Descartes' Love Letter

In 1650, on the streets of Stockholm, 52-year-old Descartes met 18-year-old Swedish Princess Christina. At that time, Descartes, who was down and out and penniless, led a life of begging. All he had were his tattered clothes and a few mathematics books he carried with him.

Descartes, who was proud and aloof, never asked passers-by for alms. He just silently lowered his head and wrote and drew on paper, lost in his mathematical world.

One peaceful afternoon, Descartes sat as usual on the street, basking in the sunlight and studying mathematical problems. Suddenly, someone came up to him and patted him on the shoulder, "What are you doing?" Turning around, Descartes saw a young and beautiful face with clear eyes like a blue lake, charming and alluring, and long eyelashes blinking. She was the little princess of Sweden, the king's most beloved daughter, Christina.

She knelt down, took Descartes' mathematics book and draft paper, and started a conversation with him. During their talk, he found that this little girl was quick-witted and had a strong interest in mathematics.

After saying goodbye to the girl, Descartes gradually forgot about it and continued to sit on the street every day, writing and drawing. A few days later, he unexpectedly received a notice that the king had hired him as the princess's mathematics teacher. Descartes, full of doubts, followed the guard who came to notify him to the palace. While waiting in the reception hall, he heard a tinkling laugh from afar. Turning around, he saw the girl he had met on the street a few days ago. In a hurry, he quickly bowed his head in greeting. From then on, he became the princess's mathematics teacher.

Under Descartes' careful guidance, the princess's mathematics improved rapidly, and they began to grow closer. Descartes introduced her to his new field of study - the Cartesian coordinate system. Through it, algebra and geometry could be combined, which was the prototype of analytic geometry that Descartes later created. Under Descartes' guidance, Christina entered the wonderful world of coordinates and became fascinated by curves. Their constant presence together also made them fall in love with each other. In this romantic country of Sweden, a pure and beautiful love quietly blossomed.

However, not long after, their love affair reached the king's ears. The king was furious and ordered Descartes to be executed immediately. At Christina's earnest pleading, the king exiled him back to France and imprisoned the princess in the palace. At that time, the Black Death was prevalent in Europe. Descartes, who was weak and frail, fell seriously ill shortly after returning to France. In the days when his life was running out, he missed the princess day and night and wrote to her every day, hoping for her reply. However, all these letters were intercepted by the king, and the princess never received any news from him. After Descartes sent the thirteenth letter to Christina, he passed away forever. At that time, the little princess, still imprisoned in the palace, wandered in the palace corridors, missing her lover far away. This last letter contained no words, only an equation: r = a(1 - sinθ).

The king couldn't understand it and thought that this equation contained a secret that the two of them couldn't reveal. He summoned all the mathematicians in the city to the palace, but none of them could solve this function. He couldn't bear to see his beloved daughter sad every day, so he gave her the letter. Christina was overjoyed when she received the letter. She immediately understood her lover's intention and took out paper and a pen to draw the graph of the equation. A heart-shaped pattern appeared before her eyes, and Christina couldn't help shedding tears of emotion. This curve is the famous "heart-shaped curve". After the king's death, Christine ascended the throne. Immediately after her coronation, she sent people to France to search for the whereabouts of her beloved, but the news she received was Descartes' death. This left her with a lasting regret...

This unconventional love letter that has gained worldwide fame is still preserved in the Descartes Memorial in Europe, commemorating this beautiful love story.