Leibniz and Newton have equal achievements in establishing calculus. From the time of invention, Newton was earlier than Leibniz; In terms of publication time, Leibniz preceded Newton. It is recognized that Newton and Leibniz are both inventors of calculus, and their calculus has its own characteristics. Newton and Leibniz worked from different angles, independently discovered the basic theorem of calculus and established an effective differential and integral algorithm. They all liberated calculus from the geometric form, adopted algebraic method and notation, expanded its application range from the surface, and reduced the area, volume and problems previously regarded as sum to integral (inverse differential). In this way, the problems of speed, tangent, extreme value and summation all come down to differential and integral.

Newton studied calculus from the angle of mechanics or kinematics, starting with the concept of speed and considering the problem of speed. Newton called his discovery "flow counting", and he called the continuously changing quantity flow or flow; Call an infinitesimal time interval instantaneous; Flow rate, that is, the rate of change of flow in an infinitely small time, is called flow rate or flow number. Therefore, Newton's "flow number method" is a calculus with the basic concepts of flow, flow number and instantaneous. Leibniz, on the other hand, emphasizes the concept of tangent from the perspective of geometry and starts with the problem of finding tangent. He studied the relationship between finding the tangent of the curve and finding the area under the curve, and clearly pointed out that differential and integral are two mutually inverse operation processes.

Because Leibniz's differential symbols and integral symbols are easy to understand and easy to use, they have been used by people ever since.