Chapter 183 Pretending to be beta in front of two mentors
On the side, Witten raised his head and said: "I think the Weyl group mapping of algebraic varieties is more essential. It directly reverses the application of maximum torus, which I feel is quite amazing."
After a pause, Witten then added: "This is a brand new idea, and perhaps it can be expanded upon..."
Hearing this, Professor Deligne thought for a moment, his eyes suddenly lit up, and he quickly said: "Topology and algebraic manifolds of algebraic varieties!"
Witten smiled and said: "Yes, I should be more sensitive to this aspect than you. As you know, I am better at quantum field theory, string theory and related topology and geometry."
"If we start from this aspect and continue to extend it, it may become a new tool for solving the differential form problems caused by non-singular projective complex algebra varieties..."
Before Witten finished speaking, Deligne added: "For example, Hodge's conjecture."
On the side, Xu Chuan looked at the two instructors with a smile and sighed in his heart.
As expected of two of the top experts in mathematics, they noticed the two most critical and core points in this paper on the algebraic variety correlation method in field theory after just reading it once.
One is used to solve the irreducible decomposition problem of differential algebraic varieties, and the other is extended to solve the Hodge conjecture.
Even though the two tutors in front of me are already in their sixties or seventies, their sensitivity to mathematics is still terrifyingly high.
No detail, even something that occupies a small area, cannot escape their eyes.
After hearing Deligne's words, Witten put down the manuscript paper in his hand and said: "Indeed, it may have such potential, but it is not yet known whether this path can be taken."
After a pause, he looked at Xu Chuan and continued: "I wonder if you have thought about this?"
Xu Chuan grinned and said, "Of course. In fact, I've almost finished this job."
Hearing this, Deligne and Witten were stunned at the same time.
Almost finished, what does it mean?
"Have you solved the Hodge conjecture?" Witten couldn't help but asked tentatively. If that's what he meant, it would be too scary.
Xu Chuan shook his head and said: "That's not true. I just expanded and extended the idea of generation and used it to make a mathematical tool."
"I've been working on this these days. I haven't finished it all yet. I just made a core part and haven't had time to sort it out. Otherwise, I would have brought it here today."
Hearing that Hodge's conjecture had not been solved, Witten and Deligne breathed a sigh of relief at the same time.
If we say that their student defeated the Hodge conjecture in just over a month, that would be really shocking.
This is the Hodge conjecture, one of the seven millennium problems.
A millennium is a thousand years on the calendar. As the name suggests, it means a thousand years. The first millennium is 1,000 years and the second millennium is 2,000 years.
Of course, the seven millennium problems are not problems that will take humans a thousand years to solve.
They are seven mathematical conjectures announced on May 24, 2000. Because of the special year, they are called the seven millennium problems.
Although it does not mean that it will take a thousand years to solve, when the Clay Mathematics Institute drafted these seven mathematical problems with top professors such as Wiles and Connet, they prepared that it would take the mathematics community a whole century to solve them.
prepared.
It took a century or a hundred years to solve seven mathematical problems, which shows how difficult these seven mathematical conjectures are.
Facts have also proven the difficulty of these seven questions. Up to now, more than ten years have passed, and only Pang Jialai's conjecture has been solved.
This was only accomplished through the successive efforts of countless mathematicians after the 1930s.
From the Whitehead manifold and Dean's lemma in the 1930s, to the high-dimensional Poincare conjecture in the 1960s, which were successively proven, to the Ricci curvature flow in the 1970s and 1980s...
Countless people made great contributions to the Poincare Conjecture, and finally Perleman put a roof over this century's problem.
In addition to the Poincare conjecture, if there is some progress in several other millennium problems, it may be the BSD conjecture.
In 2014, Princeton University professor Manuel Bhargava, a Fields Medal winner, said that currently “one more of the seven Millennium Problems has been solved than I expected.”
Professor Bhargava has recently reported a number of results related to the Behe and Svenetorn-Dyer conjectures.
In one of the results, he said that he and his colleagues "proved that more than 66% of elliptic curves satisfy the Behe and Sveinton-Dyer conjectures."
This means that the Behe and Svenetorn-Dyer conjecture, that is, the progress of conquering the bsd conjecture is already more than half.
Of course, no one knows how long it will take to conquer the remaining half.
Maybe it can be completed in three years, maybe in five years, maybe in thirty or fifty years.
Even if you can look up to the top of the mountain, until you reach the top, no one can know how twists and turns the road ahead will be and whether there is an abyss that cannot be crossed.
Apart from this, there has not been much progress in several other millennium problems.
As for the Riemann Hypothesis, a super difficult problem that was proposed in the 19th century and spanned three centuries, there has been almost no movement.
Finding the answer to the Millennium Prize Puzzle is akin to trying to climb Mount Everest for the first time.
Along the way, there are many steps, which symbolize the progress made.
But the real question is: "Can you make it to base camp? And even if you can, you know you're still far from the summit."
As for problems such as the Behe and Svenetorn-Dyer conjectures and the Riemann conjecture, the current mathematical community is obviously still in Nepal, which is one of the starting countries for climbing Mount Everest.
This chapter is not over, please click on the next page to continue reading! Even if you can successfully reach the Everest base camp, mathematicians may still need additional "equipment" to reach the summit.
Just like the 'p-adic perfect space theory' established by Peter Schulz, using this tool, mathematicians can make a series of major breakthroughs in the Langlands program.
The same goes for solving the seven millennium problems. Perhaps each problem requires mathematicians to build one or even multiple new tools in order to remove it from the palace of mathematics.
.......
"You mean, you made a mathematical method along the lines of the Weyl group mapping of algebraic varieties and the twist of the maximum torus?"
After soothing his violently beating heart, Witten asked impatiently.
Although I have great faith in the mathematical ability of the student in front of me, no matter how you look at it, in more than a month, while solving the problem of irreducible decomposition of differential algebraic varieties, he also made a mathematical statement that may be used in Hodge's conjecture.
The method is also incredible.
Perhaps the problem of irreducible decompositions of differential algebraic varieties has the help of another Fields Medalist, but the mathematical methods used to solve the Hodge conjecture or the types of differential forms arising from non-singular projective complex algebraic varieties, this is
his own achievement.
Are all young people today so perverted?
In the past, Schulz developed a "nearly complete geometric theoretical method" during his Ph.D., and then there was his student who also made new mathematics during his Ph.D.
More importantly, the latter is younger than the former.
Hearing this, Deligne on the side also cast a concerned look. Xu Chuan nodded and said: "Some ideas and core have been written, but they have not been sorted out and perfected yet."
After finishing his words, Witten quickly asked: "Then how long will it take you to sort it out?"
Compared to Deligne, he is more concerned about whether the Hodge conjecture can be solved.
Because the Hodge conjecture is related to a series of physical problems such as general relativity, m-theory, and three-dimensional physics.
The Hodge conjecture is one of the basic carriers of the geometric topology of general relativity and m-theory structures, and its importance to physics is beyond doubt.
As a physicist, he has solved the positive energy theorem in general relativity, and is also the main core figure of m-theory and string theory. No one pays more attention to the research and attention on these two aspects than him.
Xu Chuan thought for a moment and said, "It may take about a month?"
After a pause, he added: "Now I just made a core, it has not been verified, and it is not a simple matter to continue to improve it."
Witten took two deep breaths, suppressed his violently beating heart and random thoughts, and said, "Can I see your manuscript?"
It is actually very presumptuous to ask others to see an unfinished and unpublished manuscript, even if it is facing one's own students.
But Witten didn't care about that much at the moment, he just wanted to see hope as soon as possible.
He proposed and perfected M theory, but he also struggled on this road for most of his life. Now that he saw a glimmer of hope, he couldn't wait.
Xu Chuan nodded and said, "Of course."
...
Witten made a request, and Deligne also followed him.
A group of three people arrived at Xu Chuan's dormitory and opened the door. The poor environment even left the two old men who walked into the dormitory with no place to stay.
In the dormitory, there were waste papers all over the floor, some crumpled into a ball, some scattered in the corner, and in the corner, there was a bag of domestic garbage that had not been cleared out.
Seeing this scene, Xu Chuan smiled awkwardly and said: "I have been organizing my thoughts these days, and I haven't had time to organize the dormitory yet."
However, neither Deligne nor Witten had any dislike.
This is where science was born. No matter how dirty or messy the surface is, it cannot hide the knowledge contained inside.
Entering the dormitory, Deligne leaned over and picked up a crumpled scrap manuscript from the ground.
After opening it, the black writing inside occupies about half of the manuscript paper.
Looking from top to bottom, you can completely see the fluctuations of the writer's thoughts. From the smooth writing at the beginning without any correction, to the discontinuous writing at the end, with revisions and corrections, and the last one was written by the author before it was finished.
The formula with the horizontal line completely crossed out shows the author's struggle on this road.
Deligne didn't care that it was a useless manuscript. After smoothing the paper with his palm, he read it with relish.
As for Witten, he was not very interested in the messy manuscript papers on the ground, or he was more interested in the complete method, so when he entered the door, his eyes fell on the stack of papers on the desk.
On thick printing paper.
It records methods for solving differential formal type problems arising from non-singular projective complex algebraic varieties.
.......
The two top bosses were sitting in the dormitory. Xu Chuan could no longer remain indifferent and started to tidy up the dormitory while Deligne and Witten were browsing the manuscripts.
The manuscript paper on the ground, whether it was useful or useless, even if it was crumpled into a ball, was temporarily picked up by him and put aside.
These things, even if they are completely discarded and useless, still have extremely high collection value. At least for him, this is the case.
After all, these things witness the complete process of the birth of a new mathematics.
If this mathematical method can be used to solve the Hodge conjecture, their value will be enhanced to an unparalleled level. After all, knowledge is the most precious wealth at all times.
"Xuchuan, where is the manuscript that Professor Mirzakhani left for you?"
After reading the scrap manuscript in his hand, Professor Deligne put it on his desk and asked Xu Chuan.
Although he was also interested in Xu Chuan's research results, Witten had already occupied the manuscript and was flipping through it. Instead of leaning over to read it together, it would be better to take a look at Professor Mirzakhani's manuscript first.
The only female Fields Medal winner in history left behind something before her death that is fascinating to any mathematician.
"Wait a mininute."
Xu Chuan responded. After sorting the manuscript papers in his hands in order, he found the original manuscript from the bookcase and handed it to the mathematics tutor.
Looking at the manuscript that was completely preserved in the storage bag, Deligne showed a hint of approval in his eyes.
Respecting the achievements of others is a necessary scientific research spirit.
...
In dormitory No. 306, Deligne and Witten were each immersed in the manuscripts in their hands.
Time passed bit by bit, until the sun set over the mountain and the golden afterglow shone through the glass windows, the two elders woke up one after another.
"As expected of Professor Mirzakhani, the ideas he left behind are amazing."
Looking at the golden afterglow falling on him through the glass window, Professor Deligne pushed up the glasses on the bridge of his nose with one hand and pinched the depth of the root of his nose.
From this manuscript, he saw the initial starting point of the problem of 'irreducible decomposition of differential algebraic varieties', and also saw the female Fields Medal winner's insights on Riemannian geometry, differential geometry, Weyl groups, and algebraic groups.
.
Deligne believes that this is not all of Professor Mirzakhani, and it may not even be one percent.
But it is regrettable that such an outstanding mathematician’s life ended this year.
Sighing slightly in his heart, Deligne looked up at Witten, wanting to see his evaluation of the mathematical method in his hand.