3.4 Asia — Bridges and Mirrors

Bridges and Mirrors: How Early Modern Asia Revealed the Universality of Mathematical StructuresA bridge connects what was separated. A mirror reveals that the same face can appear on both sides.In this episode, we discover the great encounter of East-West knowledge—and the parallel discoveries that prove certain mathematical truths are universal.In 1581, an Italian Jesuit named Matteo Ricci arrived in China. For twenty-eight years, he learned Chinese, dressed as a Confucian scholar, and undertook with mathematician Xu Guangqi the first translation of Euclid's Elements into Chinese. This bridge remained open for nearly a century and a half, until the Jesuits' expulsion in 1723.You will meet Leibniz, fascinated by what he learned of China. In 1703, the Jesuit Joachim Bouvet revealed to him that the hexagrams of the I Ching formed a binary system—exactly what Leibniz had just published. "I cannot sufficiently admire this manner," he exclaimed. A fertile misunderstanding: Leibniz saw it as proof of reason's universality; the Chinese saw something quite different.You will discover Seki Takakazu, the "Japanese Newton." In a Japan closed to the world by sakoku, this samurai-turned-mathematician developed the theory of determinants on his own—before Leibniz published his own work. He discovered Bernoulli numbers before Bernoulli. These troubling mirrors suggest that mathematical structures are discoveries, not inventions.And Jyeshtadeva, in Kerala, who wrote around 1530 the Yuktibhasa—the first treatise expounding the concepts of infinitesimal calculus, a century before Newton and Leibniz. The question remains open: did this knowledge travel to Europe via trade routes? Or was it discovered independently?Early Modern Asia teaches us two things. First: bridges are fragile—the Rites Controversy ended the Jesuit exchange. Second: mirrors are everywhere—human intelligence, confronted with certain problems, tends to find certain solutions. This universality makes artificial intelligence possible.