Xueba's life simulator

Chapter 274 The Most Difficult Math Problem
After staying up all night, Zhou Ming adjusted the schedule of his biological clock back to normal, and Zhou Ming didn't stay up like this again, but he spent a lot more time on the research on Hodge's conjecture every day than before.

Hodge's conjecture is a problem belonging to algebraic geometry. More precisely, it is about the algebraic topology of non-singular complex algebraic varieties. question.

Topology is an important branch of geometry developed in the [-]th century. It is a subject that studies the properties of geometric figures or spaces that can remain unchanged after continuously changing their shapes. The term "topology" was first used It appeared in Listing's paper "A Preliminary Study of Topology" in [-].

When studying topology, we only consider the positional relationship between objects without considering their shape and size. Therefore, in topology, the most important topological properties are connectivity and compactness.

The Hodge conjecture, known as the most difficult mathematical problem in mathematics, is also called a dark cloud in topology by some people.

Someone once said that there are two dark clouds in physics, one is in the wave theory of light, and the other is in the Maxwell-Boltzmann theory of energy sharing.

After using the life simulator many times before and gaining a lot of knowledge about the future field of life sciences, Zhou Ming once believed that there are also two dark clouds entrenched in the building of life sciences, one in neurobiology. , one flower is on aging.

Nowadays, Zhou Ming uses the life simulator more times than before, and acquires more knowledge than before, but the two dark clouds over the life sciences are still there, and Zhou Ming's views have not changed.

However, after so many simulations and the rapid development of life science-related technologies in the simulated world, the two dark clouds entrenched above the life sciences also faintly dissipated.

Although Zhou Ming's understanding of the two fields of neurobiology and aging is still not that deep, but compared to the current understanding of these two fields, it is not on the same level.

Zhou Ming believes that with his continuous use of the life simulator, the two dark clouds over the life sciences will one day completely dissipate.

Now, another dark cloud appeared over topology. It seems that the sky of the scientific community is already covered with dark clouds.

In fact, whether the sky in the scientific world is clouded or not is purely how people think. Different people have different views on this matter, and every field has some problems that cannot be solved by current science and technology, which is also normal.

Let’s go back to the Hodge conjecture. The Hodge conjecture is called the Hodge conjecture because it was proposed by a British scientist named William Valence Douglas Hodge around 80. It's almost [-] years since it came out.

Hodge's conjecture is different from the simple number theory problems such as the twin prime conjecture, Goldbach's conjecture and Riemann's conjecture. The simplicity here refers to the degree of understanding of ordinary people, not that it is easy to solve these conjectures.

The twin prime number conjecture and Goldbach's conjecture are the easiest to express, and they are also the simplest among the mathematical problems that Zhou Ming has solved and is currently solving. Anyone who has received compulsory education in the ninth grade can understand these two problems.

And because Goldbach's conjecture is easy to understand and famous, so most of the people who touch porcelain are also Goldbach's conjecture.

Although the Riemann conjecture is so easy to understand compared to the twin prime number conjecture and Goldbach conjecture, if someone explains it to them in detail, or if you specifically understand it, you will generally have a high school mathematics knowledge or a university non-mathematics conjecture. This level of professional undergraduate mathematics knowledge is also understandable.

Therefore, although Pongci Riemann's conjectures in Minke are not as many as Pengci Goldbach's conjectures, there are still some more or less.

But Hodge's conjecture is different. Hodge's conjecture is not to mention solving the problem, but to understand the problem itself. It may be difficult for those who are not born in mathematics.

This is also the reason why Pingci Hodge's conjecture is rarely seen in civil science. After all, you can't even understand the topic, let alone solve it.

Therefore, to explain Hodge's conjecture clearly, it is necessary to start from the beginning briefly and in popular language, that is, to start from the twentieth century.

During the twentieth century, mathematicians discovered powerful ways to study the shape of complex objects.

When they first started, their basic idea was that we could form the shape of a given object by gluing together simple geometric building blocks of increasing dimensions.

To describe it in words that are not very accurate, the meaning of this sentence is to say, can you find the corresponding equation for any shape?This is the original Hodge conjecture.

But after decades of development, in 8, an American mathematician named Michael Friedman discovered a strange figure, which he described as Call it a Friedman E[-] manifold.

The Friedman E8 manifold is a graph in four-dimensional space. Michael Friedman discovered that no matter how it changes, no algebraic equation can describe it.

Therefore, Hodge's conjecture becomes "under what conditions can a geometric body be transformed into a figure determined by an equation".

The trick with it is that you have to take into account every conceivable shape and approach.

It is precisely because the Hodge conjecture requires us to sort out the entire messy geometric world, and more importantly, to integrate geometry and equations, that people say that it, together with Fermat's last theorem and Riemann's hypothesis, has become the fusion of general relativity and quantum mechanics. m-theoretical structural geometry topology vectors and tools.

Now that Fermat's last theorem and Riemann's conjecture have been solved, if Hodge's conjecture is really solved, then it will definitely cause a sensation all over the world when Fermat's last theorem and Riemann's conjecture were solved before Much bigger.

Quantum mechanics has laid the foundation for particle physics, nuclear physics, condensed matter physics, etc., while general relativity has developed cosmology, astrophysics, and research on black holes and gravitational waves. Once the Hodge conjecture is really confirmed Solved, then this means that general relativity can be fused with quantum mechanics.

The day when the general theory of relativity and quantum mechanics merge, I am afraid that the grand unified theory of physics will not be far away.

It is very likely that I will see the emergence of a grand unified theory in my lifetime. Such a thing is much more important than just solving a Fermat's last theorem or a Riemann conjecture. I am afraid that scientists around the world, especially Scientists in the fields of physics and mathematics will focus on this matter.

This incident seems to be a bit confusing. How can the solution of a mathematical problem promote the development of physics?
In fact, although each science seems to be independent and irrelevant to each other, in fact, each seemingly irrelevant subject is inextricably linked.

What's more, mathematics is also the foundation of the sciences learned, and it is the foundation that must be built first when building a house.

Whether the house is built firmly depends on the foundation. If the foundation is not built well, no matter how beautiful the house you build is a castle in the sky, it will collapse sooner or later.

Moreover, the higher you build a house with a weak foundation, the easier it is to collapse.

Moreover, Hodge's conjecture is closely related to physics. Many researchers who study Hodge's conjecture are scholars in the field of mathematical physics who aim to study physical problems.

The so-called mathematical physics is a mathematical theory and mathematical method aimed at studying physical problems. It explores the mathematical model of physical phenomena, that is, seeks the mathematical description of physical phenomena, and studies the mathematical solutions to the physical problems whose models have been established. To interpret and predict physical phenomena, or to modify the original model based on physical facts.

As big as the movement of celestial bodies, as small as the movement of particles, which one does not require mathematics?
Not only physics, but biology, chemistry, materials science, etc., are inseparable from mathematics.

It is precisely because of the particularity of Hodge's conjecture that Zhou Ming was also very surprised when he discovered a method that might improve the artificial intelligence algorithm.

After all, although the foundation of the algorithm of artificial intelligence lies in mathematics, without the development and breakthrough of mathematics, there would be no present and future artificial intelligence technology, but in Zhou Ming's mind, the information about the future obtained from the simulated world when using the life simulator In the artificial intelligence knowledge, there is no mathematical knowledge related to Hodge's conjecture.

Therefore, what Zhou Ming discovered this time was also something he had never experienced in his previous simulations.

Every choice we make in life, whether it is a big choice concerning national affairs or a small choice about what to eat tomorrow morning, will determine our future direction. This is what Zhou Ming has used more than a dozen times It's a life simulator, but there are many different reasons for each experience.

The Nobel Prize Committee of the Royal Swedish Academy of Sciences officially announced to the outside world that during the few days when this year's Nobel Prize winners were awarded the Nobel Prize in Physiology or Medicine, Zhou Ming's life was still affected.

Anyway, this is a Nobel Prize anyway, and people's attention is still not small.

But because Zhou Ming was famous all over the world before he won this award, in the eyes of many people, it is not Zhou Ming's honor to be awarded the Nobel Prize, but Zhou Ming receiving the Nobel Prize. Award of honor.

Just like Grigory Perelman, who won the Fields Medal in [-] for solving the Poincaré conjecture, but did not go to accept the award.

Just because Grigory Perelman rejected the Fields Medal, one does not regret that he did not go to the International Congress of Mathematicians in Madrid that year to receive the award.

For Zhou Ming now, receiving these awards is indifferent, on the contrary, it will keep him busy for a few days, busy with many messages and calls from many people.

The reason why Zhou Ming accepted these awards was not because he was worried about offending people, but because he really felt that the bonuses of these awards were not for nothing.

After his life returned to calm and he focused his research on artificial intelligence and Hodge's conjecture, Zhou Ming's life was back to normal.

Time slipped away like this again. Zhou Ming, who had never conducted too in-depth research on Hodge's conjecture before, realized that if he really put all his thoughts into Based on Hodge's conjecture, relying on his own strength alone, it may take far more time than he previously expected.

Although he has gone through so many simulations, gained so much future knowledge, and acquired some experience and skills, Zhou Ming's intelligence has not actually improved much.

With the knowledge and some experience and skills gained from so many simulations, what Zhou Ming gained was the vast amount of knowledge and experience.

And what is intelligence?
Intelligence is the general spiritual ability of living beings. It is the ability of people to recognize and understand objective things and use knowledge and experience to solve problems. It includes memory, observation, imagination, thinking, and judgment.

Some people have such a strong memory that they can remember almost anything after watching it once or twice.

Some people have very keen observation skills, and they can quickly and accurately observe people or events that are difficult for others to notice.

Some people have very rich imaginations and can write or draw all kinds of unconstrained and fascinating works.

……

There can be many manifestations of outstanding intelligence, but Zhou Ming himself does not have these.

The knowledge he has learned from the world simulated by the life simulator is instilled in him by the life simulator in a way that he still cannot understand, and he will not forget it.

If Zhou Ming now recites an ancient prose by himself that he has never read in his mind, let alone read it two or three times, if he simply reads it, even if he reads it seven or eight times, it is impossible for Zhou Ming to recite it.

It was because Zhou Ming chose to keep his skills at the end of the previous simulation using a life simulator, and thus obtained a skill called [Mathematical Skills], which strengthened his talent in mathematics.

It is precisely because of [mathematical skills] that Zhou Ming was able to solve the Riemann conjecture with his own strength, instead of putting the results of other people's proofs in the simulated world on himself in the future like the twin prime number conjecture.

But even if he had acquired [Mathematical Skill] and improved Zhou Ming's mathematical talent, it would not be easy to quickly and completely solve Hodge's conjecture.

However, although Zhou Ming still spends a lot of time on Hodge's conjecture every day, he has already given the burden of solving Hodge's conjecture to his future self.

The reason why he spends time on this now is because he doesn't want to waste his mathematical talent for a long time, and even let the future of the real world be the same as the previous simulation, and mathematics will not be too big in the next few decades progress.

Secondly, it is naturally because I want to speed up the development of artificial intelligence and complete the task earlier so that I can use the life simulator to start the next simulation as soon as possible.

(End of this chapter)