesitantly with a complicated look in his eyes. After a moment of hesitation, he finally shouted at Wang Yiming and the others, "Quick, contact Elder Rong and inform Professor Qu!" Then, as if he was talking to himself, he asked, "Who here specializes in the study of elliptic curves and modular curves? Little Sun from Tsinghua University? No, he's still far from that. Who else could it be? Aiya, who else could it be? " This matter was too big and too shocking. Not only him, even many of the mathematicians at the venue were confused.
A middle-aged professor with a thin face reminded, "Fellow Wan from the Chinese Academy of Sciences seems to be....."
"Right! Fellow Wan is the authority in this field! Quickly contact him! "That old professor facepalmed and remembered," Get all the relevant mathematics experts to come over! "
Wang Yiming immediately replied, "Understood!"
Xin Ya also went to make the call to gather everyone.
......
"Hello, Professor Qu!"
"Oh, it's Xiao Wang. I have something to do here. Let's talk about it later."
"Don't hang up, Professor Qu. Can you make a trip to Summer Palace?"
"I'm in the lab, so I can't leave. Summer Palace? Are you talking about the International Math Olympiad today? What's so urgent that I have to go? Let's talk about it tonight. "
"We can't wait until night time. The American mathematicians brought up Dale's Conjecture again at this year's exchange event. Now, someone is trying to prove it and a portion of it has been proven. Dale's Conjecture has been simplified by a large step, so we invited you here to help us verify it!"
"What did you say!?"
"It's true. We are also contacting Academician Wan and Elder Rong."
"Who's checking? Which country is this mathematician from? "
"It's … it's from our country!"
"Hahahahaha! Good! Good! Good! I'll be right there! "
"I'm counting on you!"
…
"Hey."
"Hello, who are you looking for?"
"Is Elder Rong here? I'm Xin Ya. "
"Oh, it's Professor Xin. My grandfather is talking to a friend. Can you tell me if there's anything? I'll help you pass the message to him? Why don't I get my grandfather to call you? "
"It's an urgent matter. Can I trouble you to tell Elder Rong that someone is trying to solve Dale's Conjecture at this year's International Math Olympiad? He has already proven it to be about 20% complete!"
"Ah? Dale's Conjecture? "
"Yes, it's something that requires a huge amount of calculations to verify. I would like to invite Elder Rong to help out."
"Wait for a moment, Professor Xin. I'll inform my grandfather immediately!"
About a few minutes later.
"Hello, Little Xin."
"Elder Rong, sorry to disturb you!"
"It's not a bother. I've heard about it from my grandson. I just have one question. Which country is the person who is trying to prove Dale's Conjecture? Is it a foreigner … or one of us? "
"It's one of us!"
"Good! Very good! Just wait for me! Hahahaha! "
"With you around, we'll feel more at ease!"
…
One phone call.
Five phone calls.
Ten phone calls.
Not only did they contact some of the most famous and authoritative experts in the mathematics world, they even contacted several organizations related to mathematics. This was because they needed some professional computers and manpower to support them. Although some of them could understand Zhang Ye's calculations and deductions and felt that it was feasible, mathematics was still a very rigorous field of science after all. There was no room for error in any aspect and it required extremely rigorous verification and proof. Hence, team support was extremely important.
Furthermore, mathematics was also categorized into different fields.
Some specialized in linear algebra, some specialized in equations and functions, and so on and so forth. Although at their level, every mathematician would definitely have some knowledge beyond their main field of research and might even be very proficient in some fields, there was still a huge difference between proficiency and authority. Very few people were well-rounded in the field of mathematics and there would always be some areas of emphasis. For example, for those singers, some of them specialized in singing love songs. If you asked them to sing a rock song, they would also be able to sing it and would definitely be better than a non-professional singer. But since they were not professional rock singers, they would still have to be discounted. This was the same logic applied to the mathematics field. Naturally, for a calculation as crucial as Dale's Conjecture, they would definitely need to find the most authoritative people in the various fields of mathematics.
It was the same for those foreign mathematicians around him. Many of them had already made phone calls to their friends or mathematicians in their own countries. Some of them were informing them of the big event that was happening over here, while some of them did not understand some of the calculations and were discussing it with their friends in the mathematics world.
"(#%?"
"% # @&… … $!"
Foreign languages were being spoken everywhere and the atmosphere was like a United Nations conference!
In the end, even the American, Louis, who had been staring blankly at Zhang Ye's whiteboard for more than ten minutes, also took a deep breath and picked up his phone to call an old friend back in America. "Smith, it's me. You have to be mentally prepared. Dale's Conjecture … might be about to have a major breakthrough!"
He did not say it for sure as he had not done the verification yet. As such, whether or not this major breakthrough would be able to pass the test would still require further verification. Even though he was already 80-90% sure that there would not be any problems with the verification based on his experience and judgment, but who knew if there would be any accidents?
Besides, he was still in disbelief. As a mathematician, he knew very well that there were no unsolvable conjectures in the field of mathematics. Once a rigorous conjecture appeared, it would definitely be verified. Either the conjecture was proven or it was not proven. It was either the time was not right or the person who could solve it had not appeared yet. But now, Dale's Conjecture had actually been broken through by a person from China, and by such a young person at that. This was something that he could not accept. In America, there was also a large group of people who had been trying to solve this conjecture, and he believed that America was more advanced than any other country in the field of Dale's Conjecture. This conjecture was also proposed by the Americans, but now, the reality before his eyes had given him a huge blow to his sense of superiority!
… …
The change in the situation could not be said to be slow.
From the previous disdain and ridicule, to the current shock and amazement, it had only taken a little more than an hour. How did Zhang Ye's few whiteboards cause such a huge uproar? The reason was that Zhang Ye did not follow the old path of solving Dale's Conjecture, but had opened up a different path by proposing his own theoretical direction. He had simplified Dale's Conjecture into a different kind of proof!
The conjecture was as follows:
If p is a prime number and E is an elliptic curve over Q (rational number field), then we can simplify the equation to define E modulo p. Except for a finite value of p, we will get an elliptic curve over a finite field Fp with np elements, ap = np p. This is an important invariant of the elliptic curve E. Every modular form will also produce a sequence of numbers. An elliptic curve whose sequence is the same as the sequence obtained from the modular form is called modular.
It might seem like it had nothing to do with Dale's Conjecture, but in fact, when Zhang Ye wrote down the analytical formula to solve it, everyone was shocked to discover that there was a special case of this conjecture — the case of a semi-stable elliptic curve — that was directly related to Dale's Conjecture. Correspondingly, any example of Dale's Conjecture would result in a non-modular elliptic curve. It could be said that as long as they could prove this point, as long as they could prove Zhang Ye's conjecture, or even if it was just this special case, then Dale's Conjecture would basically be proven to be 80-90% true!
Even if it could not be proven, just the concept and concept that Zhang Ye had proposed was enough to cause a stir in the mathematics world. That was why all the mathematicians were so shocked!
This was the finishing touch!
It could even be said to be the most miraculous stroke of the pen!
And this stroke was done by Zhang Ye. In order to prove Dale's Conjecture, he had opened a new door to the world. This contribution was already very big!
But Zhang Ye did not seem to be satisfied with just this.
Shua shua shua. Zhang Ye was not affected by the calls and exclamations from the others. He pulled over another blank whiteboard and continued writing.
A French contestant's jaw dropped. "He's still writing?"
A young British contestant said, "You can even calculate it?"
On the American side, a teenager exclaimed, "He, doesn't he need to think? Why was there no pause at all? This … This deduction is also too fast! "
There was no jam!
There were no signs of thinking at all!
Zhang Ye was just moving his pen very quickly. After simplifying Dale's Conjecture, he was still trying to overcome it, pushing Dale's Conjecture forward bit by bit!
"Eh, this formula!"
All the mathematicians were shocked!
"Ah, this is …"
The mathematicians were shocked again.
"The third curve?"
All the mathematicians were shocked!
"Mental arithmetic to the eleventh power?"
All the mathematicians … were trembling non-stop!
Looking at the back view of the Chinese youth, all the mathematicians present had a shocking thought in their minds — F * * k, could this person really solve Dale's Conjecture in one go???
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