Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz (or Leibnitz) was a German polymath who lived from 1646 to 1716. He made big contributions in many areas like math, philosophy, science, and even diplomacy. One of his biggest achievements, along with Isaac Newton, was creating calculus, a type of math that helps us understand change.

Leibniz also invented the binary number system, which is the basis of modern computers. He was very interested in many subjects and wrote about theology, ethics, politics, law, history, philology, games, music, and more. His ideas have influenced many fields even today.

Besides math, Leibniz worked on machines that could do calculations automatically. He improved on an earlier machine called Pascal's calculator and designed a new part called the Leibniz wheel that helped make these machines better. His work shows how one person can make a big difference in many areas of knowledge.

Biography

Gottfried Leibniz was born in 1646 in Leipzig, in what is now Germany. His father was a professor, and Leibniz grew up with access to a large personal library. This early exposure to books helped him learn Latin and study many subjects on his own.

Leibniz studied at the University of Leipzig and later the University of Altdorf, where he earned a law degree. He held various positions, including working for an alchemical society and advising important leaders. He traveled to Paris, where he made friends with scientists and mathematicians, and began his own work on mathematics. During this time, he developed his version of calculus.

Later, Leibniz moved to Hanover, where he served the House of Brunswick in many roles, including as a librarian and advisor. He continued his work in mathematics, philosophy, and other subjects, writing many important papers. Despite facing some criticism over his work on calculus, Leibniz remained respected for his wide-ranging contributions to knowledge.

Philosophy

Gottfried Wilhelm Leibniz made many important contributions to philosophy. He wrote several books and many shorter works, though some were published after his death. One of his major works, the Théodicée, was published during his lifetime.

Leibniz’s ideas were shaped by his studies and the thinkers he read. He developed several key philosophical principles, including the identity of indiscernibles, which states that two things are the same if they share all the same properties. He also believed in the principle of sufficient reason, meaning everything must have a reason for existing. Another important idea was pre-established harmony, where everything in the universe works together without directly affecting one another.

Leibniz is especially known for his theory of monads, tiny, simple substances that make up the universe. These monads are unique and reflect the entire universe in their own way. He also wrote about theodicy, trying to explain how a good and powerful God could allow evil and suffering in the world. For Leibniz, this world is the best possible one, created by a perfect God.

Mathematics

Leibniz made many important contributions to mathematics. He was the first to use the word “function” to describe certain geometric ideas, linking shapes and curves in new ways. He also worked on calculating the value of life insurance and helped develop early methods for handling complex math problems, like solving sets of equations together.

Leibniz, along with Isaac Newton, is famous for creating calculus—the math that helps us understand how things change. He introduced important symbols we still use today, like the integral sign ∫ for adding up tiny pieces, and the d for showing small changes. Leibniz also thought about very tiny amounts, called infinitesimals, which helped shape how we do calculus even today. His ideas influenced many areas of math, including shapes and patterns.

Science and engineering

Leibniz made many important contributions to science and engineering. He developed new ideas about motion and energy, and he thought about space and time in ways that were different from other scientists of his time. His ideas about energy influenced physics, and he also had thoughts about the nature of the Earth and living things.

Leibniz was also interested in how the mind and body work together. He believed that our minds and bodies work in harmony, even though they operate in different ways. He also studied how we learn and remember, and his ideas helped shape the field of psychology. In addition to his work in science, Leibniz designed many useful machines and inventions, showing how important it is to combine ideas with practical work.

Law and morality

Leibniz had many ideas about law, ethics, and how governments should work. He believed that while people should usually obey their leaders, there are rare cases where this might not be right. He also dreamed of a united Europe where countries worked together, which some think inspired the European Union much later.

Leibniz studied law and tried to use logical and mathematical thinking to solve legal problems. He thought that learning law should help people think for themselves rather than just follow rules. He also worked hard to bring together different Christian churches, hoping that reason could help heal old divisions.

Philology

Leibniz loved studying languages and was always eager to learn about new words and grammar rules. In 1710, he wrote an essay using ideas about slow, steady change to explain how languages develop. He did not believe that Hebrew was the first language ever spoken, nor that all languages came from a single source. He also disagreed with the idea that an early form of Swedish was the ancestor of the Germanic languages. Leibniz was very interested in the origins of the Slavic languages and was fascinated by classical Chinese. He was also skilled in reading Sanskrit.

He helped publish the first modern edition of a Latin book called the Chronicon Holtzatiae, which told the history of the County of Holstein.

Sinophilia

Leibniz was one of the first major European thinkers to show deep interest in Chinese culture. He corresponded with European Christian missionaries in China and read their works, including Confucius Sinarum Philosophus. Leibniz believed Europeans could learn a lot from the Confucian ethical traditions.

He noticed that the I Ching hexagrams matched binary numbers, which excited him as it connected to his work in mathematics. Leibniz even shared his ideas about the binary system with the Emperor of China, hoping it might help share Christian beliefs. His interest in Chinese philosophy shaped some of his own ideas, like "simple substance" and "pre-established harmony."

Polymath

Gottfried Wilhelm Leibniz traveled across Europe researching the Brunswick family history. While in Vienna from 1688 to 1689, he worked on legal and diplomatic tasks for the Brunswicks. He visited mines, spoke with engineers, and suggested using lamps burning rapeseed oil to light the streets of Vienna, which actually happened. Leibniz also shared ideas with the Austrian Emperor about improving the economy, changing money systems, and setting up new research and archive projects. He also wrote an important paper about mechanics.

Main article: Mechanics

Posthumous reputation

When Leibniz died, people remembered him mostly for one book, Théodicée. A famous writer named Voltaire made fun of Leibniz’s ideas in his book Candide, which affected how people saw Leibniz’s work for a long time. Over the years, more of Leibniz’s writings were published, and people began to appreciate his ideas more.

In the 20th century, scholars started studying Leibniz’s work in depth. Today, many think Leibniz was one of the greatest thinkers of his time. His ideas are still used in philosophy and other subjects. Many places and awards are named after him, like Leibniz University Hannover and the Leibniz Prize. Even today, Leibniz remains a well-known figure, appearing in books, online celebrations, and even giving its name to a popular German biscuit, the Choco Leibniz.

Writings and publication

Leibniz wrote in Latin, French, and German. During his life, he published many articles and two major philosophical books: De Arte Combinatoria and Théodicée. After his death, an important book called Nouveaux essais sur l'entendement humain was found and published much later.

Leibniz left behind thousands of letters and writings, many of which are still being studied today. His works are organized into several groups, including political, philosophical, and mathematical writings. Scholars have been working on collecting and organizing all of his writings since 1901, and this work continues even now. A new edition of his philosophical papers is planned for release in April 2026.

Selected works

The year given is usually that in which the work was completed, not of its eventual publication.

• 1666 (publ. 1690): De Arte Combinatoria ('On the Art of Combination')
• 1667: Nova Methodus Discendae Docendaeque Iurisprudentiae ('A New Method for Learning and Teaching Jurisprudence')
• 1667: "Dialogus de connexione inter res et verba" ('A dialogue about the connection between things and Words')
• 1671: Hypothesis Physica Nova ('New Physical Hypothesis')
• 1673: Confessio philosophi ('A Philosopher's Creed')
• Oct. 1684: "Meditationes de cognitione, veritate et ideis" ('Meditations on Knowledge, Truth, and Ideas')
• Nov. 1684: "Nova methodus pro maximis et minimis" ('New method for maximums and minimums')
• 1686: Discours de métaphysique
• 1686: Generales inquisitiones de analysi notionum et veritatum ('General Inquiries About the Analysis of Concepts and of Truths')
• 1694: "De primae philosophiae Emendatione, et de Notione Substantiae" ('On the Correction of First Philosophy and the Notion of Substance')
• 1695: Système nouveau de la nature et de la communication des substances ('New System of Nature')
• 1700: Accessiones historicae
• 1703: "Explication de l'Arithmétique Binaire" ('Explanation of Binary Arithmetic')
• 1704 (publ. 1765): Nouveaux essais sur l'entendement humain
• 1707–1710: Scriptores rerum Brunsvicensium (3 volumes)
• 1710: Théodicée
• 1714: "Principes de la nature et de la Grâce fondés en raison"
• 1714: Monadologie

Posthumous works

• 1717: Collectanea Etymologica, edited by Johann Georg von Eckhart
• 1749: Protogaea
• 1750: Origines Guelficae

Collections

Six important collections of English translations are Wiener (1951), Parkinson (1966), Loemker (1969), Ariew & Garber (1989), Woolhouse & Francks (1998), and Strickland (2006).