Infinitesimals are quantities that are extremely small, approaching zero but never actually reaching it. They are used in mathematics, particularly in calculus, to help understand concepts like limits and derivatives. The idea allows mathematicians to analyze changes and motion in a precise way, even when dealing with very tiny values. The concept of infinitesimals was formalized in the 17th century by mathematicians such as Isaac Newton and Gottfried Wilhelm Leibniz. In modern mathematics, infinitesimals are rigorously defined within the framework of non-standard analysis, which provides a way to work with these tiny quantities systematically.