The path to reaching the truth is not unique.

This is also what mathematics itself tells Wang Qi.

In the eyes of the general public, space is flat. For them, Euclidean geometry is the naturally occurring geometry of this material world.

But in reality, there are no "straight lines" in nature. The traces of artificial craftsmanship in the concept of "straight line" are no less than those in "arc" and "hyperbola." And Euclidean geometry is not naturally occurring either. It merely simulates nature, simulating space based on human perception.

If there were an intelligent species whose primary sense was completely different from that of humans, their concepts in geometry would also be completely different from humans.

Take the Sea God Species for example. The geometry they first developed was not Euclidean geometry but Li's geometry, which has positive curvature. This is because they have no so-called "vision"; their main sense is similar to spiritual sense. On the other hand, their bodies are too large, which made them realize the curvature of the planet itself early on.

And Wang Qi recently learned that, in fact, there is another known species whose innate spatial concept is Luo's geometry, which has negative curvature.

That is the Dragon Clan.

Throughout history, the dialogue between the Human Clan and the Dragon Clan was very sparse. Even when humans and dragons occasionally got together due to shared interests, the first things they would do were to fight and exchange cultivation methods. The more eccentric ones would eat, drink, and experience the cultures of alien clans, occasionally trading some rare items. But sitting down together to discuss geometry... that was rare.

It was Wang Qi. In recent days, apart from methodically developing the Dataized Cultivation Method, he was preparing lessons for Gou Dabao at home. During this period, he discussed similar issues with anyone he could talk to—mainly Chen Youjia and Mi. If Yue Luo Liu Li weren't so bored, Wang Qi wouldn't have thought to talk with her.

However, through this conversation, Wang Qi realized the wonders of creation.

Today, the Dragon Clan is almost omnipotent, freed from the shackles of innate bloodlines, and has developed its cultivation system to its peak. But such a powerful race also had its weak periods.

More than a billion years ago in the Mesozoic era, the Dragon Clan was just an ordinary race in the sea. At that time, they didn't have innate spiritual senses like they do now. Like many reptiles, the ancient dragon clan had very weak eyesight. Plus, in the sea, there are too many factors affecting the propagation of light.

At that time, the future overlords of Shenzhou could only rely on sound. They communicated through sound, and also used it for locating prey.

Sound for the ancient Dragon Clan was equivalent to light for the Human Clan.

And the problem was that light always propagates in a straight line. But sound waves in seawater do not always travel in straight lines. At certain depths, the speed at which sound travels is directly proportional to the water pressure—in some sense, also directly proportional to the distance from the water surface. In other words, sound travels in a curve underwater.

If accurately describing that curve, it is "an arc with the center on the ocean surface."

In the world of the Dragon Clan, curvature is always negative.

In their concept, the sum of the interior angles of a triangle is always less than 180 degrees, there are no rectangles, and right-angled pentagons are the easiest concepts to understand.

Through hundreds of millions of years of evolution, the sonar which ancient dragons relied on for survival has transformed into a majestic dragon roar unlike any other marine creature. Yet some of the concepts from back then have remained unchanged.

For instance, in Dragon Clan Martial Arts, it's hard to find straightforward "stabbing" techniques.

For the Dragon Clan, Non-Euclidean Geometry is called the "Yuan Painting Method," while Euclidean Geometry is termed the "Highland Painting Method," and Li's Geometry is "Dome Painting Method."

Back in the day, Mathematics Lord joked, perhaps there are alien life forms viewing the world through the lens of Non-Euclidean Geometry. When he said this, he didn't realize there was indeed such a species on Shenzhou.

In this regard, whales, which also use sonar for location, do not have the same perspective as the Dragon Clan. This is because modern Demon Clan's cultivation methods are mostly borrowed from the Human Clan, with many concepts originating from humans. In terms of civilization, they are a part assimilated by human civilization.

Gou Dabao was once again deeply shocked by Wang Qi's discourse.

And then, came the crux of Wang Qi's narration.

"So, do you think the Human Clan, the Dragon Clan, and that large-bodied alien race I previously mentioned [referring to the Sea God Species] are unable to understand each other?"

Gou Dabao took a deep breath: "Not at all... As you've said, our Human Clan can already understand the so-called Luo's Geometry and Li's Geometry..."

"Actually, in mathematics, Luo's, Li's, and Euclidean are equivalent. It's like Divine Tao, Martial Arts, and Ghost Path. Despite the differences in cultivation methods, they are all cultivators whose ultimate goal is Longevity Sight," said Wang Qi. "This illustrates two points: First, the true 'geometry' transcends the conventional perception and thought of ordinary beings. Even the mighty Dragon Clan cannot solely perceive in this 'regulated' realm directly. Second, all paths lead to the same destination. Whether starting from zero curvature Euclidean geometry, positive curvature Li's geometry, or negative curvature Luo's geometry, we can eventually reach that ultimate realm, the true 'geometry'."

"Three thousand roads of the Great Dao, all paths lead to the same destination..." Gou Dabao felt strangely moved. He almost wanted to bow down and pay respect to Wang Qi.

At this moment, he no longer held any grudges against the Wanfa Sect's cultivation methods.

Wang Qi nodded slightly. He never believed science is the only truth in the world. However, the greatest advantage of science is that it's a path "one person's dao can be a dao for ten thousand people," allowing one to present their thoughts without reservation to others, fostering collaboration. Furthermore, it can continuously self-overturn and freely reconstruct, undergoing constant Nirvana. Therefore, science possesses indomitable and nearly eternal vitality.

Wang Qi was already quite satisfied with Gou Dabao's change in mindset.

He stood up and instructed Gou Dabao, saying: "Continue to cultivate the Yibi Calculation Scripture. Cultivate for another three days. After you have some understanding of the mathematical cultivation method, discard your current mana and start anew!"

"Understood." Gou Dabao nodded seriously. Seeing Wang Qi about to leave, he hurriedly called out: "Mr. Wang! Wait a moment! I still have questions to ask!"

Seeing Wang Qi stop, Gou Dabao respectfully performed a disciple's salute and asked: "Disciple heard that the Master of Calculation has produced a book which is essentially a Mathematics Scripture. And within this scripture, there are five hundred pages discussing 'one plus one'. I earnestly request, sir, that you explain this 'one plus one' to me."

Wang Qi frowned: "Given your current level, it seems a bit early to be reading that scripture."

Gou Dabao's level in mathematics was equivalent to middle school at best, definitely not reaching high school. And theoretical treatises are often challenging even for college students.

This is like asking a Foundation Establishment Stage cultivator to challenge a Nascent Soul Stage cultivator. Although there are unique individuals like Wang Qi in the Foundation Establishment Stage, a Nascent Soul overpowering a Foundation Establishment is the norm.

"The disciple does not dare to hope to fully understand, only to comprehend the principle within it."

Wang Qi thought for a moment; this should be Gou Dabao's first expression of interest in mathematics. It was genuinely difficult to refuse this request, so he said: "Alright, then let me explain it to you."

The two sat down again. Wang Qi started from Set Theory, explaining to Gou Dabao the definition that "when a set containing one element merges with another set containing one element, the resulting union always contains two elements," and expanded from there to cover many other concepts.

Gou Dabao became more confused: "One plus one equals two... one plus one equals two... There is actually so much content to discuss here..."

Wang Qi chuckled lightly: "That's how it is."

"It's truly amazing!"

But Wang Qi shook his head: "It's a pity that, for now, this is still just a castle in the air, only looking beautiful."

Gou Dabao was puzzled: "Why is that?"

"Because its foundation has not yet been proven," Wang Qi said with a heartful addendum: And it's impossible to prove.

Gou Dabao widened his eyes: "Why? Isn't this self-evident... Ah..."

Wang Qi had once told him, "Self-evident" is a taboo in Seeking Dao. Ultimately, everything must be expressed in words.

Gou Dabao looked as if his worldview was collapsing: "Are you saying, it's possible that one plus one could equal three? Or zero?"

"Logically, that possibility cannot be denied," Wang Qi said: "We have yet to prove that Set Theory is completely consistent, so logically, we can't assert that it's impossible to prove one plus one equals three..."

"How can that be..."

Wang Qi questioned back: "Can you find 'one' and 'two'?"

What is "one"? What is "two"?

This is also a simple yet complex problem. It's simple because even a non-speaking child can distinguish it. It's challenging because even a Master of Calculation like Pang Jialai would be perplexed by it.

Gou Dabao initially wrote a "1" on the ground, but Wang Qi casually drew a circle and said: "Now, I stipulate that this circle means 'one', 'single', 'a unit'."

Gou Dabao suddenly understood. He then held up a finger. Wang Qi still shook his head: "This is 'one finger', not 'one'."

What is "one"?

"One" is a concept, an objective fact that transcends human thought.

In the face of this Zen, Gou Dabao trembled. He said: "I beg the teacher to enlighten me."

"'Numbers' themselves exist inherently, and humans just extract them from nature. This doesn't just apply to integers; imaginary numbers and transcendental numbers are included as well. A typical imaginary number, the square root of two, is derived from a square. A typical transcendental number, pi, is derived from a circle." Wang Qi said calmly: "We never invented numbers. We discovered numbers. To understand numbers, we rely not on rational thinking but on an innate sense."

"Is this the essence of 'numbers'?"

Wang Qi nodded and continued: "Numbers themselves are products of nature; they have no need to conform to human concepts. Yet, from the beginning to the end, no one worries that 'one plus one equals three'. Why do you think that is?"