Why did Isaac Newton and Gottfried Wilhelm Leibniz argue about the invention of calculus?

The dispute between Isaac Newton and Gottfried Wilhelm Leibniz over the invention of calculus was a bitter conflict centered on priority and the relative merits of their respective mathematical methods.1

Both men independently discovered the fundamental theorem of calculus—Newton in the 1660s and Leibniz in the 1670s—but their approaches differed significantly. Newton developed a method of "fluxions" based on kinematics, viewing variables as magnitudes that flow over time. Conversely, Leibniz developed a general algorithm using infinitesimals and introduced the now-standard notation of $d$ and $\int$.21

The argument arose because both mathematicians sought credit for the invention of this powerful new tool. Newton’s tendency to delay publication and his personal reticence allowed Leibniz to publish his work first in 1684, leading to a priority dispute. Ultimately, history has distributed the credit: Newton is recognized for his early originality, while Leibniz is credited for developing the superior, highly influential symbolic notation that remains the foundation of modern calculus.12