Early Winter, 1787 — East Wing of the Palace of Versailles
Joseph sat quietly in a chamber decorated with Rococo gold patterns and tall oil paintings. An examination paper lay on the desk before him. After reading it for a moment, he slowly shook his head.
Above him, a large crystal chandelier glittered with dozens of candles. Their light spread across the quiet chamber. The marble floor reflected the soft glow.
An elderly man stood beside the desk wearing a white curled wig and a lace cravat. He looked at the examination paper for a moment. Then he sighed softly.
"Your Royal Highness, the Crown Prince… if the examination seems difficult, perhaps it would be better to begin again with the basic courses."
Joseph blinked and returned to his thoughts. He inclined his head politely toward the old man. His voice remained calm.
"Mr. Lagrange, I believe there has been a misunderstanding."
"I asked to take the final examination for your course."
"Not the entrance test."
The old man was not ordinary. His name was Joseph-Louis Lagrange. He was one of the greatest mathematicians in Europe.
"Final examination?"
Lagrange looked at the thirteen-year-old boy standing before him. His brows tightened slightly.
"Your Highness… the material I teach belongs to the university curriculum."
"I'm afraid you—"
Before he could finish speaking, several noble boys nearby looked up from their desks. Some watched with curiosity. Others quietly listened to the conversation.
At that moment, a fourteen-year-old boy wearing a silk coat laughed. His voice carried clear mockery. He spoke loudly enough for everyone to hear.
"Your Royal Highness."
"If I remember correctly, you still have two years before finishing the basic courses."
He then nodded toward Lagrange. His smile did not disappear.
"Mr. Lagrange always says the ladder of mathematics must be climbed step by step."
"Anyone who jumps too high will only fall."
Joseph ignored him completely. He continued looking at Lagrange. His tone remained steady.
"Sir, I have already studied the university mathematics curriculum by myself."
"I truly need to take the final examination."
Lagrange sighed quietly and turned toward his assistant. His tone became more resigned. He pointed toward the folder on his desk.
"André, please bring me the exam paper at the bottom of my folder."
"Of course, Professor."
Soon several sheets of paper were placed before Joseph. He glanced over them quickly. The difficulty was much higher than the previous test.
From the perspective of someone from the 21st century, the questions were not very complicated. Most of them were similar to high-school mathematics. Only a small part involved calculus.
For Joseph, the problems were simple. Because half a month ago he had been a second-year graduate student. His field of study was engineering.
He had come to France with his advisor. They were working on a wind-turbine research project. The accident happened during a tower inspection.
Joseph fell from the top of the tower. When he woke up, everything had changed. His life had become something impossible.
He had traveled back in time. And he had become the eldest son of King Louis XVI of France. The Crown Prince, Louis Joseph.
For unknown reasons, the timeline had slightly changed. He was born several years earlier than in real history. Now he was already thirteen years old.
Joseph lowered his head and began solving the first question. His pen moved steadily across the paper. The room remained quiet.
However, his thoughts were not focused on the exam. They were focused on the future. A very dangerous future.
Because next year the French Revolution would erupt. The royal family would eventually be executed. And as the Crown Prince, he would not escape.
King Louis XVI was famous for repairing locks. Governing the kingdom was another matter. France's finances were already collapsing.
The kingdom owed more than two billion livres in foreign debt. Its yearly income was only five hundred million. The situation was extremely unstable.
Civil servants had stopped receiving salaries. Government departments barely functioned anymore. Trade and administration were slowly breaking down.
Meanwhile the nobles continued living comfortably. Most of them paid no taxes at all. The burden fell entirely on the common people.
And next summer another disaster would arrive. Massive hailstorms would strike farmland across France. Combined with earlier droughts, they would cause famine.
After that, chaos would begin.
Hungry riots would spread through the cities.
The Bastille would fall.
Revolution would ignite across the country.
Joseph quietly counted on his fingers. If he wanted to survive, several problems had to be solved. The list was long.
First, France's financial crisis had to be fixed. Second, food supplies needed to be secured. Third, rebellious nobles needed to be controlled.
Finally, the surrounding powers had to be watched. Britain and Prussia would not ignore France's weakness. Their attention could become dangerous.
But the famine would begin in July. That left him less than half a year. Time was extremely limited.
Joseph rubbed his forehead slightly. Because of his age, he had no right to participate in politics yet. That made everything more difficult.
Not far away, the mocking boy noticed the movement. He believed the Crown Prince was struggling with the problems. His expression showed obvious contempt.
"What an idiot…"
"Claiming he understands university mathematics."
"How embarrassing."
Joseph ignored him completely. His pen continued moving quickly. The first page was finished within minutes.
He turned to the second page. Then the third. The answers appeared rapidly across the paper.
Across the room, Lagrange watched silently. At first he only observed out of curiosity. Soon his attention became serious.
These problems normally required years of study. Yet the Crown Prince solved them one after another. The reasoning remained clear and precise.
Lagrange felt a strange feeling in his chest. Something about the situation seemed unbelievable. He had never seen anything like it before.
"Could it be…"
"Another Leibniz?"
The thought suddenly appeared in his mind. But it sounded almost absurd. Even the legendary Leibniz had entered university at fourteen.
Lagrange quickly wrote several new problems on a blank sheet of paper. Then he handed the paper to Joseph. His eyes remained fixed on the boy.
"Your Highness, there is no need to finish the rest of the exam."
"Just solve these questions."
"I will consider you to have passed."
The slanted-eyed boy laughed quietly. His voice carried open sarcasm.
"Ha."
"Did Lagrange lower the difficulty for him?"
Joseph looked at the new sheet calmly. There were only five questions. Their difficulty was roughly the same.
He immediately began solving them. The first two were completed very quickly. The third question required a proof.
Prove Rolle's Theorem.
Joseph began writing the proof. The reasoning flowed naturally. Within minutes the solution was complete.
But suddenly he noticed something strange. Lagrange was breathing heavily beside him. The old mathematician was staring at the paper.
Joseph looked up in confusion. Then he checked the answer again. Everything seemed correct.
"I didn't make a mistake… did I?"
Lagrange suddenly grabbed the paper. His eyes moved across the lines rapidly. Then he read it again.
"So it works for all differentiable functions…"
"Why didn't I think of that?"
He looked at Joseph with intense excitement.
"Your Highness… how did you come up with this?"
Joseph froze for a moment. Then realization struck him. A small problem had appeared.
Historically, Rolle's theorem had only been proven for polynomials in this era. The general proof would not appear until the nineteenth century. He had just revealed knowledge from the future.
Joseph coughed slightly and reached for the paper.
"Mr. Lagrange…"
"I'll finish the last two questions first."