👉 Back math, also known as reverse mathematics, is a branch of mathematical logic that seeks to determine the minimal strength of logical axioms needed to prove specific theorems. Instead of starting with a standard set of axioms (like those in Zermelo-Fraenkel set theory) and trying to derive theorems from them, back math works backward by identifying the weakest possible axioms that can support a given theorem. This involves analyzing the logical strength of various mathematical statements and determining which axioms are necessary to ensure their truth. By doing so, back math provides a deeper understanding of the foundational assumptions underlying mathematics and helps clarify the relationships between different mathematical theories. It essentially asks: "What is the smallest set of axioms needed to prove this theorem?" This approach not only aids in understanding the logical structure of mathematics but also reveals connections between seemingly disparate areas of mathematics.
