Vitalik: Expect more improvements to binary field-based proofs in the coming months

Vitalik Buterin, co-founder of Ethereum, has released the latest blog "Binius: Efficient Proofs for Binary Fields". This post is mainly aimed at readers who are generally familiar with cryptography in the 2019 era, especially SNARKs and STARKs. Over the past two years, STARKs have become a critical, irreplaceable technology for efficiently making easily verifiable cryptographic proofs of very complex statements (e.g., proving that an Ethereum block is valid).
The way SNARK and STARK prove a computer program is by arithmetic: the statement of the program to be proved is transformed into a mathematical equation involving a polynomial. A valid solution to an equation corresponds to a valid execution of the program. In general, a zero-knowledge proof system works by making a statement about a polynomial, along with a statement about the underlying evaluation.
How does Binius affect "SNARK-friendly"? The basic generalization is that if you use Binius, you no longer need to care too much about whether the computation is "arithmetic-friendly": "regular" hashes are no longer more efficient than traditional arithmetic hashes, nor are multiplicative modules more efficient than traditional arithmetic hashes. I expect more improvements in binary field-based proofs in the coming months.