The morning lecture was very successful, with the one-hour presentation providing a detailed account of the proof process for Goldbach’s Conjecture and leaving ti for questions from the audience, which seed almost inconceivable.
In fact, most people in the venue felt it was quite normal.
Because it was simple.
Like navigating a complex maze, Zhao Yi found the correct path, guided others towards the direction, and while there were many twists and turns on the road, there were no direct obstructions or disputes.
Zhao Yi was explaining how to get out of the maze, not pondering how to solve it.
That was the reason for the short duration of the morning session.
The afternoon session was different.
Many top mathematicians ca for a more generalized proof of Goldbach’s Conjecture, which would help them better understand pri numbers.
Moreover, the generalized proof of Goldbach’s Conjecture was much more complex than the direct proof, and those who couldn’t understand the proof were mostly focused on the generalized thod.
Many people were interested in Zhao Yi’s proof approach.
Many top mathematicians believe that the significance of solving Goldbach’s Conjecture is not very important, unlike Riemann’s Conjecture, which has significant aning. The thods used in the proof process are more aningful than the proof itself.
At two o’clock in the afternoon.
The second lecture began on ti.
At this point, Zhao Yi felt no pressure at all, as the success of the first lecture had confird that he had solved Goldbach’s Conjecture.
Now the second proof thod was just icing on the cake.
Many people regarded the second proof thod more highly, but for Zhao Yi personally, it was still a breakthrough in Goldbach’s Conjecture, and his glory was confird, with no special significance.
Zhao Yi put his ntality completely at ease, making the presentation even smoother.
He began to explain in detail.
The second proof thod was a generalized proof, with pris and their combinations covering all even numbers except two.
In the proof process, he used the traditional sieve thod first.
All previous progress on Goldbach’s Conjecture required the sieve thod, including Chen Jingrun’s "1 2" proof, and the sieve thod itself was considered to have reached its limit, with no further progress possible.
Sieving is a simple thod to find pri numbers.
Arranging N natural numbers in sequence, you begin the sieve analysis: 1 is neither pri nor composite, so it’s crossed out; 2 is pri and retained, with all numbers divisible by 2 after it crossed out; the first number after 2 that’s not crossed out is 3, which is retained, with all numbers divisible by 3 after it crossed out; the sa is done for the next uncrossed number, 5, and so on.
By continuing this process, you eliminate all composite numbers not exceeding N and retain all pris not exceeding N.
Zhao Yi’s sieve thod was slightly different from the traditional one, as he allowed pris to pair up during the sieving process, and then conducted a detailed discussion.
When sieving numbers over a hundred, the complexity of the analysis increased.
He then used group theory.
Group theory is a mathematical thod, simply understood as a way to study, analyze, and discuss a group.
By combining the sieve thod and group theory, we can explore the expected number of pri pairs in even numbers.
Expectation refers to an estimation or range rather than an exact figure.
After continuous analysis and discussion, Zhao Yi produced an expectation curve for the number of pri pairs in even numbers.
This expectation curve is a function that increases with the increase of even numbers.
On stage.
Zhao Yi said seriously, "This is not a fixed number function; we can see that when many numbers are inserted, the results are incorrect."
"For example, if we insert 16, we get the number 2; if we insert 50, we get the number 5."
"Obviously, the results are incorrect."
"This is a fuzzy expectation curve, which ans that the result is an ideal value, or even an imagined value for how many pri pairs a number has."
"Most of the numbers in the range are close to the resulting values."
"Next, we will discuss this expectation function, analyzing its general direction and deviation problems."
Once the function was on the blackboard, there was no need to discuss the direction, as it was easy to prove that the trend of the function was upward, aning that the final result increased as the even numbers increased.
This was what Old Nash said in his interview, "The problem of how many pri pairs are contained in large even numbers."
The key, however, was the deviation range.
Next, Zhao Yi began a detailed discussion of the minimum deviation K range.
In the audience.
There were two people sitting in the corner, a young man with curly hair who was barely noticeable, and an older, slightly plump man next to him who, upon closer inspection by those in the know, would be quite astonishing.
That was Edward Witten.
Professor at the Institute for Advanced Study in Princeton, a renowned physicist and mathematician, Fields dal recipient, top expert in string theory and quantum field theory, and nad by Life magazine as the sixth most influential person after World War II.
Edward Witten, is so famous. He has completed the positive energy theorem proof in the General Theory of Relativity, supersymtry and Morse theory, topological quantum field theory, superstring compactification, mirror symtry, supersymtric gauge field theory, and conjectures on the existence of M Theory, etc.
His contributions to theoretical physics are countless.
What is most surprising is that he also won the top prize in mathematics, the Fields dal, for his mathematical shaping of string theory.
In this conference hall, Edward Witten is undoubtedly the top figure, but not many people know he is here.
His trip was low-key, and he ntioned to those who knew not to reveal the news.
Edward Witten’s seat was also in the corner, and he didn’t want too many people to know, but the people sitting next to him still glanced at him frequently as they recognized him.
Edward Witten didn’t care about the others, but listened attentively to the lecture on stage. The young man next to him was his student, Lars Selburg.
Selburg couldn’t help but turn his head and ask Edward Witten, "Professor, can he really prove it like that?"
Edward Witten’s eyes continued to watch the stage, he didn’t answer directly, but countered, "You didn’t fully understand that paper, did you?"
"I didn’t figure out so parts." Selburg pursed his lips and said.
Edward Witten nodded, "It’s still too complicated for you, listen carefully." He exclaid, "This is such a brilliant idea."
"Even you, Professor, are saying he’s a genius..." Selburg undoubtedly admired Edward Witten.
Edward Witten laughed, "He created a three-dinsional shock wave diagram and now has completed the proof of the Goldbach Conjecture. Although still very young, he is no worse than ."
After saying that, he added with a sigh, "He is really young."
"I ca this ti to discuss the wave diagram problem with him. Listening carefully to the lecture now may be very helpful for expanding your way of thinking."
"Yes, Professor."
Selburg beca serious, the two stopped talking and continued to listen to the lecture on stage.
Zhao Yi’s explanation reached a critical mont, the value of the lowest deviation K, which is the most important and ti-consuming content.
Those who did not understand the content of the paper felt very confused about the lecture, because Zhao Yi seed to be making one derivation after another without a clear goal.
This process lasted for more than half an hour.
A lot of people couldn’t keep up with the train of thought.
However, for top mathematicians, there was nothing big about it. As long as there were no controversial issues, normal derivation was easy to understand.
In the end, Zhao Yi made a substitution and ca to the conclusion: the minimum deviation K is less than or equal to the function result itself minus one.
After reaching this conclusion, Zhao Yi stopped speaking, and those who followed the thought process imdiately began clapping, while many others didn’t react yet.
After a long ti, applause filled the entire hall.
That conclusion is enough.
Zhao Yi’s generalized proof thod was to use sieve thod and group theory to create an expectation function of how many pri number pairs an even number N contains, and then analyze the deviation range of the function result Y’s accuracy.
The analysis mainly focused on the minimum deviation K of Y. The minimum deviation, also known as the lower limit deviation, is simply understood as the minimum value.
In the end, he ca to the conclusion that K is less than or equal to Y-1.
This result shows that pri numbers and their own values can be combined in pairs to cover all even numbers apart from two, or put directly, every even number has at least one pri number pair, which can be decomposed into the sum of two pri numbers.
Zhao Yi’s proof actually ca to two conclusions, one is to prove the Goldbach Conjecture, and the other is to prove that even numbers conform to the trend of having more pri number pairs with larger values.
The latter conclusion is vague, perhaps there is a large enough even number that contains only one pri number pair.
Of course.
This has nothing to do with Zhao Yi’s proof anymore.
The applause in the hall was long-lasting, and many people felt their arms were tired but didn’t put them down. The more deeply people understood the proof process, the more they marveled at the genius of the thought process.
"It really is, quite astonishing!"
"I’ve never thought there could be such a thod!"
"Actually, going deeper, you can also create a trend chart of pri number content, such as how many pri numbers are there in the range of hundreds or thousands of digits, which cannot be verified. Maybe you can calculate it according to the thod of making expectations."
"That’s another way to go..."
A lot of top mathematicians gained sothing from the report, and similar research ideas can indeed be expanded in many ways.
The applause gradually subsided.
Zhao Yi put down the water bottle in his hand, feeling exhausted, the nearly three-hour lecture without a pause had made his voice hoarse.
When the hall quieted down again, Zhao Yi took a deep breath and announced, "The proof ends here, and now I leave ten minutes for everyone to discuss."
"After ten minutes, we will enter the question-and-answer session."
After announcing the ten-minute delay, he hurried to sit in a chair nearby and gulped down water.
Laughing sounds erupted from the venue, and so people continued to clap their hands.
The applause continued for a long ti...
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