Vitalik Buterin provides a detailed introduction to Binius, a highly efficient proof system based on binary fields. The article first reviews the concepts of finite fields and arithmetization, explaining how SNARK and STARK proof systems work by converting program statements into polynomial equations. Vitalik points out that although Plonky2 has proven that using smaller 64-bit and 31-bit fields can significantly improve the efficiency of proof generation, Binius further enhances efficiency by operating directly on zeros and ones, taking advantage of the features of binary fields. Binius uses multivariate polynomials to represent computational traces and employs a series of mathematical tricks, including the concept of hypercubes and Reed-Solomon encoding, to construct proofs. Vitalik believes that the direct computational ability of binary fields and operations on bits are key to Binius's efficiency.