Explore Newton's method for finding zeroes in this comprehensive mathematics video. Delve into the ingenious technique developed by the 17th-century scientific giant Isaac Newton for approximating solutions to equations. Learn how to apply this method to the quadratic polynomial x^2, using algebraic calculus to calculate tangent lines and approximate the square root of 2. Discover the fascinating connection between Newton's method and ancient Babylonian algorithms. Follow along as the video demonstrates the step-by-step process, including recursion and different initial values. Compare two distinct algorithms for solving x²=2 and practice finding approximate square roots through guided exercises. Gain valuable insights into this fundamental mathematical concept that bridges ancient and modern problem-solving techniques.