Chapter I: A Most Unusual Pupil

Palace of Versailles, East Wing — Early Winter, 1787

A pale December light filtered through the gilded windows of Versailles, catching on the gold leaf that adorned the elaborate rococo moldings of the room. Beneath a towering crystal chandelier, which cast trembling reflections across marble and oil canvas alike, sat a boy not yet reached his full height, his delicate features bathed in flickering light.

The young Prince Joseph—eldest son of His Majesty King Louis XVI—regarded the parchment before him with a faint, amused smile, as though the mathematical symbols were little more than trifles to be toyed with.

An elderly gentleman stood nearby, bowing slightly. His white wig curled with meticulous care, and a fine lace cravat peeked from beneath his embroidered waistcoat. His tone, though respectful, bore the heavy sigh of disappointment.

"Your Highness," he said gravely, "if this proves too great a challenge, might I suggest you begin with the more elementary coursework?"

Joseph blinked, then, as if awoken from a pleasant daydream, inclined his head politely. "Monsieur Lagrange, I fear there has been a misunderstanding. I did not request the entrance examination. I am here for the final."

The elder man—none other than the eminent Joseph-Louis Lagrange, famed throughout Europe as the Prince of Mathematics—furrowed his brow. "The final? My dear Crown Prince, these are lectures in advanced mathematical theory. The realm of the university, not the nursery."

Across the room, other noble sons, bedecked in silks and powdered wigs, lifted their heads at the exchange, eyes filled with a mixture of curiosity and condescension. One among them, a youth of sixteen with half-lidded eyes and an ornate coat stitched in gold thread, scoffed aloud.

"Your Highness," he called mockingly, "should you not first master your numbers before seeking to tame the stars? As Monsieur Lagrange oft reminds us, one must ascend the staircase of knowledge step by step. Leap too quickly, and you shall surely fall."

Joseph paid him no heed. He turned once more to Lagrange, his voice firm yet respectful. "Monsieur, I have already studied these university texts on my own. I assure you, I am prepared."

The mathematician exhaled slowly and turned to his assistant. "Andrei, be so good as to fetch the examinations from the very bottom of my folder—the true final."

"Yes, Professor."

In short order, several pages, heavy with difficult problems, were set before the prince. Joseph perused them swiftly. Though markedly more complex than the earlier test, they posed little threat to one whose education had taken place not in this world—but in the next.

Only weeks before, he had stood in the 21st century, pursuing graduate studies in engineering. A fateful accident atop a modern French tower had flung him through time itself. Now he lived in the body of Louis Joseph—eldest son of Louis XVI, reborn with knowledge far beyond the reach of this age.

As his quill danced across the page, he thought grimly of the storm that brewed just beyond the horizon. In but a year, the Bastille would fall. The monarchy would crumble. France, bled by debt and swollen by famine, would rise in violent revolt. And as heir to the throne, he would find himself squarely in the path of the blade.

He considered his impossible task. To survive, he must do the following: solve the kingdom's debt crisis; secure food for the starving poor; restrain treacherous nobles; and outmaneuver Britain and Prussia, ever eager to feast upon France's weakness.

He rubbed his temples. A boy of thirteen, denied entrance to the halls of state, his hands tied by youth and protocol. A dreadful game of chess had begun—and his side was short a queen.

Not far off, the boy with the drooping eyes mistook Joseph's moment of pause for frustration. He smirked cruelly. "Fool. Thinks himself capable of university work? What embarrassment! The crown ought to be mine, not his."

Joseph ignored him, flipping the page. Once he passed this test, his agreement with Queen Marie would be fulfilled. She had promised him that upon the completion of his studies at the University of Paris, he might begin his participation in affairs of state.

With knowledge centuries ahead of this world, he had already bested most courses in mere weeks—slowed only by the need to unlearn the erroneous "truths" of the time.

Lagrange, having abandoned all interest in the other students, now stared, transfixed, at Joseph's swift progress. The boy was completing problems meant for scholars five years his senior—and without error. It defied belief.

Could it be… another Leibniz, reborn in silk and lace?

A doubt crept in. Lagrange narrowed his gaze and glanced at his assistant. Had Andrei perhaps slipped the exam questions to the prince beforehand?

No. It was too much. Too precise.

Suddenly, he tore a slip of parchment from his notes, scribbled several lines upon it, and presented it to the prince.

"Your Highness," he said with gravitas, "you needn't continue with the full exam. These few questions will suffice to prove your merit."

The boy with the lazy eyes sneered again. "Ha! Now he shields the boy, lest he fail too publicly. Fools, the lot of them."

Joseph glanced at the page. Only five questions remained, though of no lesser difficulty. He welcomed the challenge, scribbling quickly through the first two. The third made him pause—it requested a proof of Rolle's Theorem.

He smiled faintly. A simple matter.

Rolle's Theorem: If a function f is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there exists some c in (a, b) such that f'(c) = 0...

His pen flew across the parchment. Yet when he looked up, he found Lagrange clutching the paper with the awe of a man who had seen the face of God.

"This…" the old scholar whispered, "for differentiable functions… Yes, yes—it holds! Why had I not thought of it?"

He turned to Joseph, his voice trembling. "Your Highness… how came you to such an insight?"

Joseph blanched. Ah… right. This wasn't discovered until the 19th century.

He coughed, hastily retrieving the paper. "A fortunate guess, perhaps. Shall I continue with the last two questions, Monsieur?"

Lagrange nodded absently, still marveling at the boy before him. For in that gilded study, beneath the flicker of candlelight and the hush of old France, it was clear to all: the Crown Prince was no ordinary child.

He was a man out of time, and his moment had just begun.