Who invented calculus?

The dispute over the invention priority of calculus has been going on for more than one hundred years. At that time, even the British and German political circles participated in the debate, and an arbitration commission was established for this purpose. In that 100 years, the British refused to use Leibniz's system, which made their mathematics level lag behind other European countries.

It is now recognized that Newton and Leibniz invented calculus independently. Newton found something between 1665- 1666, but the result was not published until 1704. Lebniz made a discovery between 1673- 1676, and two papers were published in 1684 and 1686 respectively. Their findings all benefited from Fermat's method of finding the extreme value.

Newton made this discovery from the perspective of kinematics, which he called "flow theory". While studying Wallis' book Arithmetic. He extended the binomial theorem to the cases of fractional power and negative exponential power, thus discovering binomial series, and thus establishing the flow number theory of algebraic function and transcendental function. Newton used dots on letters to represent the number of flows, which was interpreted as "a speed, a finite value". Other letters without dots mean "Fluents", while x'o means increment, where o is an infinitesimal quantity. His method is: for a given equation, replace each variable, such as X, with x+x'o, then subtract it from the original equation and divide both sides by O; Because o is an infinitesimal quantity, the term multiplied by it can be ignored. If these terms are removed, the equation about the flow number x' is obtained. However, Newton failed to explain the essence of O.

Leibniz discovered calculus through geometric methods. He made this discovery by studying the works of Descartes and Pascal under the influence of Huygens. Leibniz's first paper on calculus was published in 1684. In this paper, differential symbols and differential laws are used, such as d(uv) = udv+vdu, d (U/V) = (VDU-UDV)/(VV); He also made it clear that dy = 0 is the extreme value and d2y = 0 is the inflection point. 1686, Lebniz published another paper, which expounded the differential law of integral and introduced the integral symbol. Since then, mathematics has entered a period of double harvest. First of all, the Beroulli brothers completely absorbed Lebniz's method, and together they established today's calculus. The first textbook on calculus appeared in 1696. The names and symbols of calculus we are using now belong to Lebnitz. However, like Newton, Leibniz's explanation of the basis of calculus is still vague: dx is sometimes finite, and sometimes it can be less than any non-zero given quantity. It is Cauchy and others who really laid a strict theoretical foundation for calculus.