👉 Heel math, also known as non-standard analysis, is a mathematical framework that extends the real number system by introducing infinitesimals—quantities smaller than any positive real number but not zero. Developed by Abraham Robinson in the 1960s, it provides a rigorous foundation for calculus and infinitesimal calculus, which traditional methods struggle to formalize. Instead of relying on limits (a concept from standard analysis), heel math uses infinitesimals directly, allowing mathematicians to manipulate them algebraically as if they were finite numbers. This approach simplifies proofs of fundamental theorems like the derivative (via infinitesimal changes in variables) and integrals (by treating infinitesimal areas or volumes as exact quantities), offering intuitive insights while maintaining the precision of standard calculus. It bridges the gap between intuitive geometric reasoning and rigorous analysis, making it a powerful tool for both theoretical exploration and practical problem-solving in fields like physics and engineering.
