Gottfried Leibniz was a German mathematician who developed the present day notation for the differential and integral calculus though he never thought of the derivative as a limit. His philosophy is also important and he invented an early calculating machine.

Gottfried Leibniz was the son of Friedrich Leibniz, a professor of moral philosophy at Leipzig. Friedrich Leibniz 

Leibniz's mother was Catharina Schmuck, the daughter of a lawyer and Friedrich Leibniz's third wife. However, his father  died when Leibniz was only six years old and he was brought up by his mother. Certainly Leibniz learnt his moral and religious values from her which would play an important role in his life and philosophy.

At the age of seven, Leibniz entered the Nicolai School in Leipzig. Although he was taught Latin at school, Leibniz had taught himself far more advanced Latin and some Greek by the age of 12. He seems to have been motivated by wanting to read his father's books. As he progressed through school he was taught Aristotle's logic and theory .

 In 1661, at the age of fourteen, Leibniz entered the University of Leipzig

He studied philosophy, which was well taught at the University of Leipzig,. He graduated with a bachelors degree in 1663 with a thesis De Principio Individui  

between his work on philosophy and logic and his day job as a politician and representative of the royal house of Hanover, Leibniz still found time to work on mathematics.

He was perhaps the first to explicitly employ the mathematical notion of a function to denote geometric concepts derived from a curve, and he developed a system of infinitesimal calculus

in Paris that Leibniz developed the basic features of his version of the calculus. 

Another of Leibniz's great achievements in mathematics was his development of the binary system of arithmetic. He perfected his system by 1679 but he did not publish anything until 1701 when he sent the paper Essay d'une nouvelle science des nombres to the Paris Academy to mark his election to the Academy. Another major mathematical work by Leibniz was his work on determinants which arose from his developing methods to solve systems of linear equations. 

Although the mathematical notion of function was implicit in trigonometric and logarithmic tables, which existed in his day, Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular.^[65] In the 18th century, "function" lost these geometrical associations.

Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system, if any. This method was later called Gaussian elimination. 

Leibniz is credited, along with Sir Isaac Newton, with the discovery of calculus (differential and integral calculus). According to Leibniz's notebooks, a critical breakthrough occurred on November 11, 1675, when he employed integral calculus for the first time to find the area under the graph of a function y = ƒ(x).^] The product rule of differential calculus is still called "Leibniz's law". In addition, the theorem that tells how and when to differentiate under the integral sign is called the Leibniz integral rule.

Leibniz , he was charming, well-mannered, and not without humor and imagination.^[41] He had many friends and admirers all over Europe. on the other hand  he never married

Leibniz died in Hanover in 1716: at the time, he was so out of favor that neither George I (who happened to be near Hanover at that time) nor any fellow courtier other than his personal secretary attended the funeral. Even though Leibniz was a life member of the Royal Society and the Berlin Academy of Sciences, neither organization saw fit to honor his passing. His grave went unmarked for more than 50 years.