👉 The fourth math, often referred to as "nonstandard analysis," extends traditional real analysis by incorporating infinitesimals—quantities smaller than any positive real number but not zero. Developed by Abraham Robinson in the 1960s, it reintroduces intuitive concepts of infinitesimals and infinite quantities in a rigorous framework using hyperreal numbers, which are extensions of the real number system. Unlike standard calculus, which relies on limits and epsilon-delta definitions, nonstandard analysis uses these infinitesimals directly to simplify proofs and provide alternative insights into calculus, such as treating infinitesimal changes in quantities as meaningful. This approach offers a more algebraic and intuitive foundation for calculus, bridging the gap between intuitive reasoning and formal rigor, and has applications in areas like mathematical physics and economics.
