In this episode, we review Cauchy’s 1847 paper, which introduced an iterative method for solving simultaneous equations by minimizing a function using its partial derivatives. Instead of elimination, he proposed progressively reducing the function’s value through small updates, forming an early version of gradient descent. His approach allowed systematic approximation of solutions, influencing numerical optimization.This work laid the foundation for machine learning and AI, where gradient-based methods are essential. Modern stochastic gradient descent (SGD) and deep learning training algorithms follow Cauchy’s principle of stepwise minimization. His ideas power optimization in neural networks, making AI training efficient and scalable.
Data Science Decoded