The Science Fiction World of Xueba

Life inside the spaceship is boring but warm.

In addition to completing the daily observation tasks of the Centaurus Samsung through the telescope, Pang Xuelin spends the rest of his time doing research on the Riemann Hypothesis and planting things in the plant cabin with Mu Qingqing.

Because of the long-term hibernation of the crew, the plant cabin of the spacecraft will only be activated when the crew is awake.

Pang Xuelin and Mu Qingqing planted potatoes, cucumbers, eggplants, tomatoes, corn, rice and other crops in the plant cabin, and also raised a lot of mealworms as a source of animal protein.

This kind of life reminds Pang Xuelin of those days in the Martian world.

But there is no doubt that life on a spaceship is much more interesting than life on Mars.

Not only because of the diversity of food, but more importantly, I am accompanied by beautiful women.

The only thing that gave Pang Xuelin a headache was that in the process of researching Riemann's conjecture, he still failed to find any clues.

But this is not surprising.

From Hilbert's Twenty-Three Questions in 1900 to the Seven Great Problems of World Mathematics proposed by the Clay Institute in 2000.

Spanning a century, the Riemann Hypothesis still stands at the top of world mathematics.

The reason is of course not only because of the difficulty of Riemann's conjecture, but also because of the significance of Riemann's conjecture itself.

The first reason is that it is inextricably linked with other mathematical propositions.

According to statistics, there are more than a thousand mathematical propositions in today's mathematical literature that are based on the establishment of the Riemann Hypothesis (or its extended form).

This shows that once the Riemann Hypothesis and its extended form are proved, it will have a huge impact on mathematics, and all the more than a thousand mathematical propositions can be promoted to theorems.

Conversely, if the Riemann Hypothesis is overthrown, it is almost inevitable that more than a thousand mathematical propositions will be buried with them.

A mathematical conjecture is closely related to so many mathematical propositions, which is unique in the history of mathematics.

Second, the Riemann Hypothesis is closely related to the distribution of prime numbers in number theory.

Number theory is a very important traditional branch of mathematics.

Known as the "Queen of Mathematics" by the German mathematician Gauss.

The distribution of prime numbers is an extremely important traditional topic in number theory, and has always attracted the interest of many mathematicians.

This "noble pedigree" deeply rooted in tradition has also increased the status and importance of the Riemann Hypothesis in the minds of mathematicians to a certain extent.

Furthermore, there is another measure of the importance of a mathematical conjecture, that is, whether some results that contribute to other aspects of mathematics can be produced in the process of studying the conjecture.

Measured by this standard, the Riemann Hypothesis is also extremely important.

In fact, one of the early results achieved by mathematicians in the process of studying the Riemann Hypothesis led directly to the proof of an important proposition about the distribution of prime numbers - the prime number theorem.

Before the prime number theorem was proved, it was also an important conjecture with a history of more than 100 years.

Finally, the Riemann Hypothesis has surpassed the scope of mathematics in a sense.

In the early 1970s, it was discovered that some research related to the Riemann conjecture was significantly related to some very complex physical phenomena.

The reason for this association remains a mystery to this day.

But its existence itself undoubtedly further increases the importance of Riemann's conjecture.

Because of this, the Riemann conjecture has attracted countless mathematicians to climb since its birth more than a hundred years ago.

Although these efforts have not been completely successful so far, some initial results have been achieved in the process.

The first phased results appeared in 1896, thirty-seven years after the Riemann Hypothesis was published.

There is only one easy-to-prove result for the non-trivial zeros of the Riemann zeta function, that is, they are all distributed in a banded area.

The French mathematician Hadamard and the Belgian mathematician Poussin eliminated the boundary of the band area through independent means.

That is to say, the non-trivial zeros of the Riemann zeta function are only distributed in the interior of that band-shaped region, not including the boundary.

This achievement may seem trivial at first glance, since the boundary of a band is virtually zero in terms of area compared to its interior.

But it was a small step in the study of the Riemann conjecture, and a giant leap in the study of another mathematical conjecture, since it led directly to the proof of the latter.

That mathematical conjecture is now known as the prime number theorem, and it describes the large-scale distribution of prime numbers.

The prime number theorem has been unresolved for more than a hundred years since it was proposed. At that time, it was something that the mathematical community expected more than the Riemann conjecture.

Eighteen years later, in 1914, the Danish mathematician Bohr and the German mathematician Landau achieved another phased achievement, which was to prove that the non-trivial zeros of the Riemann ζ function tend to "tightly unite ” Around the critical line.

In mathematical language, this result is that no matter how narrow the band-shaped region containing the critical line contains almost all non-trivial zeros of the Riemann zeta function.

However, "tight unity" belongs to "close unity", this result is not enough to prove that any zero point is just on the critical line, so it is still far from the requirements of the Riemann Hypothesis.

But in that same year, another staged result appeared: the British mathematician Hardy finally put the "red flag" on the critical line-he proved that the Riemann ζ function has infinitely many non-trivial zeros on the critical line.

At first glance, this seems to be a very important result, because the non-trivial zero points of the Riemann ζ function are infinitely many, and Hardy proved that there are infinitely many zero points on the critical line. Literally, the two are exactly the same up.

It is a pity that "infinity" is a very delicate concept in mathematics, and they are also infinite, but they are not necessarily the same thing.

In 1921, Hardy cooperated with the British mathematician Littlewood to make a specific estimate of the "infinity" in his result seven years ago.

According to their specific estimates, what percentage of the "infinitely many non-trivial zeros" that have been proven to be on the critical line account for all the non-trivial zeros?

The answer, to their dismay: zero percent!

It was twenty-one years later, in 1942, that mathematicians advanced this percentage to a number greater than zero.

That year, the Norwegian mathematician Selberg finally proved that the percentage was greater than zero.

When Selberg made this achievement, the smoke of World War II was spreading across Europe, and the University of Oslo, where he was in Norway, had almost become an island, and even mathematics journals could not be delivered.

Perhaps because of this, Selberg can complete such a remarkable achievement.

However, although Selberg proved that the percentage is greater than zero, he did not give a specific value in the paper.

After Selberg, mathematicians began to study the specific value of this ratio, among which the achievements of the American mathematician Levenson were the most notable.

He proved that at least 34% of the zeros lie on the critical line.

Levinson achieved this result in 1974, when he was over sixty years old and was about to come to the end of his life (died in 1975), but he was still tenaciously engaged in mathematical research.

After Levenson, the advancement in this area became very slow, and several mathematicians could only make a fuss about the second digit of the percentage after exhausting their efforts, including Chinese mathematicians Lou Shituo and Yao Qi (they proved in 1980 that at least 35% of the zeros lie on the critical line).

It wasn't until 1989 that anyone shook the first digit of the percentage: American mathematician Conroy proved that at least 40% of the zeros lie on the critical line.

This is also one of the strongest results in the entire Riemann Hypothesis research. After that, the Riemann Hypothesis has hardly any progress in the mathematical community.

Two years passed unknowingly.

On this day, Pang Xuelin was floating in front of the porthole of the command and control cabin, some looking at the distant starry sky.

For two years, Pang Xuelin's research on Riemann's conjecture has been stagnant.

This made him a little helpless.

Mathematics is sometimes like this. No matter how clever you are, if you can't find a suitable breakthrough when facing a difficult problem, you will basically lose your eyes.

Now Pang Xuelin has entered this situation when facing the Riemann conjecture.

Pang Xuelin took a deep breath and turned his gaze to the upper right corner of the porthole.

On one side of the starry sky, a fireball the size of a tennis ball has appeared, and it is spraying hot flames into the universe. It is Alpha Centauri B.

On the other side, there is another bright star, whose brightness is many times higher than the brightest star Venus seen on the earth, that is Alpha Centauri A.

In the past two years of observations, Pang Xuelin has a relatively clear understanding of the situation of Alpha Centauri.

There is only one terrestrial planet in the Alpha Centauri A/B binary star system, which is about the size of Venus.

This planet revolves around the A/B binary star in a figure-eight shape, and its orbit is stable, but this planet is not in the habitable zone of the two stars, and through spectral analysis and observations in various bands, it is shown that this planet is basically not a mountain. There is an atmosphere, and the surface is densely covered with impact craters, which is basically meaningless to humans.

At this time, Pang Xuelin suddenly shrugged his nose, and a scent of fragrance came from behind him.

Immediately afterwards, a warm body embraced Pang Xuelin from behind.

"What's wrong?"

Pang Xuelin felt Mu Qingqing's delicate body tremble slightly, as if she was crying.

He quickly pulled the girl to him.

Mu Qingqing's eye circles were a little red, and she sobbed, "Alin, I just received a message from Brother Shuiwa that Brother Liu Qi... has left."

In the past two years, Pang Xuelin and Mu Qingqing have received messages from the solar system almost every week.

These messages were all estimated by the Earth after Ark 1 arrived at Alpha Centauri.

Naturally, it also included messages from Liu Qi and Shui Wa.

Pang Xuelin was stunned for a moment, his mind was a little dazed and he said, "Old Liu... died?"

Mu Qingqing nodded, and said: "It should have happened four years ago. Brother Liu's heart has never been very good. In addition, he is over eighty years old. It is said that he suddenly left while walking in the yard."

Pang Xuelin froze in place.

In the past two years, it was the greatest comfort for Pang Xuelin to receive messages from Liu Qi and Shui Wa from time to time.

There is always a trace of concern about the blue planet four light-years away.

Now another person worthy of concern is gone.

Although Pang Xuelin was mentally prepared, at this moment, he was still panicked.

In the train carriage many years ago, the fat man with a cheap smile still seems to be still in front of him.

In the blink of an eye, the Sri Lankan had passed away, and he was already far away.

Pang Xuelin took a deep breath and said, "Qingqing, let's hibernate too."

Mu Qingqing looked up at Pang Xuelin, nodded, and said, "Okay!"

...

Skimming Alpha Centauri, the next target of Ark One is Sirius.

Sirius, also known as Alpha Canis Majoris, is the brightest star in the whole sky except the sun. Although it is darker than Venus and Jupiter, it is brighter than Mars most of the time.

Sirius is a binary star system in which two white stars orbit each other with a distance of about 20 astronomical units (approximately the distance between the sun and Uranus), but the revolution period is only more than 50 years.

The brighter star (Sirius A) is an A1V main-sequence star with an estimated surface temperature of 9,940K.

Its companion star, Sirius B, has passed the process of being a main sequence star and has become a white dwarf.

Although Sirius B is now spectrally 10,000 times dimmer than Sirius A, it was once the more massive of the two stars.

The binary star system is estimated to be about 230 million years old.

Early in its life, it was conjectured that there were two blue-white stars orbiting each other in an ellipse with a period of 9.1 years.

Sirius A is so bright not only because of its inherently high luminosity, but also because it is very close to the sun, about 8.6 light-years away, and is one of the nearest stars.

The mass of Sirius A is about 2.1 times that of the sun. Astronomers used an optical interferometer to measure its radius, and estimated the angular diameter to be 5.936±0.016mas. Its star rotates at a relatively slow rate of 16 kilometers per second, so the star is not obviously oblate.

Celestial models indicate that Sirius A was formed in a molecular cloud collapse, and after 10 million years, its energy production has been completely provided by nuclear fusion. Its core is the troposphere and uses the carbon-nitrogen-oxygen cycle to generate energy.

Astronomers predict that Sirius A will run out of hydrogen stored in its core within a billion years of its formation, at which point it will go through a red giant phase before becoming a gentle white dwarf.

Sirius B is one of the most massive white dwarfs known. Its mass is almost equivalent to that of the sun (0.98 M☉), which is twice the average mass of white dwarfs (0.5-0.6 M☉), but so much matter is compressed to be as big as the earth.

Sirius B currently has a surface temperature of 25,200 K.

However, since there is no energy generated inside, the remaining heat will be emitted in the form of radiation, and Sirius B will eventually cool down gradually, which will take more than 2 billion years.

A star goes through the main sequence and red giant stages before it becomes a white dwarf.

Sirius B became a white dwarf when it was a little more than half its current age, about 120 million years ago.

As a main-sequence star, it is estimated to be 5 solar masses in mass and a B-type star.

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