# Account of the life and accomplishments of gottfried von leibniz

Version for printing Gottfried Leibniz was the son of Friedrich Leibniz, a professor of moral philosophy at Leipzig. Friedrich Leibniz [ 3 ]: Leibniz's mother was Catharina Schmuck, the daughter of a lawyer and Friedrich Leibniz's third wife. However, Friedrich Leibniz died when Leibniz was only six years old and he was brought up by his mother. Certainly Leibniz learnt his moral and religious values from her which would play an important role in his life and philosophy.

## Gottfried Leibniz

Although he was taught Latin at school, Leibniz had taught himself far more advanced Latin and some Greek by the age of 12. He seems to have been motivated by wanting to read his father's books. As he progressed through school he was taught Aristotle 's logic and theory of categorising knowledge. Leibniz was clearly not satisfied with Aristotle 's system and began to develop his own ideas on how to improve on it. In later life Leibniz recalled that at this time he was trying to find orderings on logical truths which, although he did not know it at the time, were the ideas behind rigorous mathematical proofs.

As well as his school work, Leibniz studied his father's books. In particular he read metaphysics books and theology books from both Catholic and Protestant writers.

He studied philosophy, which was well taught at the University of Leipzig, and mathematics which was very poorly taught. Among the other topics which were included in this two year general degree course were rhetoricLatin, Greek and Hebrew. In this there is the beginning of his notion of "monad". Leibniz then went to Jena to spend the summer term of 1663. At Jena the professor of mathematics was Erhard Weigel but Weigel was also a philosopher and through him Leibniz began to understand the importance of the method of mathematical proof for subjects such as logic and philosophy.

- Sophie, his wife, became Leibniz's friend and supporter and through her Leibniz was able to continue his scientific activities;
- Leibniz realised that his knowledge of mathematics was less than he would have liked so he redoubled his efforts on the subject;
- Sophie, his wife, became Leibniz's friend and supporter and through her Leibniz was able to continue his scientific activities;
- As the War of the Spanish Succession broke out in 1701, Hanover and Prussia had to face each other in opposite sides, which naturally made Leibniz's position even more troublesome;
- Leibniz settled in Frankfurt am Main.

Weigel believed that number was the fundamental concept of the universe and his ideas were to have considerable influence of Leibniz. By October 1663 Leibniz was back in Leipzig starting his studies towards a doctorate in law. He was awarded his Account of the life and accomplishments of gottfried von leibniz Degree in philosophy for a dissertation which combined aspects of philosophy and law studying relations in these subjects with mathematical ideas that he had learnt from Weigel.

A few days after Leibniz presented his dissertation, his mother died. After being awarded a bachelor's degree in law, Leibniz worked on his habilitation in philosophy.

In this work Leibniz aimed to reduce all reasoning and discovery to a combination of basic elements such as numbers, letters, sounds and colours. Despite his growing reputation and acknowledged scholarship, Leibniz was refused the doctorate in law at Leipzig. It is a little unclear why this happened. It is likely that, as one of the younger candidates and there only being twelve law tutorships available, he would be expected to wait another year.

However, there is also a story that the Dean's wife persuaded the Dean to argue against Leibniz, for some unexplained reason. Leibniz declined the promise of a chair at Altdorf because he had very different things in view. He served as secretary to the Nuremberg alchemical society for a while see [ 187 ] then he met Baron Johann Christian von Boineburg. By November 1667 Leibniz was living in Frankfurt, employed by Boineburg. During the next few years Leibniz undertook a variety of different projects, scientific, literary and political.

He also continued his law career taking up residence at the courts of Mainz before 1670. One of his tasks there, undertaken for the Elector of Mainz, was to improve the Roman civil law code for Mainz but [ 3 ]: Boineburg was a Catholic while Leibniz was a Lutheran but Leibniz had as one of his lifelong aims the reunification of the Christian Churches and [ 30 ]: Another of Leibniz's lifelong aims was to collate all human knowledge.

Certainly he saw his work on Roman civil law as part of this scheme and as another part of this scheme, Leibniz tried to bring the work of the learned societies together to coordinate research. Leibniz began to study motion, and although he had in mind the problem of explaining the results of Wren and Huygens on elastic collisions, he began with abstract ideas of motion.

In this work he claimed, as account of the life and accomplishments of gottfried von leibniz Keplerthat movement depends on the action of a spirit.

He communicated with Oldenburg, the secretary of the Royal Society of Londonand dedicated some of his scientific works to the Royal Society and the Paris Academy. Leibniz was also in contact with Carcavithe Royal Librarian in Paris. As Ross explains in [ 30 ]: All his life he prided himself on his poetry mostly Latinand boasted that he could recite the bulk of Virgil 's "Aeneid" by heart. During this time with Boineburg he would have passed for a typical late Renaissance humanist.

Leibniz wished to visit Paris to make more scientific contacts. He had begun construction of a calculating machine which he hoped would be of interest.

He formed a political plan to try to persuade the French to attack Egypt and this proved the means of his visiting Paris. His first object in Paris was to make contact with the French government but, while waiting for such an opportunity, Leibniz made contact with mathematicians and philosophers there, in particular Arnauld and Malebranchediscussing with Arnauld a variety of topics but particularly church reunification.

In Paris Leibniz studied mathematics and physics under Christiaan Huygens beginning in the autumn of 1672. On Huygens ' advice, Leibniz read Saint-Vincent 's work on summing series and made some discoveries of his own in this area. Also in the autumn of 1672, Boineburg's son was sent to Paris to study under Leibniz which meant that his financial support was secure.

Accompanying Boineburg's son was Boineburg's nephew on a diplomatic mission to try to persuade Louis XIV to set up a peace congress. Boineburg died on 15 December but Leibniz continued to be supported by the Boineburg family. In January 1673 Leibniz and Boineburg's nephew went to England to try the same peace mission, the French one having failed.

Leibniz visited the Royal Societyand demonstrated his incomplete calculating machine. He also talked with HookeBoyle and Pell. While explaining his results on series to Pellhe was told that these were to be found in a book by Mouton. The next day he consulted Mouton 's book and found that Pell was correct. At the meeting of the Royal Society on 15 February, which Leibniz did not attend, Hooke made some unfavourable comments on Leibniz's calculating machine.

Leibniz returned to Paris on hearing that the Elector of Mainz had died. Leibniz realised that his knowledge of mathematics was less than he would have liked so he redoubled his efforts on the subject. Leibniz met Ozanam and solved one of his problems. He began to study the geometry of infinitesimals and wrote to Oldenburg at the Royal Society in 1674. Oldenburg replied that Newton and Gregory had found general methods.

Leibniz was, however, not in the best of favours with the Royal Society since he had not kept his promise of finishing his mechanical calculating machine. Nor was Oldenburg to know that Leibniz had changed from the rather ordinary mathematician who visited London, into a creative mathematical genius.

In August 1675 Tschirnhaus arrived in Paris and he formed a close friendship with Leibniz which proved very mathematically profitable to both. It was during this period in Paris that Leibniz developed the basic features of his version of the calculus. In 1673 he was still struggling to develop a good notation for his calculus and his first calculations were clumsy.

- As always Leibniz took the opportunity to meet with scholars of many different subjects on these journeys;
- However, when Newton wrote to him directly, Leibniz did reply and gave a detailed description of his discovery of the differential calculus.

In the same manuscript the product rule for differentiation is given. Newton wrote a letter to Leibniz, through Oldenburg, which took some time to reach him. The letter listed many of Newton 's results but it did not describe his methods.

Leibniz replied immediately but Newtonnot realising that his letter had taken a long time to reach Leibniz, thought he had had six weeks to work on his reply. Certainly one of the consequences of Newton 's letter was that Leibniz realised he must quickly publish a fuller account of his own methods.

Newton wrote a second letter to Leibniz on 24 October 1676 which did not reach Leibniz until June 1677 by which time Leibniz was in Hanover. This second letter, although polite in tone, was clearly written by Newton believing that Leibniz had stolen his methods.

In his reply Leibniz gave some details of the principles of his differential calculus including the rule for differentiating a function of a function. Newton was to claim, with justification, that. Leibniz never thought of the derivative as a limit. This does not appear until the work of d'Alembert. Leibniz would have liked to have remained in Paris in the Academy of Sciencesbut it was considered that there were already enough foreigners there and so no invitation came.

The rest of Leibniz's life, from December 1676 until his death, was spent at Hanover except for the many travels that he made. His duties at Hanover [ 30 ]: He undertook a whole collection of other projects however. For example one major project begun in 1678-79 involved draining water from the mines in the Harz mountains. His idea was to use wind power and water power to operate pumps.

He designed many different types of windmills, pumps, gears but [ 3 ]: Leibniz himself believed that this was because of deliberate obstruction by administrators and technicians, and the workers' fear that technological progress would cost them their jobs. The Harz project had always been difficult and account of the life and accomplishments of gottfried von leibniz failed by 1684.

However Leibniz had achieved important scientific results becoming one of the first people to study geology through the observations he compiled for the Harz project.

- As he progressed through school he was taught Aristotle 's logic and theory of categorising knowledge.
- This second letter, although polite in tone, was clearly written by Newton believing that Leibniz had stolen his methods. The next day he consulted Mouton 's book and found that Pell was correct.
- In particular he read metaphysics books and theology books from both Catholic and Protestant writers.
- The paper contained the familiar d notation, the rules for computing the derivatives of powers, products and quotients. The contributions Leibniz made to a wide range of philosophical and scientific fields is among the most stunning achievements by any single individual in all of history.
- While explaining his results on series to Pell , he was told that these were to be found in a book by Mouton.

During this work he formed the hypothesis that the Earth was at first molten. Another of Leibniz's great achievements in mathematics was his development of the binary system of arithmetic. He perfected his system by 1679 but he did not publish anything until 1701 when he sent the paper Essay d'une nouvelle science des nombres to the Paris Academy to mark his election to the Academy.

Another major mathematical work by Leibniz was his work on determinants which arose from his developing methods to solve systems of linear equations. Although he never published this work in his lifetime, he developed many different approaches to the topic with many different notations being tried out to find the one which was most useful.

An unpublished paper dated 22 January 1684 contains very satisfactory notation and results. Leibniz continued to perfect his metaphysical system in the 1680s attempting to reduce reasoning to an algebra of thought. Another major project which Leibniz undertook, this time for Duke Ernst August, was writing the history of the Guelf family, of which the House of Brunswick was a part.

He made a lengthy trip to search archives for material on which to base this history, visiting Bavaria, Austria and Italy between November 1687 and June 1690. As always Leibniz took the opportunity to meet with scholars of many different subjects on these journeys.