Pang Xuelin looked at the two white-haired old men on the screen blankly, the past thirty years ago is still as vivid as yesterday.

In this world, the only thing that is unstoppable is time, which is like a sharp blade, silently cutting through everything hard and soft, constantly moving forward, nothing can make the slightest bump in its movement, but it changes everything.

After a long time, Pang Xuelin let out a long sigh.

The Chinese Sun World is not the longest in the world he has ever been, nor is it the most dangerous, but it is the most unforgettable for him.

In this world, he gained friendship, family affection, and love, established his own career, and achieved unimaginable achievements for ordinary people, but he was separated from everyone in such a helpless way.

The world is impermanent, even a time and space walker like Pang Xuelin has times of helplessness.

Laugh at......

The airlock behind him suddenly opened.

Pang Xuelin turned his head and saw Mu Qingqing, who had woken up at some point, floating in.

"Arin!"

Seeing Pang Xuelin, Mu Qingqing looked a little excited, and with a slight effort, he came to Pang Xuelin's face in an instant.

"Qingqing!"

Pang Xuelin took his wife into his arms, and the two hugged each other for a long time.

After a long time, Pang Xuelin slowly separated Mu Qingqing.

Mu Qingqing has also received a lot of video messages in the past 30 years, including Mu Donglai, Feng Wanying, and Liu Qi, and the content is similar to what Pang Xuelin received.

It's just that girls are sensitive after all, and Mu Qingqing only finished reading less than half of it, so she threw herself into Pang Xuelin's arms and cried silently.

By the time Mu Qingqing came out of her depressed mood, it was already a few days later.

For explorers aboard the Ark spacecraft, the most important thing to make as few mistakes as possible on the rest of the journey is to be rational at all times and not let emotions dictate their actions.

After a few days of adjustment, Pang Xuelin and Mu Qingqing's lives began to become regular.

In addition to sleeping in a sleeping bag every day, the rest of the time, the two basically spent the rest of the time in non-stop busyness.

In the past thirty years, there have been a lot of failures on the Ark spacecraft, although the redundancy involved in the system is very high, but without the intervention of others, the failures will continue to appear, and one day the spacecraft will completely collapse.

Therefore, in the past few days, Pang Xuelin and Mu Qingqing have conducted an all-round inspection of the spacecraft's software and hardware systems.

Some parts that have been damaged or have problems can be directly replaced with spare parts, or the materials of the original parts will be restored and updated through 3D printing technology.

In addition, Pang Xuelin and Mu Qingqing also performed more than a dozen spacewalk missions to repair some worn nanomirror films.

Of course, there is also an essential mission, which is to detect Proxima Centauri through the telescopes and probes carried on the spacecraft.

Almost every day, Pang Xuelin and Mu Qingqing will make new discoveries.

Proxima Centauri's actual diameter is only one-seventh the diameter of the Sun, its mass is 150 times that of Jupiter, and its lifetime is several times that of the Sun, more than 80 billion years.

Nearly three-quarters of the stars in the Milky Way are red dwarfs.

For a long time, few astronomers devoted themselves to the scientific study of red dwarfs due to their size and brightness. For decades, scientists believed that there could be no intelligent life near red dwarfs.

The reason is simple: if a red dwarf is surrounded by planets, they will be too close to each other, and the planets will be completely "locked" by the red dwarf, just as the Moon is locked by the Earth. The planet will only face its "sun", the red dwarf, with only one side, while the other side will remain in perpetual darkness.

As a result, the planet will have an extremely harsh environment, with any atmospheric gas frozen on the night side and completely exposed to stellar rays on the day side.

It is inconceivable that life would survive in such a planetary environment, and as a result, red dwarfs are almost indisputably excluded from the list of targets for extraterrestrial life exploration.

Of course, it is also believed that nuclear fusion on red dwarfs is slow, which makes them very long-lived and can maintain a stable state for billions of years or more, which is beneficial for the development of life on the surrounding planets.

By comparison, the Sun will only support life on Earth for about another 5 billion years, after which it will expand into a red giant that will scorch and engulf the Earth.

It's just a pity that although Pang Xuelin and Mu Qingqing observed the existence of three planets around Proxima Centauri through telescopes, these three planets can basically be determined to have no life.

One of the planets closest to Proxima Centauri is only five million kilometers away from Proxima Centauri, and at such a distance, one side of the planet is basically completely locked by tidal forces.

The temperature of the sunny side of this planet exceeds 500 Kelvin, but the temperature of the shaded side is only a few tens of Kelvin, and this planet is as desolate as Mercury in the solar system, with no atmosphere, no water, and no life.

The second planet, on the other hand, is in the habitable zone of Proxima Centauri.

Although the planet has an atmosphere, the atmospheric pressure is only 3/1000 of the Earth's, and observations indicate that the new planet is less geologically active, with most of the surface landforms formed during the more active period of antiquity, with dense craters, volcanoes and canyons, and another topographical feature is the stark difference between the northern and southern hemispheres: the south is an old, crater-filled highland, and the north is a younger plain.

Obviously, such a world is also lifeless.

The third planet, an ice giant, is more than an astronomical unit away from Proxima Centauri, and nothing can be seen except for the observation of storms on the surface.

A month later, Ark-1 finally passed Proxima Centauri two astronomical units away.

Even at such a distance, Proxima Centauri was just a dark red fireball the size of a ping-pong ball in the eyes of the two, dyeing the dark night sky with a different kind of glow.

After passing Proxima Centauri, it will take another two years to reach α A/B Centauri.

During these days, life is much more boring.

The faults in the spacecraft that should be repaired have also been repaired, and the daily observation data is also lackluster, which can be automatically recorded by the spacecraft's computer and then sent to Earth through a huge antenna.

However, Pang Xuelin and Mu Qingqing are not disappointed, but they are enjoying their time very much.

After entering the Chinese Sun World for so many years, Pang Xuelin has focused most of his energy on making money and industrial development, and has not had much time to engage in scientific research.

After abandoning his main business for so many years, this time, Pang Xue finally had time to engage in academic research, and he felt like he was enjoying it.

As for Mu Qingqing, being able to accompany Pang Xuelin is the greatest satisfaction for her.

Get along with each other day and night, and occasionally do exercises that are good for physical and mental health and promote feelings, and both of them feel very satisfied.

That night (still retaining the 24-hour time system on the earth), after doing the exercise, Pang Xuelin took Mu Qingqing to the shower room on the spaceship to take a bath, Mu Qingqing fell asleep tiredly, but Pang Xuelin couldn't sleep for a while, so he simply came to his small study, spread out the manuscript and started his own research.

Because of the limited space and the mass that can be carried, Ark 1 did not carry much experimental equipment.

Unable to carry out large-scale scientific experiments, Pang Xuelin had to refocus his attention on the study of mathematical conjectures.

So far, Pang Xuelin has completed the proof work of BSD conjecture, ABC conjecture, twin prime conjecture, Polygnac conjecture, and Hodge conjecture.

There are not many heavyweight conjectures left, including the P and NP problems, the Young-Mills existence and mass gap, the existence and smoothness of the Navell-Stoke equation, the famous Riemann conjecture, and the Goldbach conjecture, which is said to be the most difficult mathematical conjecture to date.

The P and NP problem is actually a logical problem.

To put it simply, on a Saturday night, you attended a gala party.

Feeling cramped and uneasy, you wonder if there are people in this hall that you already know.

The host of the banquet suggests to you that you must know the lady Rose who is in the corner near the dessert plate.

It doesn't take a second for you to glance there and see that the host of the banquet is correct. However, without such a hint, you have to look around the hall and look at each one one one to see if there is anyone you know.

This represents a phenomenon that it often takes much more time to generate a solution to a problem than it does to validate a given solution.

This is an example of this general phenomenon.

Similarly, if someone tells you that a number 13717421 can be written as the product of two smaller numbers, you may not know whether you should trust him or not, but if he tells you that it can be broken down into 3607 times 3803, then you can easily verify that this is correct with a pocket calculator.

It has been found that all completely polynomial non-deterministic problems can be transformed into a class of logical operation problems called satisfying problems.

Since all possible answers to such problems can be calculated in polynomial time, people wonder if there is a deterministic algorithm that can directly calculate or search for the correct answer to this kind of problem in polynomial time.

This is the famous NP=P conjecture. Regardless of whether we are clever in writing a program, determining whether an answer can be quickly verified with internal knowledge or takes a lot of time to solve without such a hint is considered one of the most prominent problems in logic and computer science.

While the Young-Mills existential and mass gap, the laws of quantum physics are held for the world of elementary particles in the same way that Newton's laws of classical mechanics apply to the macroscopic world.

About half a century ago, Yang and Mills discovered that quantum physics revealed a remarkable relationship between elementary particle physics and the mathematics of geometric objects.

The predictions based on the Young-Mills equation have been confirmed in high-energy experiments carried out in laboratories around the world: Brockhaven, Stanford, the European Institute for Particle Physics, and Standing Waves.

Despite this, there is no known solution to their mathematically rigorous equation that describes both heavy particles.

In particular, the "mass gap" hypothesis, confirmed by most physicists and applied in their explanations of the invisibility of "quarks", has never been mathematically satisfactorily confirmed.

Progress on this issue requires the introduction of fundamentally new ideas, both physical and mathematical.

As for the existence and smoothness of the Navel-Stok equation, it is a problem in the field of fluid mechanics.

The undulating waves follow our boat as it winds its way through the lake, and the turbulent air currents follow the flight of our modern jets.

Mathematicians and physicists are convinced that both breezes and turbulence can be explained and predicted by understanding the solutions of the Navier-Stokes equations.

Although Ponzi geometry has enabled scientists to make substantial progress in solving systems of nonlinear partial differential equations, the mysteries hidden in the Navier-Stokes equations still require the joint efforts of mathematicians.

As for the Riemann conjecture, its significance is even less significant.

The Riemann conjecture was proposed in 1859 by Bonhard Riemann, a mathematician born in 1826 in the small town of Breslenz, then part of the Kingdom of Hanover.

In 1859, Riemann was elected a corresponding member of the Berlin Academy of Sciences.

In return for this high honor, he submitted a paper to the Academy of Sciences in Berlin entitled "On the number of prime numbers smaller than a given value".

This paper, which is only eight pages long, is the "birthplace" of the Riemann conjecture.

Riemann's paper examines a problem that mathematicians have long been interested in: the distribution of prime numbers.

Prime numbers are also known as prime numbers. A prime number is a natural number like 2, 3, 5, 7, 11, 13, 17, 19 that is greater than 1 and cannot be divisible by any positive integer other than 1 and itself.

These numbers are of great importance in the study of number theory, because all positive integers greater than 1 can be expressed as their sum.

In a sense, their place in number theory is similar to that of the atoms used to construct everything in the physical world.

The definitions of prime numbers are so simple that they can be taught in middle school or even elementary school classes, but their distribution is so mysterious that mathematicians have worked so hard to understand them thoroughly.

One of the major achievements of Riemann's paper is the discovery that the mystery of the distribution of prime numbers is completely contained in a special function, especially the series of special points that make the value of that function zero, have a decisive influence on the detailed laws of the distribution of prime numbers.

That function is now called the Riemann ζ function, and that particular set of points is called the nontrivial zero point of the Riemannian ζ function.

Interestingly, although the results of Riemann's article are significant, the text is extremely concise, even excessive, because it includes many "proofs omitted".

Unfortunately, "proof omitted" was supposed to omit obvious proofs, but this is not the case with Riemann's paper, some of which took decades of work by later mathematicians to complete, and some of which remain blank to this day.

However, Riemann's thesis, in addition to the many "proofs omitted", notably contains a proposition that he explicitly admits that he cannot prove, and that proposition is the Riemann conjecture.

The Riemann conjecture has been "born" for 160 years since its "birth" in 1859, during which time it has been like a majestic mountain, attracting countless mathematicians to climb it, but no one has been able to reach the top.

It has been calculated that there are more than 1,000 mathematical propositions in the mathematical literature today that presuppose the establishment of the Riemann hypothesis (or its generalized form). If the Riemann conjecture is proved, all those mathematical propositions can be elevated to theorems; Conversely, if the Riemann conjecture is disproved, at least some of those mathematical propositions will be fun.

It took Pang Xuelin a few days before deciding to focus on the Riemann conjecture as the next key research direction.

Of course, given the difficulty and importance of the Riemann conjecture, Pang Xuelin did not expect to be able to solve this conjecture smoothly.

In the process of studying the Riemann conjecture, he just hoped that in the process of studying the Riemann conjecture, he could deepen his understanding of the distribution of prime numbers, so as to further improve his theory of Ponzi geometry.

The stones of other mountains can be used to attack jade.

Perhaps the study of the Riemann hypothesis can lead to progress in other fields.