What mathematical advances occurred during the Scientific Revolution of the 17th century?

The 17th century, a pivotal era of the Scientific Revolution, was a period of intense mathematical innovation that shifted the focus of the field from classical Greek geometry toward analysis.1

Key advancements during this period included:

• Analytic Geometry: Developed independently by René Descartes and Pierre de Fermat, this breakthrough connected algebra and geometry by using coordinate systems to represent curves through equations.23
• Calculus: The invention of differential and integral calculus emerged from methods for finding tangents, maximum/minimum points, and areas under curves. Isaac Newton significantly advanced this field through his work on infinite series, which he viewed as an algebraic extension of arithmetic.124
• Logarithms: John Napier introduced logarithms as a computational device to simplify complex calculations, such as multiplication and division, which were essential for astronomy.5
• Notation and Methods: Mathematicians adopted symbolic algebra and improved notation, allowing for greater flexibility in symbolic manipulation and the systematic study of polynomial equations.13

These developments, often closely associated with advancements in physics and mechanics, established the foundation for modern mathematical practice.1