Chapter Nineteen: Registered Disciples

A few days later, Fei Qian truly did not expect that Li Ru would recommend him to Cai Yong.

Speaking of Cai Yong, he was truly a remarkable figure among scholars. Simply the aura surrounding him was enough to dazzle any ordinary person.

A great literary master, historian, musician, painter, and calligrapher of the Eastern Han—such an array of talents in one person made one wonder if Cai Yong was even an ordinary human.

In literature, Cai Yong was most famous for leaving behind the "Xiping Stone Classics" for posterity.

During the reign of Emperor Ling, Cai Yong noticed that many Confucian classics contained numerous forced interpretations and textual errors. To prevent misleading future scholars, he petitioned to have these texts corrected. After receiving imperial approval, Cai Yong personally inscribed the corrected texts on stone tablets, which were then carved and erected outside the Taixue (Imperial Academy). The stele consisted of forty-six slabs, collectively known as the "Hongdu Stone Classics," or "Xiping Stone Classics." It quickly became a model text for scholars to reference and correct their writings. The area outside the academy was bustling with people daily—thousands of carriages blocked the roads as scholars came to study and copy the inscriptions.

In music, besides the well-known tale of the Jiaowei qin, Cai Yong also composed the "Five Variations of Cai," which included "Spring Outing," "Clear Water," "Quiet Reflection," "Sitting in Sorrow," and "Autumn Longing." These, along with the "Four Variations of Ji" composed by another musical master, Ji Kang—namely "Long Qing," "Short Qing," "Long Ce," and "Short Ce"—were collectively known as the "Nine Variations of the Qin." After the Han dynasty, these pieces even became part of the imperial examination standards for selecting scholars.

Of course, later generations also took interest in Cai Yong because of his daughters, Cai Yan and Cai Zhaoji, but that is a story for another time.

So when Li Ru informed Fei Qian that he had recommended him to Cai Yong, Fei Qian could hardly believe it. Even as he entered the Cai residence, he felt as if still in a dream.

Cai Yong sat at the head of the hall, somewhat uncertain about how to proceed. He had not accepted disciples for many years—for one, his reputation had grown, and taking on students required caution; two, the troubles his daughters had faced weighed heavily on him; and three, his advancing age left him little energy for teaching. He had simply shut his doors to new disciples. Now, however, Li Ru had somehow obtained a token from Cai Yong’s past correspondence with a friend, which was sent back with the condition that Fei Qian be accepted as a disciple. This left Cai Yong in a delicate predicament.

When Li Ru delivered the token, he spoke casually but clearly, explaining that Fei Qian’s father had once helped him. Now that Fei Qian showed a desire to study, Li Ru had used his connections to retrieve Cai Yong’s token. Whether to accept Fei Qian was entirely Cai Yong’s decision; Li Ru had done his part and held no regrets.

The crucial phrase was “with a clear conscience.” Li Ru’s conscience was clear, but if Cai Yong were to refuse, it would contradict his own promise of “bringing this token and granting whatever is within my power without refusal.” How could he then claim to have a clear conscience? If news spread that Cai Yong had gone back on his word, his reputation would be irreparably damaged. What kind of man would he be then?

Cai Yong looked at the young man before him—tall and slender, with a reserved demeanor and refined features. He was certainly presentable enough. Yet regardless of whether he accepted him, Cai Yong felt a pang of unease. But since the young man was here, he decided to probe first.

“What studies do you pursue? What are you skilled at?”

“I have a rough grasp of the Six Classics but prefer mathematics,” Fei Qian replied humbly. Thanks to his predecessor Fei Qian, he had retained some knowledge of the Six Classics, though he couldn’t claim deep understanding of their subtleties. Mathematics, however, was different. After all, future generations had gone through high school and university—no matter how formidable the Eastern Han was, had they even encountered matrices, calculus, probability theory, or operations research?

He wanted to add that he even knew some “washing in the gutters,” “Bayesian inference,” and “arithmetic mean,” but such concepts were utterly useless in the Eastern Han.

Cai Yong was quite surprised—mathematics was considered one of the most advanced fields in the Eastern Han, not something ordinary people could master. The "Zhoubi Suanjing" had been compiled only two or three centuries prior and was full of obscure and cryptic language. Without a strong imagination and deductive ability, even reading the text would leave one baffled. For instance, the "Zhoubi Suanjing" described the Pythagorean theorem: “To find the hypotenuse, treat the vertical as the ‘leg,’ the horizontal as the ‘base,’ multiply each by itself, add the two, then extract the square root to obtain the hypotenuse.” Anyone who merely glanced without understanding was hopeless in mathematics.

Another text, somewhat more accessible though still challenging, was the famous "Nine Chapters on the Mathematical Art." However, at this time, it had yet to be organized and annotated by Liu Hui and remained quite disorganized. Though it addressed practical problems, it was still not an easy read.

Cai Yong’s interest was piqued. Since few in this era studied such matters, finding a kindred spirit was rare. He casually presented a problem from the Nine Chapters to test Fei Qian:

“There is a square city of unknown size. From the north gate, a tree stands twenty steps away. From the south gate, one walks fourteen steps, then turns west and proceeds 1,775 steps before seeing the same tree. What is the area of the city?”

Though brief, the problem involved considerable reasoning: beyond basic arithmetic, one needed to understand the theorem of similar triangles and solve simultaneous linear equations—a medium difficulty problem in the Nine Chapters. Cai Yong selected it to see if Fei Qian truly understood mathematics.

For Fei Qian, a high school-level problem was no challenge. He requested paper and brush, sketched a diagram, set up equations, and calculated the answer directly.

Cai Yong craned his neck to observe. The diagram was evidently a schematic, but what were the cryptic labels like ABCD and 1234? He was intrigued, yet too shy to ask.

Fei Qian had considered flaunting a modern trick question about a 30-yuan hotel fee but wisely refrained. Such a misleading problem might be amusing in casual settings, but before a great scholar like Cai Yong, it could lead to unfavorable judgments—perhaps branding him as cunning, a label that could ruin a life.

Better to appear earnest—after all, everyone admires sincerity.

After finishing the calculations, Fei Qian stood respectfully, adopting the demeanor of a well-behaved student.

Cai Yong measured him carefully, hesitated, then acknowledged Fei Qian’s mathematical knowledge.

“Very well,” he said. “I shall accept you as a registered disciple. On the third and twelfth days of each month, you may come to the Taixue to attend my lectures. On the fifth and twentieth days, if you have questions, you may visit here to inquire. How does that sound?”

Being a registered disciple was still being a disciple and did not violate his prior promise. Whether Fei Qian would have the chance to become a full disciple later was to be decided in the future. For now, Cai Yong resolved to send the solution paper to his precious daughter to see if she could understand it.