Chapter 771: A Single Math Problem Sets Off a Storm (Part 2)

After the clerk examinations that day, Xuanfu Town soon boiled over with excitement — especially once this "Two Generals Firing Cannons" problem, also called the "Wang's Calculation Problem," spread, the entire town plunged into a wave of mass problem-solving.

This finale problem, a major question personally set by the Marquis of Yongning, captured the interest of countless people. According to what was learned afterward, among the several thousand candidates who took the exam, not only did no one solve it, they could not even propose a viable line of thought. Some even coughed blood from the strain, drawing widespread concern.

Fortunately, he was not seriously hurt, which set everyone's mind at ease.

Difficulty is what makes a challenge — who would not be tempted to become a grandmaster who founds a school of thought? Not just the primary, secondary, and university students of Xuan Town, but even the town's officials, commoners, gentry, civilians, and soldiers were all working calculations on paper in their spare time. Books on every kind of arithmetic sold like wildfire in Xuanfu Town.

Even Li Banghua gathered Zhu Zhifeng, Ma Guolei, Wu Zhi, and others to discuss this problem together.

Zhao Xuan also became famous from this.

In truth, Zhong Xiancai was just as famous as he was, but Zhong Xiancai was currently at Guihua City, far from the storm's center of public attention. Zhao Xuan, however, was in the garrison town, and many officers and officials who saw him would tease him: "Brother Zhao... with one cannon shot, your entire flock of doves is wiped out."

Zhao Xuan paid no mind to everyone's teasing. His whole heart was immersed in this arithmetic problem designed by Wang Dou. He keenly sensed the Grand General's many painstaking intentions behind this problem, and even more keenly foresaw that this arithmetic problem was the key to making his own cannon battalion soar like a tiger with wings.

As the commanding officer of the cannon battalion, Zhao Xuan had some modest study of arithmetic. Among his subordinate officers, clerks, and others, there were quite a few proficient or partially proficient in mathematics.

He gathered his elite officers and strong troops and for days on end they researched this "Wang's Calculation Problem." Yet staring at the densely packed equations written in chalk on the blackboard — his subordinates had filled several blackboards with chalk calculations, sheet after sheet of four-variable techniques laid out — they still could not even touch the door to solving it.

Zhao Xuan's head throbbed as if about to split. There is a saying about cutting a tangled knot with a sharp blade; he keenly felt he must first find a key point — but where was that key point?

Staring blankly at that math problem, he felt the same urge to cough blood.

Very soon, all the clerk examination questions appeared in that issue of the Xuanzhen Times. The "Two Generals Firing Cannons Problem" was prominently listed. Paired with the shocking content about a candidate coughing blood from the exam, the storm it stirred swept outward from the town like a hurricane.

Everywhere the newspaper reached, every place seemed to boil over. When it reached the capital, the whole city was likewise thrown into an uproar. Not to mention the heated discussions in every teahouse and tavern, even illiterate commoners would toss in a few words: "Did you hear? At the Xuanfu Town clerk examinations, a candidate calculated until he coughed blood..."

"Really? What kind of problem is that hard?"

"I heard the Marquis of Yongning personally set the problem. They're all calling it Wang's Calculation Problem now..."

Countless people grew interested in the Xuanfu Town exam questions. For the first time, many felt that arithmetic could actually be this fascinating.

The Xuanfu Town clerk examinations naturally drew the attention of the capital's hundred officials. They all read the newspaper, analyzing the questions one by one. Yet the earlier classical literature questions were tacitly ignored by them. Judging by the questions Xuanfu Town set, how many could they themselves answer correctly?

Could it be that after decades of bitter study, they were not even qualified to serve as clerks in Xuanfu Town?

This was too devastating — and too terrifying.

Moreover, the policy essay questions Xuanfu Town set were each one piercingly sharp. Take the first one: "There is a department which at the dynasty's founding had a population of over 340,000, with summer tax and autumn grain totaling over 140,000 shi per year. Now it has a population of over 600,000, yet summer tax and autumn grain total only 50,000 shi per year. Why is this? Please explain."

Any clear-eyed person could see at a glance that this touched on the gentry problem. Without the gentry's tax evasion, tax resistance, and vast land annexation, how could the population increase while tax grain decreased instead?

People say the dynasty's fate is exhausted, but is it not really that the problems of land, population, and finances have erupted to their breaking point?

Yet such topics have been evaded in every dynasty. Everyone understood them in their hearts, but no one would ever raise them. For Xuanfu Town to present them as exam questions this time — could it be that the Marquis of Yongning intends to challenge the privileged immunities the officials and gentry have enjoyed for thousands of years? What game is he playing?

The several questions that followed were all of the same nature, which left many people deeply displeased.

But Wang Dou is now at the height of his power, with strong troops and sturdy horses — who dares openly challenge his authority? Do they not know that Li Banghua, the Left Censor-in-Chief of the Chief Surveillance Bureau, was banished by His Majesty the Emperor to a frontier military town precisely because he targeted the Marquis of Yongning, Wang Dou?

So the various officials ignored these questions and shifted their attention entirely to the arithmetic problems at the end — and deliberately steered public opinion in that direction.

Publicly, they still dismissed these arithmetic problems with disdain, emphasizing that a scholar's energy should be devoted to the classics. As Senior Grand Secretary Zhou Yanru declared on behalf of the officials: "Mathematics and computation are but minor arts. The Four Books and Five Classics, the subtle words and profound meanings of the sages — that is the grand and proper path."

His words appeared in the newly established Huangming Times. Yet privately, Zhou Yanru and his advisors were studying these arithmetic problems with keen interest — especially that "Wang's Calculation Problem." The more they studied it, the more unfathomably profound they found it.

To solve it, he even dug out from his piles of old papers the Nine Chapters on the Mathematical Art and other books he had long since forgotten, and began studying them meticulously.

If Zhou Yanru was like this, the capital's hundred officials all the more followed the trend. In their spare time, they would all toss out a few mathematical terms, as if without doing so they could not keep up with the fashion.

"Clack-clack-clack-clack..."

The sound of abacus beads was like a torrential rainstorm. In the Eastern Warm Pavilion, the large gilded plaque reading "Rising Before Dawn, Eating After Dark" hung high. Inside the pavilion, the Chongzhen Emperor stood with his hands behind his back, holding the Xuanzhen Times, staring blankly outside in a daze.

Inside the pavilion, numerous eunuchs were gathered. Led by Wang Dehua, the Seal-holding Eunuch of the Directorate of Ceremonial, they were calculating intensely.

Before them, long narrow tables were arranged, each bearing an abacus — all the large, long, black abacuses used by the Ministry of Revenue. These great abacuses were extremely long, some reaching five or six meters, and their counting units were correspondingly vast.

One could tell from the digits marked on them: from units, tens, hundreds, thousands, ten-thousands, all the way up — hundred-millions, trillions, jing, gai, zi were all included, and some were even marked to the extreme units of rang, gou, run, zheng, zai.

Of course, in actual calculation, reaching hundred-millions or trillions was already quite good.

Now the many eunuchs and their abacuses were arrayed in a single line, clacking away at the beads — a magnificent spectacle.

These large abacuses were also shared by several people working together, to enhance computing power.

Some eunuchs were also writing and calculating on blackboards. Xuanfu Town's blackboards and chalk had spread to the capital as well, and were indeed more convenient for drafting calculations.

How could the Chongzhen Emperor not care about the Xuanfu Town clerk examinations? When the newspaper arrived, he studied it question by question. Wang Dou's policy essay prompts at the front actually resonated deeply with him, for they reminded him of recent events in the capital.

Chen Xinjia had proposed training a new army in the capital on a large scale. The Chongzhen Emperor was very much in favor, but training troops required provisions and pay, and the various ministers were calculating. Senior Grand Secretary Zhou Yanru proposed having wealthy households and officials contribute donations, and even set up a yellow silk register.

Zhou Yanru's plan seemed perfect. At this critical juncture of dynastic peril, surely the capital's gentry, officials, and wealthy households would all generously open their purses to meet the state's urgent need. Yet — what happened in reality?

The officials all passed the buck to one another. No one was willing to donate. In the end, under the Emperor's implicit prompting, Senior Grand Secretary Zhou Yanru took the lead by donating ten thousand taels of silver. Then the Grand Secretaries donated — one giving ten thousand, another five thousand. Down to the hundred officials, it became one giving a thousand, another five hundred. The final sum obtained was a mere drop in the bucket.

The Emperor was greatly displeased. The officials then said the ennobled relatives were wealthy and could be ordered to contribute — especially the imperial relative Retainer Bo, Zhou Kui, who had just been promoted to Marquis. It was said Zhou Kui was rich, and as an imperial relative, he should take the lead. The Chongzhen Emperor thought this reasonable. Zhou Kui and the others were, after all, relatives, and Zhou Kui himself was his own father-in-law by marriage; surely he would help him in this matter.

So he dispatched the eunuch Xu Gao to proclaim an edict seeking aid: "In weal and woe we are bound together. You must coordinate efforts and make arrangements to prepare for emergencies."

Zhou Kui, however, replied: "How could this old minister have much money?"

Xu Gao tearfully exhorted him three times. Zhou Kui had no choice and finally donated ten thousand taels. Then the various ennobled relatives gave — one ten thousand, another five thousand. The great eunuchs gave — one ten thousand, another five thousand. The wealthy households of the capital, clamoring helplessly, likewise dug into their pockets. The whole capital was thrown into noisy turmoil, and in the end only three hundred thousand taels of silver were obtained — far short of even the initial investment needed for the new army. How could training even begin?

And because of this, Zhou Yanru came under heavy impeachment.

There was also Hong Chengchou, who had been ordered to reorganize the capital. Though his methods were gentle, seasoned, and step-by-step, there were always those whose interests were harmed and who were dissatisfied. An impeachment storm was about to rise. Whether Hong Chengchou would follow in Li Banghua's footsteps was extremely hard to say.

Furthermore, Cao Bianjiao and Wang Tingchen returned to their posts at the beginning of the intercalary month and nearly incited a mutiny. It was because they had been away from their garrisons for so long, and their subordinate troops had suffered heavy casualties, while nearby officials and gentry had seized the opportunity to swallow up the new army's fields and mature lands. Cao Bianjiao flew into a rage and executed a large batch of the local gentry who had annexed the land, causing public sentiment to boil over.

Memorials attacking Cao and Wang came in like clouds again, and there were even dark, cold whispers spreading: "The new army is truly a calamity for the Great Ming — all it knows is to contend with the people for profit..."

Although the Chongzhen Emperor kept all the attacking memorials and did not issue them, he was still utterly exhausted in mind and body. He had intended to let the two men continue organizing and training the new army in Yutian and other places, but there was no money or grain, so he had to abandon the idea. In the end, he decided to grant Cao Bianjiao and Wang Tingchen's request and transfer them to Liaodong to guard Yizhou and other areas.

All these matters left the Chongzhen Emperor scorched and battered. In particular, the lack of money in his hands tormented him beyond measure. But was the Great Ming truly without money? Clutching the Xuanzhen Times in his hand, the Emperor did not believe so, and he felt even more deeply that Xuanfu Town's policy essay prompts this time had been excellently set.

Yet this was something he could only ponder in his heart. The Great Ming's imperial examination system was exceedingly mature; for hundreds of years, scholars had all followed it in their examinations. A sudden change would only add chaos atop chaos. The matter of the new army was already headache-inducing enough; the Chongzhen Emperor did not want to add more vexations.

However, regarding the "Wang's Calculation Problem" within, the Emperor was still very curious. He had heard people say this problem was extremely difficult, and that the capital's hundred officials and students were all calculating it privately, yet not a single person could solve it.

The Chongzhen Emperor simply could not believe that he, who possessed a billion subjects and countless talents, could not even solve a mere arithmetic problem set by a frontier warlord. He ordered Wang Dehua to find eunuchs in the palace proficient in arithmetic and resolved to solve this problem.

Yet after half a day, the crowd still showed no sign of stopping their calculations. The storm-like sound of abacus beads still clattered on without cease.

The Chongzhen Emperor furrowed his brow, then paced back to his desk and flipped through the Huangming Times lying on it. Compared to the Xuanzhen Times, the Huangming Times was like a reprint of the official gazette — rather dry and flavorless. Few people were willing to buy it of their own accord, so after publication, it was apportioned to each ministry and each household, with a monthly newspaper fee deducted from the heads of the hundred officials.

After reviewing memorials for another stretch, the abacus-clicking in the hall still showed no sign of stopping. The Chongzhen Emperor grew impatient — a mere arithmetic problem, and so many people still couldn't solve it?

"Well? No result yet?"

The Emperor's brow furrowed deeper. He was impatient, but at the same time even more curious — was this "Wang's Arithmetic Problem" truly so difficult?

Wang Dehua smiled bitterly and begged forgiveness: "Your slaves are useless, please let His Majesty punish us…"

He wiped his forehead and said: "Truly, this problem from the Marquis of Yongning, this problem…"

In the dead of winter, fine beads of sweat covered his head, making his sleek, glossy face glisten all over — clearly the result of excessive mental strain. Finally, he offered the Emperor a suggestion: "Perhaps we could send this problem to the Imperial Academy. After all, they are proper scholars, and some among them even specialize in the arithmetic discipline."

……

The Imperial Academy in the capital was located inside Andingmen in the eastern part of the city. Though not as vast as the Imperial Academy in Nanjing, it still had a great many students. Besides studying the Four Books and Five Classics, they also had to take supplementary courses in law, calligraphy, and arithmetic. There were even dedicated Erudites for law, calligraphy, and arithmetic.

But truth be told, these men held low status. Even the highest-ranking Erudite among them was no more than a rank 9b official — nothing like the Erudites of the Five Classics, every one of whom was rank 5a or above. This alone showed how low the status of law, calligraphy, and arithmetic was in the Great Ming.

Yet today, the Erudite of the arithmetic discipline suddenly received an imperial edict, ordering them to calculate that "Wang's Arithmetic Problem." It had to be solved, to demonstrate the court's capability and authority.

The entire Imperial Academy was thrown into an uproar. The arithmetic Erudite dared not be negligent and immediately assembled all the teaching assistants, lecturers, and elite arithmetic students to calculate it by imperial command.

But despite their utmost efforts, they ran into the same problem Zhao Xuan had encountered — where was the entry point? Dynamic solid geometry — where should one even begin?

Watching the arithmetic Erudite at a complete loss, his face pale and his body swaying as he calculated, the Chancellor of the Imperial Academy and the Directors waiting nearby were greatly alarmed. Could this problem truly be so profound? Even their own academy's arithmetic Erudite was utterly helpless?

With an imperial edict at stake, they dared not slack off. They kept throwing more students proficient in arithmetic into the calculation effort, until finally the entire Imperial Academy was mobilized.

……

"Fathers, our opportunity has arrived…"

The speaker was a man in the Imperial Observatory — high-nosed, deep-eyed, wearing the official robes of the Great Ming. He was about fifty years old, with a thick, full beard, and from time to time a glint of wisdom surfaced in his deep-set eyes. This was the Western missionary serving in the Imperial Observatory, Tang Ruowang.

This German, born in the twentieth year of the Wanli reign, was originally named Johann, with the surname Adam. He had studied at the Three Kings' School founded by the Jesuits, and later at the Roman College and the Academy of the Lynx in Rome. At the end of the Wanli era, he had journeyed east to the Great Ming together with Deng Yuhan, Luo Yagu, and several other missionaries, dispatched under the name of the Portuguese government.

At this time, the missionaries were continuing Matteo Ricci's methods of proselytizing — "expel Buddhism and supplement Confucianism," "merge with Confucianism and surpass Confucianism." Everyone who set foot on Chinese soil was required to study the Chinese language and culture, to research China's classics, histories, and ethics, in order to find a breakthrough point for their missionary work.

Ricci's approach had once achieved great success. Toward these Western missionaries — each of whom took a Chinese name, wore Chinese robes, understood astronomy above and geography below, and was thoroughly versed in Chinese classics — the literati and scholar-officials of the time held great goodwill and trust. This even produced high-ranking Jesuit members like Xu Guangqi.

However, after Ricci's death, some zealous missionaries felt that Ricci's thinking had accommodated the Chinese too much, compromising the "purity" of Catholicism and making the conversion of followers far too slow. So they began to alter Ricci's missionary approach and adopt more aggressive methods.

They resolutely rejected Confucian thought and strictly forbade Chinese converts from offering sacrifices to Heaven, to ancestors, or to Confucius. This provoked enormous antipathy and suspicion among the people of the time. Some said: "There are men like Li Madou and Ai Rulue who, claiming to come from the Great West, borrow the name of Confucian learning to attack Buddhist teachings as false, calling themselves the Catholic faith, also called the Heavenly Learning."

They further said: "These men steal beams and swap pillars, secretly replacing our sacred teachings of the Lord Above and the Holy Scriptures — this is the presumptuous intent to use barbarians to transform the Xia. Moreover, the Catholic faith forbids the keeping of spirit tablets for sovereign and father, forbids sacrifices to ancestors and parents — truly they would lead all under Heaven to have no sovereign and no father."

After the Nanjing Incident, all missionaries were expelled and could only reside in Macau. Johann resolved to change this situation. He too donned Chinese robes, chose a name from among them, taking the Chinese name Tang Ruowang. Seizing the opportunity of the war against the Later Jin, he came to the capital with the other missionaries under the title of military advisor.

Thereafter, Tang Ruowang continued Ricci's approach — preaching gently and permitting converts to perform ancestral rites and venerate Confucius. His work made great progress. He alone personally baptized as many as fifty people, among them members of the imperial clan, the imperial house, and many eunuchs.

Because of his achievements, in the thirteenth year of the Chongzhen reign he was appointed by the Church as the head of the Beijing mission district. And because Tang Ruowang was highly proficient in mathematics and astronomy, the Chongzhen Emperor appointed him as an official in the Imperial Observatory, where he translated and compiled almanacs, tracked the heavens, and crafted instruments.

Using this opportunity, he developed converts such as the eunuch Pang Tianshou of the Imperial Horse Administration, and also brought many more missionaries into the Observatory to serve. At this moment, gathered around him were several golden-haired, blue-eyed Westerners, every one of them wearing the official robes of the Great Ming.

Tang Ruowang and the other missionaries had long been secretly paying attention to Wang Dou. Especially after Wang Dou was enfeoffed as Count and then Marquis, Tang Ruowang and the others focused on him with particular interest. When the Jingbian Army marched to Liaodong, and again when they returned in triumph to the capital, they had made a point of going to observe in secret.

Afterward, Tang Ruowang sighed to those around him: "What fine, crack young lads — not one whit inferior to our soldiers in Europe. The future of the Great Ming lies with them. Fathers, we must see to it that this warlord of the Great Ming enters the embrace of the Lord."

But to the disappointment of Tang Ruowang and the others, Wang Dou had always been indifferent toward them, and even forbade missionaries from entering his territory.

Moreover, what alarmed Tang Ruowang and the others was that Wang Dou seemed to understand the world very well, understood these missionaries very well, and even understood Europe very well. This left Tang Ruowang and the others utterly baffled. How could a warlord who rose from a common soldier possibly know so much?

Tang Ruowang even wondered: "The people of the East have a saying — a sage sent by Heaven knows by Heaven and perceives by Heaven. Could it be that this Marquis of the Great Ming is a sage sent by Heaven?"

Beyond this, he could not explain the "numinous strangeness" surrounding Wang Dou, and it only made them strive with ever more tireless diligence, hoping to win Wang Dou's favor and, ideally, ultimately bring him into the faith.

At this moment, Tang Ruowang smiled at those beside him and said: "Fathers, the opportunity has come. Display your talents — the accumulated knowledge of our Europe, the crystallized wisdom of sages like Archimedes and Euclid. Let the people of this Eastern land be utterly astonished."

One missionary beside him laughed and said: "Yes, Father. Word came from the Imperial Academy yesterday — they assembled the strength of the entire school and still could not solve it. It seems this problem from the Marquis will still need us to resolve it. After all, mathematics is a rigorous discipline."

Another Father also laughed: "The people of the East are full of romantic fancy in their logic, while we Europeans are like Jews counting gold coins… Yet it is precisely this trait that makes us suited to studying rigorous, logic-filled learning. It is time to open the eyes of these Cathayans."

Tang Ruowang said: "Father, I must correct you on one point. After my careful research, the people of the Ming nation have no connection to the Cathayans. If one must speak of a connection, the Cathayans were like the barbarian tribes of Europe's past — a complex situation much like that between the Han people and the northeastern savages today. Even the old city of Khanbaliq was merely the Tatar name for Beijing. We should not use the term 'Cathayan' in speaking to them, or we will provoke their fury. After all, those were a branch of barbarians, and now they consider themselves civilized people."

He continued: "We may call them the people of Serica, or the Seres. Of course, their own terms are very complicated — now they are called the Ming people, and also the people of the Central Kingdom. The more closely I study this country, the more bewildered I become."

Another Father said: "The Central Kingdom — that is what they call their central empire. I think they are far too arrogant."

Tang Ruowang said: "This is a wealthy and powerful nation — they have the right to be arrogant… Fathers, the name is not important. This is a matter of great consequence. We should wield the weapon of our learning, display our brilliance to full effect, and ultimately make these heathens gaze upward in reverence and convert to the embrace of the Lord."

All the Fathers together made the sign of the cross, each one brimming with passion. The Emperor had already issued his edict, yet the students of the Imperial Academy could not solve it. If they were to calculate that mathematical problem, what a sensation it would cause — how many people would look up to them in awe?

Then they could even send one of their number to Xuanfu Garrison to serve as a Grand Master, seizing the chance to draw closer to the Marquis.

Tang Ruowang composed his expression, took out the Xuanfu Times in his hand, and said: "Very well, Fathers, let us begin calculating. Solve these mathematical problems in the newspaper, one by one."