The Science Fiction World of Xueba

The resupply mission came just right at the time when Pang Xuelin's research came to a standstill.

The advent of the supply ship made Pang Xuelin break away from the state of selflessness, otherwise the state would continue forever, which may not be a good thing for him.

In the next two months, Pang Xuelin built a new living cabin on the side of the energy cabin in accordance with the mission log sent by the Ares Plan Command. The new living cabin was connected to the energy cabin, and the energy cabin was planted with tomatoes. The cabins and potato planting cabins are connected to form a four-cabin structure.

Both the structural strength and service life of the new living module are much higher than the original habitat. At least when Pang Xuelin enters and exits the airlock chamber through the new living module, he no longer needs to worry about gas explosion.

After that, Pang Xuelin conducted a large-scale inspection of the habitat, replacing some of the more worn parts, such as the oxygenator system, water circulation system, air conditioning system, nickel-metal hydride battery, solar battery, and so on.

In order to facilitate Pang Xuelin's heavy physical labor, Ares Plan Command also specially equipped two sets of exoskeleton equipment in this supply.

One set for EVA tasks and one set for in-cabin tasks.

Sufficient material security and perfect living facilities have made Pang Xuelin's survival safety and quality of life in Mars further improved.

几个月 After several months of busy life, Ping Xuelin set his sights on ABC conjecture again.

多 With more than one year of intensive study and research, Pang Xuelin has a clearer understanding of Far Abelian geometry and the general theory of Teichmuller geometry.

He is almost certain that there is a big problem in the work of Mochizuki Shinichi.

But he did not think about finding out the details of the errors in the new paper of Mochizuki, and then set off a drool war. He had a higher goal.

He will take advantage of the rare opportunity to be undisturbed in the past few years, and on the basis of Far Abel's geometry, create a new theory to completely solve the ABC conjecture.

This is very difficult.

In the field of mathematics, it is easy to overcome a conjecture, but it is extremely difficult to create a system.

Anyone who can create a whole new mathematical system is almost a master-level figure of the founding school.

For example, Galois, who pioneered group theory. Although he died early at the age of 21, Galois is in the top five and even the top three in any of the greatest mathematician rankings ever.

For another example, Grothendieck, the founder of modern algebraic geometry, EGA, SGA, FGA, spreading thousands of pages, is an immortal masterpiece in the history of algebraic geometry, giving new energy to this ancient branch of algebraic geometry, which eventually led to his Student Pierre Deligne fully proved the Weil conjecture, which is considered to be one of the greatest achievements of pure mathematics in the 20th century.

Due to the leadership of Grothendieck, in the 1960s and 1970s, the Paris Institute of Advanced Studies was recognized as the center of world algebraic geometry research, for which he also won the Fields Prize in 1966.

Therefore, Pang Xuelin can say that he has set up a Mount Everest in front of himself. When can he climb this mountain, Pang Xuelin himself has no idea.

Even now, Pang Xuelin has not been able to find a suitable route into the mountains.

Xi Pang Xuelin can only think while living on Mars with peace of mind.

Of course, this kind of thinking is only intermittent. When there is inspiration, he will concentrate on thinking. When there is no inspiration, he will work and live step by step. When he is free, listen to music in the living room, watch movies, and relax himself. a bit.

Later Pang Xuelin discovered a better way of thinking.

That is to wear an EVA spacesuit, with the perch as the center and a radius of 100 meters, walking around the perch.

A person walking in this desolate and lonely world has a unique sense of loneliness, which makes it easier for his head to enter a state of emptying.

Especially at night, the surface of Mars is dark, with only the faint lights of the habitat and the starry sky overhead.

At a time when such a complex world is hidden in the dark, and only a little bit of starlight is left, Pang Xuelin can feel that in the number theory universe, prime numbers are like glittering stars, showing a complex mathematical configuration.

经常 He often walks for hours, until the EVA's carbon dioxide filter sounds an alarm, and then he will return to the habitat and return to the habitat.

Later, he learned well, and brought a spare carbon dioxide filter with him. One was used up, and the other was replaced at any time. When the inspiration was exhausted, he returned to the habitat.

Time passes day by day.

One month, two months ...

One year, two years ...

The cold Martian atmosphere sharpened Pang Xuelin's thinking. During the long ideological journey, the logical system of Far Abel's geometry gradually disappeared in Pang Xuelin's mind. Instead, it was a more messy, but closer to the essence of mathematical logic.

Xi Pang Xuelin's thinking became more and more clear, and the logic became more and more sharp.

Unconsciously, Pang Xuelin has lived on Mars for more than five years, and Ares Mission 4 has also started a new journey to Mars.

On the 1468th solar day, Ares Command sent a MAV five hundred meters away from the habitat. One month later, the Hermes spacecraft set off from the geosynchronous orbit space station. Task Team officially went to Mars. Their main task was to bring Pang Xuelin back to Earth safely.

On the 1689th solar day, there is more than a month before Ares IV arrives on Mars.

That night, Pang Xuelin got out of the cabin again and began another journey of thought.

"The absolute Galois group Gal (Qˉ / Q) can be applied to all smooth algebraic curves, because each smooth algebra curve corresponds to a polynomial whose coefficient is an algebraic number, and the absolute Galois group Gal (Qˉ / Q) as the symmetry of the algebraic number group……"

Uh ...

"The simplest non-trivial transformation in the absolute Galois group Gal (Qˉ / Q) is the complex conjugate. In the complex plane, the complex conjugate is a mirror symmetry along the real number axis, so it acts on the smooth algebra curve. It is also the mirror symmetry of a smooth algebraic curve. If the mirror symmetry of a smooth algebraic curve is still itself, according to the Belay theorem, a complex conjugate acting on the corresponding algebraic curve will definitely obtain the original algebraic curve, that is, all coefficients are real numbers If two smooth algebraic curves are mirror-symmetrical to each other, the coefficients of their corresponding algebraic curves must be conjugate to each other, which means that at least some coefficients are imaginary ~ www.readwn.com ~ In the smooth algebraic curve, there are many Combination invariants, they remain unchanged under the transformation of the absolute Galois group Gal (Qˉ / Q): the number of vertices, the vertices, the number of faces, the degree of faces, etc. In addition to these seemingly simple invariants, We can also assign a group to each smooth algebraic curve. This group can be called a single-valued group of smooth algebraic curves. These groups have more complex structures, Also remained unchanged in the transformed absolute Galois group Gal (Qˉ / Q) is. "

Uh ...

"Then, can the absolute Galois group Gal (Qˉ / Q) act on the Teichmuller level? All higher parts of the Teichmuller level can be combined from the first two levels. The first level provides Element, the second layer provides the relationship between the elements. The first two layers correspond to smooth algebraic curves, and the second layer corresponds to the elliptic curve widely used in number theory ... "

Uh ...

Secretly, Pang Xuelin seemed to have caught some wonderful clues.

He raised his head, the starry sky above his head reflected on the glass shield of the spacesuit helmet.

Prime numbers have ripples in the universe of number fields. Below the surface of complex number fields, a more intuitive connection between prime numbers begins to appear in Pang Xuelin's eyes.

"The smooth algebra curve itself has many symmetries. For these symmetry, it can be determined that it must come from the absolute Galois group Gal (Qˉ / Q). If you know this, it is equivalent to describing the absolute Galois group Gal (Qˉ / Q). itself!"

A breach appeared in the digitally constructed starry sky, and Pang Xuelin's eyes became brighter and brighter.

A flash of lightning struck his brain, illuminating the prime starry sky, which was hidden in the darkness, and gradually filled with regularity.