This supply mission came at the right time, just when Pang Xuelin's research came to a standstill.

The arrival of the supply spaceship allowed Pang Xuelin to get out of that state of selflessness, otherwise it might not be a good thing for him to continue that state.

In the next two months, Pang Xuelin built a new living cabin on the side of the energy cabin according to the mission log sent by the Ares Project Command, which was connected to the energy cabin, and the energy cabin was connected to the tomato planting cabin and potato planting cabin to form a four-compartment structure.

The new living cabin is much higher than the original perching cabin in terms of structural strength and service life, at least when Pang Xuelin enters and exits the airlock chamber through the new living cabin, he no longer has to worry about an air explosion.

After that, Pang Xuelin re-conducted a large-scale inspection of the perching cabin and replaced some parts that were more seriously worn, such as oxygenator system, water circulation system, air conditioning system, nickel-metal hydride battery pack, solar cell pack and so on.

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

One for EVA missions and one for in-cabin missions.

Sufficient material support and perfect living facilities have further improved the safety and quality of life of Pang Xuelin's survival on Mars.

After a busy few months, life has settled down again, and Pang Xuelin has also turned his attention back to the ABC conjecture.

In the past year or so, he has gained a clear understanding of Far Abelian geometry and the generalized Tehimüller geometry theory.

He was almost certain that Shinichi Mochizuki's job was very problematic.

But he didn't think about finding out the details of Shinichi Mochizuki's paper, and then starting a war of words, he had a higher goal.

He wanted to take advantage of the rare opportunity of no one to disturb him in the past few years to create a new theory on the basis of far-abelian geometry to completely solve the problem of the ABC conjecture.

This is very difficult.

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

But anyone who can create a new mathematical system is almost always a great master level figure of the founding sect.

For example, Galois, who pioneered group theory, although he died young at the age of 21, is in the top five or even top three in any standard for ranking the greatest mathematicians of all time.

For example, the founder of modern algebraic geometry, Grothendieck, EGA, SGA, FGA, is an immortal masterpiece in the history of algebraic geometry, which gave new vitality to the ancient branch of mathematics of algebraic geometry, and finally led to his student Pierre Deligne fully proving the Wey conjecture, which is considered one of the most significant achievements of pure mathematics in the 20th century.

Thanks to Grothendieck's leadership, in the sixties and seventies of the last century, the Institut Hautes Etudes in Paris was recognized as the world's center for the study of algebraic geometry, for which he was awarded the Fields Medal, the highest award in international mathematics, in 1966.

Therefore, Pang Xuelin can be said to have set up a Mount Everest in front of him, and when he can climb this mountain, Pang Xuelin himself has no bottom in his heart.

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

Pang Xuelin can only think while living in peace on Mars.

Of course, this kind of thinking is only intermittent, when he is inspired, he will concentrate on thinking, when he is not inspired, he will work and live step by step, and when he has free time, he will listen to music in the living cabin, watch movies, and let himself relax.

Later, Pang Xuelin found a better way of thinking.

That is, wearing an EVA spacesuit, with the perching capsule as the center of the circle and a radius of 100 meters, walking around the perching capsule.

Walking alone in this desolate and lonely world, there is a unique sense of loneliness, and it is easier to let one's head enter a state of emptiness.

Especially at night, the surface of Mars is pitch black, with only the faint lights of the perching chamber and the stars overhead.

At the moment when this complex world is hidden into darkness and only a little starlight remains, Pang Xuelin can feel that in the number theory universe, prime numbers are like shining stars, showing a complex mathematical configuration.

He often walked away for hours until the EVA's carbon dioxide filter sounded an alarm, and he would come back to his senses and return to the perching pod.

Later, he learned to be obedient, carrying a spare carbon dioxide filter with him, and when he ran out of one, he could replace it with another at any time, and return to the perch when his inspiration ran out.

Time passed.

One month, two months......

One year, two years......

The cold Martian atmosphere sharpened Pang Xuelin's thinking, and in the long journey of thought, the logical system of far-abelian geometry gradually dissipated in Pang Xuelin's mind, and was replaced by a more messy, but closer to the essence of mathematical logic.

Pang Xuelin's thinking is getting clearer and clearer, and his logic is becoming sharper and sharper.

Unknowingly, Pang Xuelin has been living on Mars for more than five years, and the Ares 4 mission team has also started a new journey to Mars.

On the 1468th solar day, the Ares program command dropped a MAV 500 meters away from the perching module, and a month later, the Hermes spacecraft set sail from the geosynchronous orbit space station, and the Ares 4 mission team on board officially went to Mars, and their main task was to bring Pang Xuelin back to Earth safely.

On the 1689th solar day, there is still more than a month before the Ares 4 mission team arrives on Mars.

That night, Pang Xuelin went out of the cabin again and started another journey of thought.

"The absolute Galois group Gal (Q ̄/Q) can act on all smooth algebraic curves, because each smooth algebraic curve corresponds to a polynomial whose coefficient is an algebraic number, and the absolute Galois group Gal (Q ̄/Q) acts as a symmetric group of algebraic numbers......"

……

"The simplest nontrivial transformation in the absolute Galohua group Gal (Q ̄/Q) is the complex conjugation, and in the complex plane, the complex conjugation is the mirror symmetry along the real number axis, so it acts on the smooth algebraic curve, and the mirror symmetry of the smooth algebraic curve is obtained. If the mirror symmetry of a smooth algebraic curve is its own, according to Beret's theorem, the complex conjugation must give the original algebraic curve when applied to the corresponding algebraic curve, that is, all coefficients are real numbers. If two smooth algebraic curves are mirror symmetrical to each other, the coefficients of the corresponding algebraic curves must be conjugated to each other, i.e., at least some of the coefficients are imaginary. ”

……

"In smooth algebraic curves, there are a number of combinatorial invariants that remain constant under the transformation of the absolute Galois group Gal (Q ̄/Q): the number of vertices, the degrees of vertices, the number of faces, the degrees of faces, and so on. In addition to these seemingly simple invariants, we can also assign a group to each smooth algebraic curve, which can be called a single-valued group of the smooth algebraic curve. These groups have a more complex structure, but they also remain unchanged under the transformation of the absolute Galois group Gal (Q ̄/Q). ”

……

"So, can the Absolute Galohua Group Gal (Q ̄/Q) act on the Tehimele level? All the higher parts of the Tehimele level can be combined from the first two levels, the first providing the elements, and the second providing the relationships between the elements. The first two layers correspond to smooth algebraic curves, and the second layer corresponds to elliptic curves, which are widely used in number theory......"

……

Faintly, Pang Xuelin seemed to have caught some kind of wonderful clue.

He looked up, and the starry sky above him was reflected on the glass shield of the spacesuit helmet.

Prime numbers ripple layer by layer in the universe of number domains, and under the surface of complex number domains, a more intuitive connection between prime numbers begins to appear in Pang Xuelin's eyes.

"The smooth algebraic curve itself has many symmetries for which it must come from the absolute Galois group Gal (Q ̄/Q), and if we can know this, it is equivalent to characterizing the absolute Galohua group Gal (Q ̄/Q) itself!"

There was a breach in the digitally constructed starry sky, and Pang Xuelin's eyes became brighter and brighter.

A bolt of lightning streaked through his brain, illuminating the prime-numbered starry sky that had been hidden in the darkness and had become more and more regular.