What Is the Future of Mathematics?

For thousands of years, since the Babylonians and before, humans have studied the mysteries of pure mathematics. These studies probably started practically, as ways to understand the stars and the world around us as well as economics and government, but quickly turned to the beauty of pure math: number theory, proofs, irrational numbers and geometry. Unlike most other sciences, which have direct application to human lives [^astro], we don’t study pure math in the hope of improving human lives, curing disease, inventing new technology or saving the planet. It’s just beautiful and deep and mysterious. [^astro]: With the possible exceptions of astrophysics, which is fairly remote from practical applications, and a few others like logic, arguably a branch of mathematics. Of course all studies can lead to applications; cryptography and modern crypto-based finance are good examples. With the recent near-lightspeed improvement of large language models and AI reasoning systems, machines are…