Mathematical concepts from quaternions to tensors power modern AI

Robin Arionhold explores the history of mathematics in his new book, "Vectors," tracing how mathematical language shaped modern science.

The author explains how the evolution of physics, from Isaac Newton's classical mechanics to Albert Einstein's theory of relativity, relied on revolutionary ways to represent the world. The book focuses on vectors and tensors as foundational tools. Unlike simple numbers, vectors represent both magnitude and direction, while tensors handle information across multiple dimensions.

These concepts allowed scientists to describe the movement of objects and the laws of nature. Arionhold notes that these ideas faced intense debate in the late 19th century, with figures like Peter Tait and Josiah Willard Gibbs arguing over vector analysis in journals like Nature. Today, these mathematical tools extend far beyond physics. They help search engines process data like publication dates and authors, and they allow researchers to analyze brain waves and heart signals.

The author concludes that the mathematics powering modern artificial intelligence is the result of 5,000 years of human discovery and scholarly dispute.