Chapter 522: All the mathematicians were constantly feeling stunned!
At the venue.
Voices of exclamation were heard one after another!
The people who were attending this event today were the top mathematicians of their countries and some were even established and famous veteran mathematicians of the global mathematics world. Having just witnessed this young Chinese mathematician advancing the study of Dale's Conjecture that had stumped the world for several decades sent their hearts fluttering. Several old foreign mathematicians in their 60s-70s, who were following closely Zhang Ye's calculations had cheered like children at every key validation and deductions!
"A quintic function?"
"N value stacking?"
"That's such an important step! This step is way too important!"
"So that's why he wrote down the derivative formula earlier! It was meant for this step!"
"This is the thought process of a genius!"
"This key step in the calculation is really too beautiful!"
"Art, this is truly an unrivaled mathematical art form!"
It was as though the the eight-power allied forces had invaded the city again. At the venue, everyone from different countries were speaking in their languages over one another! Zhang Ye's highly artistic writings and that unimaginable math projection had won over a lot of the foreigners of the mathematics world!
Of course, the Chinese mathematicians were feeling the same as well.
Those Chinese mathematicians, who had earlier been opposing Zhang Ye and even had harsh words for him, were in a little bit of a predicament now.
The young mathematician kept quiet.
Han Henian also did not utter another word.
Wang Yiming and Xin Ya looked at each other, knowing that this incident today was going to make the news for sure!
Over there, an old professor wanted to speak, but seemed to hold back as he looked on at Zhang Ye. He had a perplexed expression on his face as he hesitated a little before finally calling out to Wang Yiming saying, "Quick, contact Elder Rong and Professor Qu!" Then he seemingly said to himself or possibly to anyone around him, "Which of our people are experts at elliptic curve and modular forms? Is it Tsinghua University's Little Sun? No, no, he's still lacking. Who else is there? Aiya, who else is there?" This matter was a very big deal and it was also too astonishing. Not only him, even all the other mathematicians were in a state of confusion right now.
A middle-aged professor with a thin face reminded everyone, "Fellow Wan of the Chinese Academy of Sciences might be....."
"Right! Fellow Wan is the authority figure in this regard! Quickly find him!" The old professor smacked his forehead when he thought of this and added, "Invite all the experts from the related fields of study!"
Wang Yiming immediately acknowledged, "Understood!"
Xin Ya also went to make some calls to gather more resources to handle this matter.
......
"Hello, Professor Qu!"
"Oh, it's Little Wang? I've something to attend to over here, let's talk again another time."
“Professor Qu, don't hang up on me first. Could you make a trip to Summer Palace Park?"
"I'm in the lab now and can't get away at the moment, but why Summer Palace Park? Are you talking about the International Math Olympiad? What's so urgent that you need me there for? Let's talk again tonight."
"This can't wait for tonight. The American team has brought out Dale's Conjecture as their question again this year and someone is currently attempting to solve it. A portion of it has already been proven and advanced the study of Dale's Conjecture by a huge step. We need your help to verify if everything is valid!"
"What did you say?!"
"It's true, we're also contacting Fellow Wan and Elder Rong as we speak."
"Who is attempting to solve it? Which country's mathematician?"
"It's....It's our country!"
"Hahahaha! Fine! Fine! Fine! I'll be right there!"
"We'll count on you then!"
......
"Hello."
"Hello, who are you looking for?"
"Is Elder Rong there? This is Xin Ya."
"Oh, so it's Professor Xin. My grandpa is having a meeting with a friend right now. Do you want to leave a message? I'll pass the message for you? Or I could get grandpa to call you back later?"
"The matter is very urgent and requires his immediate attention. Could you let Elder Rong know that someone at the International Math Olympiad is currently solving Dale's Conjecture and we believe he is 20% done!"
"Ah? Dale's Conjecture?"
"Yes, we would like to invite Elder Rong to come help to verify as this requires a huge amount of validation work."
"Wait a moment, Professor Xin. I will immediately inform grandpa!"
After a few minutes.
"Hello, Little Xin."
"Elder Rong, I'm sorry to interrupt your meeting!"
"It's fine. I've heard about it from my grandson. I just want to ask one question right now. The person who is attempting to solve Dale's Conjecture... from which country does that person come from? Is it a foreigner or one of our own?"
"He's one of us!"
"Alright! That's great! Just wait for me then! Hahahaha!"
"With you coming to join us, we'll be much better!"
......
One call.
Five calls.
Ten calls.
The Chinese team was suddenly dealing with a lot of calls, some incoming and some outgoing. Not only did they contact the authority figures and experts, they even contacted several mathematics organizations requesting for professional support from them. Although some of them could understand Zhang Ye's calculations and projections, and even felt that it was possible to work out as written, but math was, after all, based on rigorous verification and had no room for errors. They definitely needed support to be able to test this proof and so teamwork was the most important thing now.
Besides, mathematics also branched out to many fields of study.
There were people who researched linear algebra, some who focused on functions with no closed forms, etc. Although at their level, every mathematician still knew a bit beyond their main research field. They were even proficient in other topics, however, there was a very great difference between being proficient and being authoritative. Very few people were all-rounded in the world of mathematics. There was always an inclination. For example, many singers would professionally sing love songs. If you were to ask them to sing rock, they could sing it, and would definitely be better than non-professional singers. However, they were not professional rock singers, so their abilities would definitely be slightly discounted. This was the same rationale in the mathematics field. Naturally, when handling the calculations for an important question like Dale's Conjecture, they would have to get help from proper authority figures from the respective fields.
The foreign mathematicians were reacting the same way too. Many of them made calls back home and contacted their friends or fellow mathematicians. Some of them were just informing them of the happenings over here while others, who could not understand some of the equations, had called home to discuss with them.
"$%^&"
"^&*)(*&^%..$!"
It was a mixture of many foreign languages as the atmosphere seemed to be that of a United Nations Conference!
Finally, even Louis from the American team, who had been staring at the whiteboards for more than 10 minutes, had to draw a deep breath before taking out his cellphone to make a call. He had reached out to an old friend back in the United States, "Smith, it's me. You have to be prepared for what I'm going to tell you. Dale's Conjecture........might have an important breakthrough today!"
He did not use confirmed terms because the verification of the proof had not even begun yet, and so whether or not this breakthrough could stand up to scrutiny was still left to be seen, but in any case, from his experience and deductions, he thought that the proof offered was probably 80-90% correct, but who knew if there might be any surprises?
He still found it quite unbelievable. As a mathematician, he knew clearly that there wasn't any theorem that would forever remain a mystery. A serious conjecture would eventually be rigorously validated. The theorem would either be proven true or false, be it just a matter of time or that the person that could crack it had yet to appear, but now, such a young man from China had made such a major breakthrough with Dale's Conjecture was something he found hard to accept. A number of people in America had been specially studying the conjecture, and he believed that America was far ahead of other countries when it came to the research of Dale's Conjecture. The conjecture itself was proposed by an American, but now, the truth before his eyes slammed his sense of superiority with a stick.
......
The development of the situation was really quick.
From ridicule and laughter at the start, it had become a sense of shock and amazement. In just a short hour, how did Zhang Ye's whiteboards stir up such a great reaction? This was because of the fact that Zhang Ye had not taken the path that past mathematicians of this world had gone down in regards to solving Dale's Conjecture. He opened up another way and suggested his own direction of reasoning to simplify Dale's Conjecture into another kind of theorem!
The conjecture went like this:
If p was a finite value, while E was an elliptic curve in Q (all rational numbers), reducing the coefficients modulo p, except for a finite number of primes p, there would N_p elements in the finite field extensions of F_p. Np = p - a_p This was an important invariant of the elliptic curve, E. Every modular form would produce a sequence. A subsequence and each modularity form that formed a similar sequence was a modular form.
Looking at it, it was hard to tell if this had anything to do with Dale's Conjecture, but in fact, after Zhang Ye wrote out his analysis and used it in his calculations, everyone was stunned by its discovery. A special case of this conjecture was — the situation with semistable elliptic curves was directly related to Dale's Conjecture. Correspondingly, any solution to Dale's equation could be used to generate a semistable elliptic curve that was not modular, and so it could be said that as long as this was proven, as long as the special case of this conjecture that Zhang Ye had suggested could be proven, then Dale's Conjecture proof would be at least 80-90% established!
Even if it wasn't fully proven, just with what Zhang Ye had proposed and the ideas that he had provided were enough to stir up the mathematical community; hence, all the mathematicians were extremely shocked.
This was the crowning touch!
It could be said that it was a divine crowning touch!
And this touch was drawn by Zhang Ye. To prove Dale's Conjecture, he had opened a brand new door for the entire world. This contribution was humongous!
However, Zhang Ye did not seem to be satisfied with this.
Shua, shua, shua. Zhang Ye was completely unaffected by others talking on their phones or exclaiming. He wheeled over a brand new whiteboard and continued writing.
A young French contestant gaped and said, "He’s still writing?"
A young British female contestant said, "It can still be calculated further?"
On the American side, a youth exclaimed, "Does...Does he not need to think? Why doesn't he stop at all? He...he is calculating too quickly!"
There was no pause at all!
No signs of him even thinking!
Zhang Ye was just moving his pen quickly. After he simplified Dale's Conjecture, he was still constantly attacking the problem, constantly approaching the proof for Dale's Conjecture!
"Eh, this formula!"
All the mathematicians were stunned!
"Ah, this is..."
All the mathematicians were stunned once again!
"The third modular form?"
All the mathematicians were stunned a third time!
"He mentally calculated an equation at the eleventh order?"
All the mathematicians...were constantly feeling stunned!
Looking at the Chinese youth's back, all the mathematicians present had a stunned idea rise up in their hearts—Holy shit, surely this person isn't solving Dale's Conjecture in one fell swoop?