Gottfried Wilhelm Leibniz
Born: 1st July, 1646, Leipzig, Germany
Died: 14th November, 1716, Hanover, Germany
Influenced: Ferdinand Georg Frobenius
Education: Leipzig University, University of Altdorf, University of Jena
Influenced by: René Descartes, Baruch Spinoza, Blaise Pascal
Leibniz
pioneered the common discourse of mathematics, including its continuous,
discrete, and symbolic aspects. His ideas on symbolic logic were not pursued
and it was left to Boole to reinvent this almost two centuries later.
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.
Leibniz arranged the coefficients of a system of linear
equations into an array, now called a matrix, in order to find
a solution to the system if it existed. This method was later called Gaussian
elimination. Leibniz laid down the foundations and theory of determinants,
although Seki Takakazu discovered
determinants well before Leibniz. His works
show calculating the determinants using cofactors. Calculating the
determinant using cofactors is named the Leibniz formula.
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 11 November 1675, when
he employed integral calculus for the first time to find the area under the
graph of a function y = f(x).
Leibniz expressed the inverse relation of
integration and differentiation, later called the fundamental theorem of calculus.