Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz was a genius in many fields including law, religion, statecraft, history, literature, logic, metaphysics, and speculative philosophy. Leibniz, born on July 1, 1646, applied mathematical reasoning to the phenomena of the physical universe. He imagined calculus and combinatorial analysis.

Leibniz lost his father at the age of six and so he was largely self-taught by constant reading in his father’s library. At the age of eight he began the study of Latin and by age twelve had mastered it enough to compose creditable Latin verse. From Latin he went on to Greek which he also learned largely by his own efforts. Classical studies soon were not enough for Leibniz’s mental development, therefore he began studying logic. Before the age of fifteen he came up with the first clues to his metaphysics while attempting to reform logic.

Leibniz received his bachelor degree from the University of Leipzig in 1663 at the age of seventeen with a magnificent essay foreshadowing one of the doctrines of his mature philosophy. Leibniz received his doctor’s degree from the University of Altdorf for his essay on a new method of teaching law. In his essay called a “schoolboys essay”, Leibniz describes a general method in which all truths of reason would be reduced to a kind of calculation. “At some time this would be a sort of universal language or script, but infinitely different from all those projected hitherto; for the symbols and even the words in it would direct the reason; and errors, except those of fact, would be mere mistakes in calculation. It would be very difficult to form or invent the language or characteristic, but very easy to understand it without dictionaries.” (p. 123, Bell) In 1664, Leibniz introduced the word function into mathematics, symbolizing it by dy/dx with the concept being: if y and x are two variables so related that whenever a numerical value is assigned to x there is determined a numerical value of y, then y is called a (one-valued, or uniform) function of x. This can be symbolized by writing  y = f(x).

In a letter written on September 8, 1679, Leibniz speaks of geometry in particular and tells Christian Huygens of a “new characteristic, entirely different from Algebra, which will have great advantages for representing exactly and naturally to the mind, and without figures, everything that depends on the imagination.(p.123, Bell) This new characteristic is now called symbolic logic. Leibniz formulated the principal properties of logical addition and logical multiplication, negation, identity, the null class and class inclusion.

Leibniz also invented a calculating machine which handled addition, subtraction, multiplication, division and extraction of roots. Prior to Leibniz, calculating machines could only add and subtract. He was elected a foreign member of the Royal Society for his work on his calculating machine. He and his mathematical rival, Isaac Newton, became the first foreign members of the French Academy of Science. There is no way to mention in an article of this size everything that Leibniz did in his lifetime and the many discoveries that were influenced after his death on November 14, 1716. Leibniz was a “universal genius” responsible for many discoveries in the world of mathematics as well as many other fields of study.

Contributed by Kristen Shelton


  1. Bell, E.T., Men of Mathematics, Simon and Schuster, New York 1937.
  2. Boyer, Carl B., A History of Mathematics, John Wiley & Sons, Inc., New York 1989.
  3. Calinger, Ronald, Classics of Mathematics, Prentice Hall, New Jersey1995.

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