The Dead End of the Divide Between Two Schools?

"Mathematics... incomplete?" Upon hearing those words, Bo Xiaoya's first reaction was—Are you fucking kidding me?

Mathematics could be incomplete?

How could mathematics possibly be incomplete?

Mathematics had to be complete!

Even those whose views on mathematics were utterly different from the Arithmetic Sovereign's agreed with his famous words: "We shall know; we must know."

To the Arithmetic Sovereign and his followers, mathematics had to be complete, and it also had to be consistent. In the eyes of these cultivators, the essence of mathematics was "form," assembled from mathematical symbols. Every statement composed of such symbols could be judged "true" or "false," and every true statement could certainly be proven through another combination of symbols. Furthermore, a statement could only ever be judged "true" or "false." There could be no such thing as "both true and false," or "neither true nor false."

Completeness, consistency, and decidability were the bedrock of the Arithmetic Sovereign's and the Gottingen Sect's beliefs.

And for ordinary Mathematicians, while this part was inevitable, they simply instinctively felt that mathematics had to be complete.

Those cultivators who exhaustively studied the laws governing the flow of matter had repeatedly discovered in astonishment that whenever they launched an assault upon some field, the Mathematicians of the Myriad Dharma Sect had already prepared the "tools for seeking the Dao"—mathematical formulas—for them. From the earliest Primordial Force Sect to the Returning to One Alliance, and now the Misty Palace, these sects that investigated heaven and earth through empirical evidence had continuously supplied the Myriad Dharma Sect with more and more formulas—exquisite formulas drawn from all things under heaven, where the Dao followed nature. These formulas, in turn, nourished the development of mathematics.

In the eyes of Myriad Dharma Sect cultivators, everything in the universe moved with utmost obedience along the laws of