Chapter Six: Hongli's Mathematics Examination

Hongli then explained to Lady Niuhuru the reason why Haitang had come to see him. Upon hearing this, Lady Niuhuru was naturally overjoyed and expressed her sincere gratitude toward the Primary Consort, Lady Ulanara.

Before long, however, Hongli received word that Yongzheng had unexpectedly returned to the manor and wished to see him after dinner. Hongli had no choice but to head to Yongzheng’s study once he had finished his meal.

Yongzheng’s return had indeed been a last-minute decision. Upon his arrival, he first held a secret meeting with Wu Sidao.

"Master Wu, I have good news for you: the Nian woman is pregnant again!" Yongzheng said with a smile as he greeted him.

Upon hearing this, Wu Sidao’s face lit up with joy. He rose, bowed, and offered his congratulations: "Congratulations, Fourth Prince!"

Yongzheng waved his hand, signaling for Wu Sidao to sit. "I have already sent a letter to have this news quietly delivered to Nian Gengyao."

Wu Sidao smiled. "The Nian woman has just given birth to a son for you, and now she is pregnant again. One would think that Nian Gengyao, as the Governor-General of Sichuan and Shaanxi who controls the grain and provisions for the Northwest army, will have no choice but to set his heart more firmly on you, Fourth Prince."

Yongzheng nodded, sighing, "That servant is slippery. Without something tangible to bind him, it is difficult to make him truly submissive."

"You are right, Fourth Prince. But in my humble opinion, you should not focus solely on Nian Gengyao; it would be wise to make some subtle preparations within the palace as well," Wu Sidao reminded him.

Yongzheng stood up, lost in thought, and began to pace the room. After a moment of contemplation, he agreed, "Master Wu is right. By living in such seclusion, I am easily forgotten. I fear even the Emperor, my father, might forget his fourth son. I need someone by his side to keep my presence known."

"Today, while instructing the imperial grandsons, I encountered something that I should report to you," Wu Sidao said with a smile.

Yongzheng glanced back at him. "What is it?"

Wu Sidao gritted his teeth and pushed himself up from the edge of the table. "It is the matter of Hongshi bullying Hongli, and Hongli choosing to endure it." He then recounted the details of what he had witnessed to Yongzheng.

Yongzheng listened and said meaningfully, "In that case, Hongli is indeed suited to stay by the Emperor’s side, so that he may be reminded of his fourth son, who lives in seclusion and devotes himself to Buddhism."

"Exactly. Hongshi’s restless nature actually works in your favor, Fourth Prince. You can turn a blind eye to him for now, which will signal to others that you are truly so immersed in Buddhist practice that you have no heart to discipline your own household," Wu Sidao added.

Yongzheng nodded, his expression icy. "I shall indulge that scoundrel for a little while longer!"

It was only after meeting with Wu Sidao that Yongzheng saw Hongli in his study.

*Woof! Woof!*

As Hongli approached the study, he heard the sound of barking dogs. Through the fence beside the study, he could see a small garden where many dogs were kept. They were well-groomed, but because he rarely visited, they were unfamiliar with him and barked wildly. Hongli walked toward them, knowing Yongzheng’s fondness for dogs. He had even had Haitang bring a bone with meat in a food box. As he approached, he tossed the bone inside, and the dogs scrambled for it.

Hongli then entered Yongzheng’s study. The room was spotless, every item arranged in perfect order. To his surprise, a dog was lying beside Yongzheng—a quiet, snow-white creature with eyes like polished lacquer, watching Hongli intently.

Yongzheng held a string of Buddhist prayer beads, grooming the dog's fur with one hand while transcribing Buddhist scriptures with the other. Anyone unaware of history would assume this "Cold-Faced Prince" had truly lost all ambition, turning his back on worldly power struggles to focus solely on scriptures and his dogs. In reality, the princes, ministers, and elite of the Qing Dynasty could never imagine that this was a man who had long endured in silence for the sake of the dynasty’s foundation—a ruthless man who would eventually turn the sharp blade of reform against his own people, including his own kin.

Hongli, naturally, did not object. Besides, as the future Qianlong Emperor, he hoped Yongzheng would reform as ruthlessly as possible, for that would leave him with more capital to squander in the future.

"Sit. There is a test paper on the table. Complete it and hand it to me," Yongzheng said without looking up, pointing with his left hand to a paper on the desk.

"Yes, sir!" Hongli acknowledged and sat down. On the desk, along with the paper, were brushes, ink, a bright candle, an abacus, and scratch paper.

Hongli glanced at the contents—it was a mathematics test. The problems were practical, involving canal transport, river management, construction, disaster relief, and military logistics. He hadn't expected a math exam. In his previous life, he had always been the one setting the tests; now, he was the one being tested.

He began to answer seriously. While these problems were likely carefully prepared by Yongzheng, they held no real difficulty for him. The only annoyance was converting numbers into Arabic numerals and translating the logarithmic and trigonometric functions from Chinese characters into Western notation. He needed to translate them to perform the calculations.

Yongzheng, though transcribing, kept an eye on Hongli. He noticed Hongli sketching strange diagrams on his scratch paper—lines, curves, dashed lines, and symbols he had only seen before with his ninth brother, Yintang, who was well-versed in foreign languages.

"Who taught you these strange symbols?" Yongzheng appeared behind him, asking suddenly.

Hongli stood up. "I learned them from reading books by foreign missionaries."

Yongzheng asked no more. Shortly after, Hongli handed over the completed paper. "Father, I have finished."

Yongzheng compared the answers against a slip of paper he pulled from his sleeve. "They are all correct!" he exclaimed, looking at Hongli in disbelief. "These are difficult problems based on the *Essential Principles of Mathematics*. Even your sixteenth uncle took many days to solve them all."

The "sixteenth uncle" was Yinlu, favored by the Kangxi Emperor for his mathematical prowess and currently in charge of the palace’s Institute of Mathematics.

Yongzheng then snatched up the scratch paper, studying it closely. He pointed to some arrows. "What are these?"

"I call them vectors," Hongli explained, describing the concept of using them to build coordinate systems for three-dimensional objects.

Yongzheng nodded solemnly as he listened, then gripped Hongli’s shoulders with both hands. "Hongli, I never imagined you had such talent for mathematics, even creating new theories! But you must know, during grand celebrations, your grandfather often selects young princes with specialized skills to keep by his side. If you can use this to catch his eye, you might be allowed to serve in the palace. That would benefit you, and it would benefit our Prince Yong’s manor. I hope you succeed."

"I understand, Father," Hongli replied. "But I wonder if there are any other princes with better mathematical skills than mine."

Yongzheng said, "I think not. Your third uncle’s sons focus on Confucian classics; your ninth uncle’s sons know these foreign symbols but do not apply them to mathematics. Your sixteenth uncle is skilled, but he is the one who set these very problems, and you know his level."

Hongli nodded. He knew Yongzheng wanted his help in the struggle for succession. "Father, rest assured. If I am allowed to serve in the palace, I will perform well and ensure the Emperor knows of your diligence."

Yongzheng smiled. "Go and rest."

Hongli returned to his small courtyard and slept soundly. The next day, he went to the schoolhouse as usual. Because Hongshi often visited the Eighth Prince’s manor, Hongli spent his time studying and writing with Hongzhou, and they grew closer.

The day of Hongli and Hongzhou’s birthday arrived. In previous years, they received few gifts, but this year was different. Hongli received many, forcing him to rise early to thank everyone. Hongzhou received few, but Hongli had prepared a generous gift for him, which delighted Hongzhou. When Hongzhou learned that Hongshi had only celebrated Hongwang’s birthday in the first month of the sixtieth year of Kangxi, he remarked to Hongli, "Fourth Brother is the only one who treats me well!"

In the culture of the Eight Banners, gift-giving was a serious matter. When Yongzheng learned that only Hongli had gifted Hongzhou, while Hongshi had ignored him to celebrate Hongwang, he was furious. On the day of the banquet celebrating the sixtieth year of Kangxi’s reign, he ordered that only Hongli accompany him to the palace.

Carrying the special gift Yongzheng had ordered him to prepare, Hongli followed his father into the palace.

"Reporting to the Emperor, the gift from the Prince Yong’s manor is a special tribute prepared by your grandson, Hongli. It is not for public display; I ask that you examine it in private," Yongzheng said when it was his turn, successfully piquing the Emperor’s curiosity.

Hongli couldn't help but smile internally. He had never imagined that the "Vieta's formulas," known to every middle schooler in his past life, would become a mysterious, grand gift for the Kangxi Emperor.