# Mathematician:Gottfried Wilhelm von Leibniz

## Contents

## Mathematician

German mathematician and philosopher who is best known for being the co-inventor (independently of Isaac Newton) of calculus.

Took some of the first philosophical steps towards a system of symbolic logic, but his works failed to have much influence on the development of logic, and these ideas were not developed to any significant extent.

Invented the system of binary notation.

Discovered and proved what is now known as Wilson's Theorem.

Posed what is now known as Leibniz's Question: "Is there an algorithm for deciding which statements of number theory are true?"

Became a friend of Christiaan Huygens, who became his mentor in mathematics.

Invented a better calculating machine than Blaise Pascal had done.

Coined the term dynamics for the study of bodies in motion.

Made significant contributions towards the understanding of kinetic energy.

Solved the problem of the catenary.

Gave the first analysis of the forces within a loaded beam.

Devised the notation $\displaystyle \int$ to denote the operation of integration, and at the same time $\d$ to denote differentiation.

Some sources credit him with inventing the technique of of the use of integrating factors, although that is generally believed to have been the work of Leonhard Paul Euler, independently of both Alexis Claude Clairaut and Alexis Fontaine des Bertins, who are also credited with this technique.

## Nationality

German

## History

- Born: 1 July 1646, Leipzig, Saxony (now Germany)
- 1652: The death of his father propelled him to self-educate
- 1661: Entered University of Leipzig to study law
- 1666: Applied for degree of Doctor of Law but was refused. Enrolled at Altdorf in Nuremberg instead.
- 1667: Secured position as legal advisor to Prince Elector of Mainz
- March 1672: Visited Paris on a diplomatic mission, in which he was unsuccessful, but stayed in Paris anyway
- January 1673: Visited England on a diplomatic mission for Elector of Mainz. Elected a member of the Royal Society.
- 1673: Death of Elector of Mainz. Took up service with John Frederick, Duke of Brunswick-Lüneburg
- 1676: Entered into a correspondence with Isaac Newton
- 1676: Left Paris to return to Hanover by way of London and Holland
- Died: 14 Nov 1716, Hannover, Hanover (now Germany)

## Theorems and Definitions

- Leibniz's Law
- Leibniz's Alternating Series Test (also known as the Alternating Series Test)
- Leibniz's Rule
- Leibniz's Integral Rule
- Leibniz's Question
- Leibniz's Formula for Pi
- Leibniz Harmonic Triangle

Results named for **Gottfried Wilhelm von Leibniz** can be found here.

Definitions of concepts named for **Gottfried Wilhelm von Leibniz** can be found here.

Axioms named for **Gottfried Wilhelm von Leibniz** can be found here.

## Publications

- 1666:
*De Casibus Perplexis in Jure*(On Perplexing Cases in the Law) - 1666:
*Dissertatio de Arte Combinatoria*(On the Art of Combination) - 1666:
*Nova Methodus Docendae Discendaeque Jurisprudentiae*(A New Method for Teaching and Learning Jurisprudence) - 1671:
*Hypothesis Physica Nova*(New Physical Hypothesis) - 1673:
*Confessio Philosophi*(A Philosopher's Creed) - 1682: Founded the journal
*Acta Eruditorum* - October 1684:
*Nova methodus pro maximis et minimis*(*Acta Eruditorum***Vol. 1684**,*no. $\text{X}$*: 467 – 473) - 1686:
*Systema Theologicum* - June 1686:
*De geometria recondita et analysi indivisibilium atque infinitorum*(*Acta Eruditorum***Vol. 1686**,*no. $\text{VI}$*: 292 – 300) - 1686:
*De geometria recondite et analysi indivisibilium atque infinitorum* - 1686:
*Discours de métaphysique* - 1703:
*Explication de l'Arithmétique Binaire*(Explanation of Binary Arithmetic) - 1704:
*Nouveaux essais sur l'entendement humain* - 1710:
*Essais de Théodicée* - 1714:
*Monadologie*

### Posthumous Publications

- 1749:
*Protogaea* - 1765:
*New Essays on Human Understanding*(written in 1704)

## Notable Quotes

*With every lost hour a part of life perishes.*

*I prefer a Leeuwenhoek who tells me what he sees to a Cartesian who tells me what he thinks. It is, however, necessary to add reasoning to observation.*

*In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.*- --- Letter to Ehrenfried Walther von Tschirnhaus

*I have so many ideas that may perhaps be of some use in time if others more penetrating than I go deeply into them some day and join the beauty of their minds to the labour of mine.*

*Music is a secret arithmetical exercise and the person who indulges in it does not realize that he is manipulating numbers.*

*How extremely distracted I am cannot be described. I dig up various things from the archives, examine ancient documents, and collect unpublished manuscripts. From these I strive to throw light on the history of Brunswick. I receive and send letters in great numbers. I have, indeed, so much that is new in mathematics, so many thoughts in philosophy, so many other literary observations which I do not wish to have perish, that I am often bewildered as to where to begin.*- -- $1695$, in a letter

## Critical View

*There is a book which should be written, and its title should be*The Mind of Leibniz*.*

## Also known as

Some sources render his name as **Leibnitz**. This is generally considered to be erroneous.

Some do not present the "von", and instead render the name as **Gottfried Wilhelm Leibniz**.

## Sources

- John J. O'Connor and Edmund F. Robertson: "Gottfried Wilhelm von Leibniz": MacTutor History of Mathematics archive

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VII}$: Master of All Trades - 1946: Alfred Tarski:
*Introduction to Logic and to the Methodology of Deductive Sciences*(2nd ed.) ... (previous) ... (next): $\S \text{II}.6$: Logical Constants (footnote) - 1951: Willard Van Orman Quine:
*Mathematical Logic*(revised ed.) ... (previous) ... (next): Introduction - 1952: H.T.H. Piaggio:
*An Elementary Treatise on Differential Equations and their Applications*(Revised ed.) ... (previous) ... (next): Historical Introduction (footnote) - 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (previous) ... (next): $\S 1.1$: Symbolic Logic and Classical Logic - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $10$ - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**Leibniz, Gottfried Wilhelm**(1646-1716) - 1991: David Wells:
*Curious and Interesting Geometry*... (previous) ... (next): A Chronological List Of Mathematicians - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($\text {1646}$ – $\text {1716}$) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $10$ - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Leibniz, Gottfried Wilhelm**(1646-1716) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Leibniz, Gottfried Wilhelm**(1646-1716) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $8$: The System of the World - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Leibniz, Gottfried Wilhelm**(1646-1716)