Prelude

Early winter, 1787, East Hall of Versailles Palace.

The Youth sat in a room covered in Rococo-style golden ornamentation and grand oil paintings, shaking his head with a bitter smile at the test paper before him.

Candlelight flickered in the extravagant crystal chandelier, two meters in diameter, illuminating his fair skin and youthful, delicate features, making him look as handsome as Paris in an oil painting.

Beside him, an elderly man wearing a white curled wig and a lace cravat sighed. Disappointment flickered in his brown eyes as he bowed slightly and said, "Crown Prince, if you find this difficult, perhaps you should begin with the foundational courses..."

The Youth called Crown Prince froze, then immediately snapped out of his wandering thoughts and nodded politely to the old man.

"Mr. Lagrange, I believe you may have misunderstood. I said I wanted to take the graduation examination for your course, not the entrance examination."

That unremarkable little old man was none other than Lagrange—the famous French mathematician and physicist known as the founder of analytical mechanics, a pioneer of group theory, and the Prince of Mathematics.

"Graduation examination?" Lagrange frowned at the Youth before him, who was only thirteen. "Your Highness, what I teach is a university course. I fear you..."

The gorgeously dressed Noble Youths around them, who had been working on their papers, immediately turned to look over, their eyes full of curiosity.

At that moment, however, a Youth around sixteen years old, wearing a silk coat with a lace collar and possessing slightly upturned eyes, revealed a disdainful expression and said loudly,

"Crown Prince, I recall that you still have two years before you can finish the foundational courses." He nodded toward the old man. "Mr. Lagrange often says that the ladder of mathematics must be climbed step by step. Those who aim too high will surely fall and smash their heads bloody. I believe Crown Prince should remember that maxim as well."

The Youth ignored him and said earnestly to Lagrange,

"Sir, I have studied university mathematics on my own. I truly need the graduation examination."

The old mathematician sighed helplessly, then turned to his assistant. "Andre, bring me the test paper at the very bottom of my folder."

"Yes, Professor."

Soon, several test papers were placed before the Youth.

He skimmed through them and found that they were several times more difficult than the previous set. Yet most were still at the level of high school in his former era, involving only a small amount of calculus. They posed no real challenge to him.

That was right. Half a month ago, he had still been a second-year graduate student in the twenty-first century. That day, he had gone to France with his advisor for a wind turbine project, only to accidentally fall from the top of a tower. When he woke up, he discovered that he had somehow become the eldest son of Louis XVI, King of France—Louis Joseph. Perhaps due to the effects of his transmigration, Joseph had been born several years earlier than in history and was already thirteen.

Under Lagrange's scrutinizing gaze, Joseph swiftly wrote down the answer to the first question, while his mind was occupied with the course of French history. The French Great Revolution will erupt next year. The entire royal family will get chopped, and as Crown Prince, I definitely won't escape... King Louis XVI knows nothing but repairing locks. France owes more than two billion in foreign debt, while its annual revenue is only five hundred million.

Financial collapse had delayed Civil Servants' salaries, making the government's daily operations difficult with every step. Foreign trade had stagnated, and the Colonies were rotting by the day. To replenish the treasury, the Cabinet had no choice but to levy taxes in great quantities. The common people had nearly been drained to the marrow, while the tax-exempt nobles spent money like dirt every day, wallowing in pools of alcohol and forests of meat.

Furthermore, France would suffer severe hailstorms in the summer of the following year. Coupled with the effects of the droughts from previous years, this would trigger a nationwide Great Famine. Next would come starving people rising up, furiously clearing the Bastille dungeon, unlocking the French Great Revolution expansion pack. The nation would fall into turmoil, and more than a hundred thousand people would go to the Guillotine...

Thus, if he wanted to keep his head, he counted on his fingers. First, he had to resolve France's fiscal deficit. Second, he had to obtain enough grain to prevent people from starving to death. Third, he had to clean up the nobles with treacherous intentions. Finally, he also had to deal with the United Kingdom and Prussia, both eyeing France like tigers watching their prey.

Famine would begin in July, leaving him only a little over half a year. He rubbed his forehead irritably. Because he was too young, he could not yet involve himself in state affairs. Even if he had strength, there was nowhere to use it.

This was a complete hellish start, with scarcely a sliver of hope for survival...

Not far away, the upturned-eyed Youth saw his movements and assumed he was fretting because he could not solve the questions. He immediately snorted disdainfully. "This idiot actually..."

...came here claiming he knew university courses. What a disgrace! Why is such a useless fool the Crown Prince while I am not?!"

While Joseph considered how to save his life, he continued writing answers at high speed and soon finished the first page.

He eagerly turned the page. Once he passed Lagrange's subject, he would have completed his studies at the University of Paris.

Half a month earlier, he had proposed to Queen Mary—his conveniently acquired mother—that he participate in government affairs to reverse his doomed fate. She had promptly refused, telling him to focus on his studies and wait until he had achieved something.

Thus, he could only make an agreement with the Queen: once he completed the University of Paris courses, he would formally enter government service.

Of course, with his level, he was a fighter jet among top students in this era. Over the previous half month, he had already completed examinations in the vast majority of subjects. The only reason it had taken so long was that he needed to memorize the incorrect knowledge—much of what this era revered as truth was actually fallacy.

Lagrange watched the Crown Prince's pen fly across the page and had long since stopped paying attention to the other students. His eyes widened more and more.

These were questions that required five years of study at the University of Paris to complete, yet the Crown Prince answered them effortlessly, with clear reasoning and not a single mistake!

He was only thirteen, and self-taught at that! Lagrange's heart shook violently. Could another Leibniz have been born?

Lagrange suddenly glanced at his assistant, narrowing his eyes. Could Andre have leaked the questions to the Crown Prince? The Crown Prince's performance was simply too monstrous. Even a super-prodigy like Leibniz had only begun university at fourteen.

He immediately took paper and pen, scribbled down several lines, and handed them to Joseph.

"Your Highness, there is no need to do the rest. So long as you finish these questions, I will consider you to have passed."

The upturned-eyed Youth sneered to himself. Heh, Lagrange sees that he cannot solve them and wants to go easy on him? What a fool sucking up to the royal family! Later, I must find a way to let everyone see the Crown Prince's paper and make him thoroughly disgrace himself.

Joseph looked at the paper in surprise. There were only five questions. The difficulty had not changed, but the number of questions had decreased. Good thing.

He quickly solved the first two questions. The third read: Please write the proof of Rolle's Theorem. He was thoroughly familiar with it and immediately wrote in the blank space:

"Rolle's Theorem: Let f be continuous on the closed interval [a,b] and continuous on the open interval (a,b). If f(a)=f(b), then there is at least one point in the open interval (a,b) at which the value of its derivative is zero."

"Proof: Since the function f(x) is continuous on [a,b], it attains a maximum value (M) and a minimum value (m) on the closed interval..."

Joseph finished writing in just a few strokes, but suddenly noticed Lagrange breathing rapidly beside him. He hurriedly looked up and saw the old mathematician staring at the paper with an excited expression, as though he had glimpsed his first love.

Joseph immediately lowered his head and scanned the question again. "I did not write anything wrong, did I?"

Lagrange grabbed the paper, carefully read through the proof several times, and muttered, "So it holds for differentiable functions as well! How had I not thought of that?"

He looked at Joseph again, his gaze burning like fire. "Your Highness, how did you think of this?"

"Ah? Wasn't it just..." Joseph suddenly remembered that Roll had merely proven that between two adjacent real roots of a polynomial equation, the equation had at least one root. It was not until the nineteenth century that someone extended it to differentiable functions.

I was careless. I didn't dodge in time...

"Cough!" He hurriedly took back the test paper and changed the subject. "Mr. Lagrange, I am going to do the last two questions now."