Leibniz, Gottfried Wilhelm

Leibniz was born in Leipzig, Germany. At a young age, he was given access to the library that his father had assembled. Leibniz thus became acquainted with a wide range of classical writers and began omnivorous reading that was his habit throughout his life. At the age of fifteen, Leibniz entered the University of Leipzig, where he received most of his formal education. His interest in mathematics was aroused by the numerous remarks on the importance of the subject that he encountered in his reading of philosophical works. Later he attended the University of Altdorf, near Nuremberg, where he received a doctorate in law. He practiced law in Paris to support his study of mathematics.

Leibniz summed sequences of reciprocal polygonal numbers and, following the work of St. Vincent, summed and analyzed geometric sequences. He studied trigonometric functions from the works of Huygens. In 1671 Leibniz developed a machine that could not only add and subtract but also multiply, divide, and extract square roots. The Leibniz calculator was gear-operated, and it provided a carry from one order to the next. His machine was the first general-purpose calculator whose principles are still used in mechanical calculating machines. Late in 1675, Leibniz laid the foundations of both integral and differential calculus. In the calculus, Leibniz developed the present-day notation and many computational methods for the derivative and integral. Although he never thought of the derivative as a limit, he discovered many of the results we now study in calculus. Along with Newton, Leibniz is given credit by most sources as the developer of calculus.

"It is unworthy of excellent men to lose hours like slaves in the labor of calculation which could safely be regulated to anyone else if machines were used."

"Taking mathematics from the beginning of the world to the time of Newton, what he has done is much the better half."