In the office of the Dean of the School of Mathematics at Anhui University of Technology, Senior Brother Zheng sat upright in front of the Dean, trembling with fear.
"I heard you are very familiar with him?"
Senior Brother Zheng naturally knew who this "he" was. He organized his words and said, "Dean, actually, I and his roommate are from the same hometown, and that's how I got to know him. Later, he became interested in mathematics, and I tutored him in advanced mathematics. Last month, he came to me for advice on analytic number theory, and I found out that he had actually taught himself to such a level. Haha, it's incredible..."
"He came to ask you for advice on number theory?" The dean was a little confused. Could it be that this unknown young man in front of him was also a person who was pretending to be a pig and eating the tiger
Is our Anhui University of Technology going to produce outstanding people
Well, I can tell from your hairline that it’s not simple.
"Your name is Zheng Hui, right?"
"Yes, Dean, this is a student named Zheng Hui, a second-year graduate student studying financial mathematics under Professor Gao..."
"Okay, I have a set of test papers here. I am satisfied with your performance. The school will focus on training you. I will personally write a recommendation letter for you when you go to study for a doctorate..."
After that, the dean opened the drawer, took out a handwritten test paper, placed it in front of Zheng Hui, and said, "The questions are a bit difficult. Do as many as you can. You can look up information on Baidu, but there shouldn't be any answers. Oh, by the way, is he still in the library?"
Zheng Hui looked confused. Holding the test paper, he felt it was heavy and his throat was blocked.
Dean, can I not do it
"Dean... Dean, I will do it seriously... Otokogawa, he has been in the library recently and didn't even go home yesterday..."
The dean smiled and said with emotion: "This is a person who treats the library as his home! I haven't met such a bookworm for a long time. When I was in college, there was also someone in our department who treated the library as his home. Now he has been elected as an academician... You do the test paper here, I'll go and take a look!"
After watching the dean leave and close the door, Brother Zheng stared at the test paper in front of him in silence for three minutes, then took out his phone and said, "Oh my god, I really can't find it on Baidu!"
…
When the dean walked to the library under the scorching sun, Yi Xiaochuan was working hard to gain math experience points. The further he advanced, the more difficult it became to gain 1%. Math level 2 was already within sight, but it seemed to be endless.
As for proving another mathematical conjecture and drastically increasing experience points, this seems to be a way.
After Zhou's Conjecture, the problem of twin primes is a good choice, and then comes the "1+1" problem of Goldbach's Conjecture.
We all know that prime numbers are natural numbers with only two factors, and twin primes refer to prime number pairs with a difference of 2, that is, p and p+2 are both prime number pairs. For example, 3 and 5, 5 and 7, 11 and 13, 17 and 19, etc. As the number gets larger, the number of twin prime pairs that can be observed becomes smaller and smaller.
There are 8 pairs of twin prime numbers within 100, but only 2 pairs in the range of 501 to 600.
As the number of primes increases, the next prime becomes further and further away from the previous one, but a conjecture just as famous and important as the Goldbach conjecture states that there are infinitely many pairs of prime numbers that differ by only 2.
For example, these two prime numbers:
2003663613x2195000-1 and 2003663613x2195000+1.
There are infinitely many prime numbers whose difference is 2, which is the famous twin prime conjecture.
In 1966, Chinese mathematician Chen Jingrun achieved great results using the sieve method.
Chen Jingrun proved that there are infinite prime numbers p such that p+2 is either a prime number or the product of two prime numbers. This result is very similar to his result on the Goldbach conjecture.
But it still cannot solve the twin prime problem.
Fortunately, on May 14, 2013, Nature magazine reported that Mr. Zhang Yitang proved that "there are infinitely many pairs of prime numbers whose difference is less than 70 million." This research was immediately regarded as a major breakthrough in the ultimate number theory problem, the twin prime conjecture. Some even believed that its impact on the academic community would exceed that of Mr. Chen's "1+2" proof.
In his latest research, Mr. Zhang Yitang discovered that there are infinite pairs of prime numbers whose difference is less than 70 million, without relying on unproven inferences, thus making a major step forward on the important issue of the twin prime conjecture.
The twin prime conjecture can be weakened to "is it possible to find a positive number such that the difference between infinite pairs of prime numbers is less than this given positive number?" In the twin prime conjecture, this positive number is 2.
The positive number Zhang Yitang found was "70 million". Although there is a long distance from 70 million to 2, the report in Nature still called it an "important milestone".
As Dan Golston, a professor of number theory at San Jose State University, said: "The distance from 70 million to 2 (referring to the unfinished work in the conjecture) is negligible compared to the distance from infinity to 70 million (referring to Mr. Zhang Yitang's work)."
On May 13, 2013, Mr. Zhang Yitang gave a keynote speech at Harvard University in the United States, introducing his research progress. According to a report in Nature, if this result holds true, it is the first time that someone has formally proved that there are infinitely many pairs of prime numbers with a spacing less than a fixed value. In other words, Zhang will make a real "head start" in proving the twin prime conjecture. The world's top mathematics journal, Annals of Mathematics, accepted the article in which Zhang Yitang made the proof, and the reviewer commented that "his proof is correct and is a first-class mathematical work."
Mr. Zhang Yitang's paper was made public on the Internet on May 14th. Two weeks later, on May 28th, the constant dropped to 60 million.
Just two days later, on May 31, it dropped to 42 million.
Three days later, on June 2, the number reached 13 million.
The next day, 5 million.
June 5, 400,000.
In the "Polymath" project initiated by British mathematician Tim Goves and others, the twin prime problem has become a typical example of collaboration among mathematicians around the world using the Internet.
People continue to improve Mr. Zhang Yitang's proof, further narrowing the distance to finally solving the twin prime conjecture.
As of today, July 9, 2014, the difference between the prime pairs has been reduced to 246.
From 246 to 2, although the crown of twin prime numbers is within reach, the road is becoming more and more difficult, and it is unknown who will win the crown and when.
Yi Xiaochuan rubbed his eyebrows, gulped down a large glass of brown sugar water, and then put the question about twin prime numbers aside, deciding not to touch this problem until he reached level 2.
The study of mathematics requires not only brainpower and IQ, but more importantly, the spark of the collision of ideas. Only by seizing that moment of inspiration can we gain something.
Otherwise, even if you invest more energy, it will only be wishful thinking and will not achieve any effect.
Mathematics is not something that will be rewarded just by investing time and energy.
Although it took several days and consumed 64 energy points, Xiao Yi decisively gave up on proving the twin prime conjecture and was not prepared to conquer this huge mathematical mountain just yet.
Xiao Yi is very self-aware. He knows that the twin prime conjecture is beyond the ability to solve with his current knowledge.
If you don't make a decision when you should, you will suffer the consequences.
"Isn't it too early for you to study twin prime numbers?" A sudden voice scared Xiao Yi. After entering into a state of meditation, the hermit's five senses became a little dull.