Black Technology Live Room

"Wow...wow..."

Zhaicheng Space Center, the lounge bedroom on the top floor.

Zhang Zhai sat cross-legged on the ground, flipping the book lightly.

The name of the book is "The Millennium Problem and the Three Modern Mathematical Problems"

Zhang Zhai flipped through the pages. This book recorded the introduction and research progress of the Millennium Prize puzzle (the world's seven major mathematical puzzles) and the world's three major mathematical puzzles, including ten mathematical conjectures.

The seven major mathematical puzzles are the most famous mathematical puzzles offering a reward of one million dollars for each question.

Inclusion: NP-complete problems, Hodge conjecture, Poincaré conjecture, Riemann hypothesis, Yang-Mills existence and mass gap, Navel-Stoke equation, BSD conjecture.

Among them, the Poincaré conjecture has been solved by the Russian mathematician Grigory Perelman.

The mathematician who proved the Poincaré conjecture is a very special person. He was the first person to reject the Fields Medal, the highest award in mathematics, and also rejected the $1 million reward offered by the Clay Institute of Mathematics.

Zhang Zhai looked at this record and smiled, "This is a very pure mathematician...well, much more pure than me."

The reason why Zhang Zhai wants to read this book is because...he wants to do something and get enough popularity points.

So he opened the book, and he only needed to solve any one of these ten mathematical problems to cause a great sensation.

"One of the seven major mathematical problems has been proved, and there are six remaining. Two of the three major modern mathematical problems have been proved, and one is left... No, strictly speaking, only one of the three major modern mathematical problems has been proved. "

Zhang Zhai continued to look through, and he looked very carefully, thinking while reading, and after thinking about which problem to choose for research.

The world's three major modern mathematical problems, including: Fermat's conjecture, four-color conjecture and Goldbach's conjecture.

Among them, the Fermat conjecture has been proved by the British mathematician Andrew Wiles in 1994, and the Fermat conjecture has become Fermat's last theorem, which is beyond doubt.

But the four-color conjecture can only be regarded as barely proven. It was completed by American mathematicians Appel and Haken with the help of computers in 1976, and it is called the four-color theorem.

Borrowing the computer's exhaustive method to prove, although from the perspective of probability and statistics, it can already be proved, but there is still no specific way of proof.

Goldbach's conjecture is the most famous conjecture among the three major mathematical problems. In 1996, Huaguo mathematician Chen Jingrun advanced it to 1+2. This is also the best result so far.

The final 1+1 has never been proved, because the previous method of proving 1+2 is not applicable to 1+1 at all, and a new method needs to be developed, so it still plagues countless mathematicians to this day.

"Seven difficult problems or eight... which one to choose as a breakthrough?" Zhang Di turned the whole book over and over, muttering in his mouth.

"The Riemann hypothesis, or the NP problem, or the Goldbach conjecture?"

"These three questions are relatively well-known, because the questions are simple and easy to understand, and everyone thinks they can answer them..." Zhang Zhai thinks that every year there are countless people who claim that they have proved the np problem or Goldbach Guess, I just want to laugh.

"Anyone can understand the title, but the connotation is extremely profound..." Zhang Zhai moved his eyes on these three questions, and finally locked on Goldbach's conjecture.

"Goldbach's conjecture has the deepest connection with Huaguo, and the best result so far is also proposed by Huaguo mathematician Mr. Chen Jingrun." Zhang Zhai said in a low voice.

"It doesn't make sense to finally prove that Goldbach's conjecture is not from Huaguo."

"Then let's start with Goldbach's conjecture..."

Zhang Zhai's eyes became firm, and he said in a deep voice, "A1, help me collect all the proofs of Goldbach's conjecture so far, as well as relevant mathematical materials."

"Okay, Father." A1 said.

"Father, the relevant information has been displayed on the holographic screen."

Zhang Di raised his head and looked at the holographic screen. Suddenly, Zhang Di looked at A1, "A1, do you have a way to prove Goldbach's conjecture?"

"Father, I can only say that after deduction, Goldbach's conjecture is correct, but... in a short time, I can't come up with a way to prove it." A1 replied.

Hearing this, Zhang Zhai shook his head and began to look at the information.

The so-called Goldbach's conjecture is very simple: any even number greater than 2 can be written as the sum of two prime numbers.

But it is such a simple topic that has caused countless mathematicians to rack their brains and spend their entire lives.

The so-called proof of 1+2 and 1+1 is actually to prove Goldbach's conjecture from the direction of almost prime numbers.

An almost prime number is a positive integer with a small number of prime factors. Assume that N is an even number. Although it cannot be proved that N is the sum of two prime numbers (prime numbers), it is enough to prove that it can be written as the sum of two almost prime numbers, that is, N=A+B.

Among them, the number of prime factors (prime factors) of A and B is not too many, for example, the number of prime factors does not exceed 10. Use "a+b" to denote the following proposition:

Every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b respectively. Obviously, Goldbach's conjecture can be written as "1+1"

Therefore, it is only necessary to prove 1+1 to prove Goldbach's conjecture.

"The question is very simple, and the idea of ​​the proof is very clear. Using the sieve method is enough to prove 1+2...but...1+1 is not applicable to any previous method. It seems...I have to be busy." Zhang Zhai Smile to.

"Spider, get me a stack of manuscript paper...forget it, just bring a box of A4 paper, and two boxes of gel pens and two boxes of marker pens!" Zhang Zhai shouted towards the door.

The spider standing at the door of the lounge hesitated for a moment when he heard the words, he suspected that he had heard it wrong.

"Is it a box of A4 paper? Mr. Zhang?"

"That's right! Speed ​​up!"

"Okay, Mr. Zhang!"

...

Five minutes later, the spider carried a box of A4 paper, two boxes of gel pens and two boxes of markers.

After the spider turned around and went out, Zhang Zhai excitedly pulled out a pen, and began to calculate with a stack of manuscript paper.

Goldbach's conjecture is definitely a super big problem, it can be said to be a bright pearl in the palace of mathematics.

But it is precisely because it is difficult enough that Zhang Zhai is so excited! Even to the point of excitement!

He doesn't believe that there are any problems in this world that he can't solve at all!

"A1! Turn off the holographic screen." Zhang Di said.

"Okay, Father!"

Zhang Zhai took two deep breaths to dispel the distracting thoughts in his mind, and then solemnly wrote down the topic of Goldbach's conjecture on the first page of manuscript paper.

Then... Zhang Zhai did not choose to directly face the ultimate proof step of 1+1, but chose to start with 9+9 and retrace the path traveled by his predecessors.

"Wow...wow..."

Without thinking for a long time, Zhang Zhai began to prove.

One page, two pages, three pages... When the fifth page of manuscript paper was moved from the top.

9+9 proof completed...

Then... 7+7...6+6...

Zhang Zhai's brushstrokes never stopped, and these relatively simple proof processes did not stop him for even a second.

Then...5+7...4+9...

When the proof reached this step, suddenly... Zhang Zhai's smooth proof was interrupted.

Zhang Zhai held the nib of the pen in his hand and hovered in the air without falling down.

The nib of the pen trembled slightly, Zhang Zhai frowned, staring at the page, motionless.

Time passed by one minute and one second...it was not until three minutes later... Zhang Zhai's stagnant body finally resumed his movements. He once again performed... 5+5 with extremely fast speed and extremely smooth strokes. Perfect proof.

...