Sunday, October 21, 2007

Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz was born on July 1, 1646 in Leipzig, Saxony which, today, is part of Germany. His father was a professor of moral philosophy at the University of Leipzig which had opened in Saxony in 1409. His father died when Gottfried was six years old. Young Leibniz inherited his father's library.

Leibniz was raised by his mother. At age seven, he entered the Nicolai School in Leibzig. Leibniz immersed himself in self-study in an effort to be able to read his father's books. By the age of 12 he had grown very advanced in Latin and had begun to study Greek. He would later write about his dissatisfaction with the logic of Aristotle.

At 14, he entered the University of Leipzig where he most likely studied philosophy, mathematics, rhetoric, Latin, Greek, and Hebrew. During the summer of 1663, he visited the University of Jena where he gained his first exposure to fundamental mathematical ideas such as proofs. Leipzig at the time was not very strong in mathematics so it is believed that Jena played a very important role in the development of his understanding of mathematics. Leibniz was greatly influenced by the ideas of Erhard Weigel who believed that all the universe could be viewed in terms of numbers.

Leibniz received his bachelors degree in law and a masters in philosophy from Leipzig. Despite this great progress, when he presented his thesis for his doctorate, his advancement was denied. The details for why this occurred are unclear. Normally, this meant that Leibniz would need to wait a year before resubmitting his doctoral thesis. Instead, Leibniz presented his doctorate thesis to the University of Altdorf where he gained his doctorate.

Leibniz was offered a position at the University of Altdorf which he decided not to accept. Later, he made the acquaintance of Baron Johann Christian von Boineburg. He soon had become "secretary, assistant, librarian, lawyer, and advisor the Baron and his family." (E J Aiton, Leibniz: A biography, Bristol-Boston, 1984) At this point, Leibniz's interests and works rested primarily in literary ambitions. One writer noted that during this period of Leibniz's life, he would have passed as "a typical late renaissance humanist." (G M Ross, Leibniz, Oxford, 1984)

In 1672, Leibniz was sent by Boineburg to meet with the French in an effort to dissuade Louis XIV from invading the German regions. Leibniz put forward a plan of invading Egypt that was very similar to the plan the Napolean would later carry out. At this point, Leibniz met the mathematicians and scientists of Paris. In particular, he studied mathematics and science under Christian Huygens from the Netherlands. His ventures in math and science in Paris were more successful than his political efforts.

Baron Boineburg died on December 15 of 1672. The Baron's family continued to sponsor Leibniz. In January of 1673, Leibniz gave up on his efforts at peace in Paris and went now to England to convince the British of peace. There, he met with Hooke, Boyle, and Pell. Leibniz presented his ideas for an automatic counting machine. On April 19, 1673, Leibniz was elected as a member to the Royal Society of London. Once again, his scientific pursuits were more successful than the political ones.

In 1674, Leibniz began to take interest in the problem of infinitesimals. He corresponded with Oldenburg from the Royal Society who let him know that Newton and Gregory had found very general methods to the problem. By autumn of 1676, Leibniz had worked out much of his notation for calculus. At this time, he received a letter from Newton. In 1677, he received a second letter from Newton. In this second letter, Newton questions whether Leibniz stole Newton's method. Newton pointed out that not a "single previously unsolved problem was solved." (Quoted in the MacTutor article) Later, Leibniz's notation would prove very important in the advancement of calculus.

Leibniz had hoped to join the Academy of Sciences in Paris but no opportunity to join came his way. In October of 1676, he accepted a position as librarian and Court Councillor to the Duke of Hanover, Johann Friedrich.

During this time, Leibniz worked on many outside projects. He worked unsuccessfully on developing wind-powered pumps to drain water from the Harz mountain mines. From these efforts, he developed his knowledge of geology and proposed a theory that the earth was at one time molten lava.

By 1679, he had developed a "binary system of arithmetic." He also worked on the problem of determinants which had written around 1684.

In 1680, the Duke of Hanover died and Leibniz began working for his brother Ernst August. Leibniz began to work on the family tree which included the House of Brunswick. As part of this effort, he traveled to Bavaria, Austria, and Italy. In each of these places, he met with scholars and other famous writers. He would publish the results of his research in nine large volumes. Still, he never completed the work that Ernst August had requested.

In 1684 and 1686, Leibniz began to publish his theory of calculus. The next year, in 1687, Newton published his Principia.

In 1710, Leibniz published Theodicee in which he argued that even if the world is not perfect, it is the best possible world. In 1714, he published his famous work Monadologia.

Unfortunately, it was the dispute with Newton that filled his last years. The main argument against Leibniz were the two letters that he had received from Oldenburg. Leibniz claimed that there was not enough information presented in the letters to give him the methods he found. In 1711, a paper by Keill was read to the Royal Society which accused Leibniz of plagiarism. In 1713, the Royal Society investigated the issue and ruled against Leibniz. Leibniz was never asked to give his version of events and Newton himelf wrote the final report.

In 1714, George Ludwig from the House of Hanover became King of England. Leibniz was not invited to join him.

Leibniz died on November 14, 1716. In his life, he had corresponded with over 600 figures of his time. The Berlin Academy of Science emerged as the result of Leibniz's work. While it is clear that Newton invented calculus first, it is also clear that Leibniz extended Newton's work in very important ways that Newton did not appreciate.