Mathematics has always been a territory of paper, pencil, and human intuition. However, a profound change is on the horizon. Researchers like Kevin Buzzard are leading an effort to translate complex theorems into a language that machines can verify. This process of formalization demands an unprecedented level of detail, challenging the traditional way of doing mathematics.
Formalization and Computer-Assisted Verification 🤖
The core of this change lies in formal verification systems like Lean. These languages force the decomposition of every statement, no matter how obvious it seems, into elementary logical steps. Thus, a classic multi-page proof can become thousands of lines of code. The goal is not only to verify known results but to build a digital library of mathematics where no error can persist, serving as a foundation for more complex explorations.
Goodbye to it is obvious and welcome to compilation error ⚠️
The traditional mathematician could skip a complicated step with an elegant the conclusion follows trivially. Now, the verifier responds with a cold type error or an "unproven goal" message. Imagine Fermat writing his famous margin note and, upon trying to compile it, receiving a notification that he is missing 357 intermediate lemmas. It is the end of the era of intellectual glamour and the beginning of the reign of compulsive rigor. Your intuition is no longer a valid argument.