Professor Lyndon Strauss had dug himself into a hole-and would have to fill it, tears and all
"Qi, your theory on the prime distribution of the Riemann zeta function is absolutely correct," several experts said with certainty.
Faltings and Linden Strauss are 200% certain. These two Phil Prize winners were technical advisors to Shen Qi's Riemann Hypothesis team. In particular, Faltings completed half of the work on the second expression of ζ(s).
Faltings said, "It takes a long time to fully digest a new theoretical system. You know, the Courant Institute a team of twenty people who specialize in the theory of prime distribution of Riemann zeta function, and their research may continue for several more years."
"That's true." Shen Qi felt much better after having coffee and chatting with the bigwigs.
Shen Qi suddenly thought of a suspicious point, "Charles, Grader, Elon, have you noticed that recently, almost all the people who claim to have proven Goldbach Conjecture are relatively unknown scholars, and even some are truck drivers, high school math teachers, and other math enthusiasts from the general public? I'm a little puzzled as to why the top number theorists haven't made any moves?"
Lyndon Strauss and Faltings exchanged a smile but remained silent.
The former is a top master specializing in number theory, while the latter specializes in Algebraic Geometry and is adept at using Algebraic Geometry methods to solve number theory problems.
Director Feierman revealed the truth. "Grader and Elon, they have already won the Fields Medal, they are the best mathematics professors at Princeton, and they have earned all the honors and respect. They don't need to rely on a Goldbach Conjecture to embellish their reputation."
Director Feierman looked at Shen Qi: "Especially after the publication of the Riemann zeta function prime distribution theory, anyone who proves Goldbach Conjecture cannot escape your shadow, Qi. Unless that person establishes a completely new system, or creates a new method that does not rely on the Riemann zeta function prime distribution theory."
Is it my fault?
Shen Qi shrugged and smiled, understanding.
Times are changing, and the landscape is quietly shifting.
Once Goldbach Conjecture's Goldbach Conjecture was downgraded after Shen Qi published the theory of prime distribution of the Riemann zeta function. While still difficult, it remains an isolated case and more like an intelligence test for advanced players.
Mid-to-low-level players are eager to prove their Goldbach Conjecture, but their skill level is limited.
Some high-level players are indifferent to fame and fortune, while others may have ideas about Goldbach Conjecture, but they do not want to live in Shen Qi's shadow; they are respectable people.
"So the final work on Goldbach Conjecture must be done by you, Qi, it's your duty. Princeton scholars always step up and take on everything when the world needs them," Director Feierman said.
"Alright, I'll clean up the mess." Shen Qi had no choice but to take on this task; he had to fill the hole he had dug himself.
"But I've been so busy lately, sigh." Shen Qi sighed and said, "The physics course has been delayed, I have to attend some events, and I also have to go on a business trip to Europe. My girlfriend isn't in good health; she's about to start her doctoral studies, and I have to take care of her."
Shen Qi revealed his difficulties in work and life, which immediately attracted the attention of the organization.
The organization helped Shen Qi overcome his difficulties. Professor Lyndon Strauss said, "I have received Ou's application. She is an excellent student. We were a team before. I happen to have a doctoral student position, and Ou can be my doctoral student."
Lyndon Strauss knew Ou Ye; he had been a technical consultant for Shen Qi Team, and Ou Ye was a team member.
"That's perfect, Elon." A major matter on Shen Qi's mind was resolved in the midst of laughter. The fact that Ou Ye could become the doctoral student of Lyndon Strauss, the Fields Medal winner specializing in number theory, was exactly what Shen Qi had hoped for.
"Your progress in physics is entirely up to you, Qi. The only thing the department can do is raise your travel standards to the highest level. Have a pleasant trip in Europe." Director Feierman offered Shen Qi some assistance within the bounds of the rules.
"Thank you." Shen Qi had no choice but to do it. The organization was doing its best to help him solve his difficulties, and all he had to do was provide the correct proof of Goldbach Conjecture.
At a high-end fashion party in New York at the end of last year, several top fashion designers sipped cocktails, embraced supermodels, chatted and laughed, and in just a few minutes, seemingly casually decided on this year's trending color - pastel tones.
During the Fall/Winter Fashion Weeks in February and March this year, a large number of minimalist designs for dresses, trousers, and skirts were showcased on the runway. This season's pastel color palette mainly consists of pink, light blue, light purple, light orange, and light green, highlighting the cute and gentle qualities of women.
In the luxury boutiques on Fifth Avenue in New York, pastel-colored women's clothing is currently the best-selling item. Shen Qi bought a pastel-orange CD dress as a gift for Ou Ye.
In many industries, trendsetting decisions are often made by a few top leaders in a flash of inspiration, making the decision casually and easily.
During a coffee break at the Princeton Mathematics Department, the bigwigs discussed the matter and decided that Shen Qi would be in charge of finishing up the Goldbach Conjecture to set things right. That's settled then, meeting adjourned.
Shen Qi took some time to reread his book, * History of Number Theory *, in search of inspiration.
The History of Number Theory states:
In a letter to Euler in 1742, Goldbach proposed a conjecture: any even number greater than 2 can be written as the sum of two prime numbers.
Goldbach was unable to prove this conjecture, so he turned to Euler, Euler equally helpless.
"For over two hundred years, the four main methods people have used to study Goldbach Conjecture are: almost prime numbers, exception sets, the three prime theorem for small variables, and almost Goldbach's problem."
"Among them, the study of near-prime numbers has yielded the best results, namely Mr. Chen Jingrun's 1+2."
"People have used Computer Science to confirm that Goldbach Conjecture holds true for even numbers up to 1000 trillion, but the conjecture itself has not yet been proven."
Based on the theory of prime distribution of the Riemann zeta function in "History of Number Theory", Shen Qi was quickly inspired and wrote down a function construction equation.
"The maximum possible result from studying the four main methods of Goldbach Conjecture is 1+2."
"Now it's the 21st century, and we need to use new methods for the 21st century."
"The fifth method, constructing equations using functions, that's it."
To perfect the fifth proof of the Goldbach Conjecture, Shen Qi needs to lay some groundwork.
Lemma 1: Wilson's Theorem
Lemma 2: Euler's formula e^±iθ=cosθ+isinθ
Lemma 3: Fundamental Theorem of Algebra
Lemma 4: Property 1 of the Gamma Function: Γ(x)Γ(1-x)=π/sinπx, 0<x<1
Lemma 5: Property 2 of the Gamma Function: The domain of the gamma function is x{γ∈Z|γ≤0}. Conversely, when x∈{γ∈Z|γ≤0}, Γ(x)=∞, or in other words, Γ(x) is undefined at this time.
Lemma 6: Under the usual addition and multiplication operations on complex numbers, the set of rational numbers Q is a field.
Lemma 7: Under the usual addition and multiplication operations on complex numbers, the set of all algebras over Q is a field.
Based on Lemma 7, Shen Qi casually spent 10 minutes proving Lemma 8.
Lemma 8: If a is an algebraic number and θ is a transcendental number, then the product of a and θ, aθ, must be a transcendental number.
With the groundwork laid by the eight lemmas and the framework established, Shen Qi naturally wrote the core content of the fifth proof of Goldbach Conjecture.
The core of this is a function construction equation: cos(1+Γ(x)/x+1+Γ(2n-x)/2n-x)π+isin(ρx+b)π=-1
The problem of Goldbach Conjecture 1+1, after Shen Qi's natural and ingenious handling, was ultimately transformed into solving the equation for constructing the above function.
Rigorous solution verification of this function's construction equation is equivalent to solving Goldbach Conjecture 1+1 problem.
Shen Qi spent three whole days doing this, staying indoors and temporarily forgetting about the progress of physics, important events in Europe, and the whereabouts of his two graduate students.
But I can't forget to call Ou Ye every day.
Three days later, Shen Qi finished the manuscript. The new fifth proof of Goldbach Conjecture had no problems, the function construction equation had a solution, and the Goldbach Conjecture 1+1 problem was solved by him.