History of mathematics

Gottfried Wilhelm Leibniz (July 1, 1646 – November 14, 1716) was one of the last polymaths of modern times. Leibniz had various talents, was a philosopher and mathematician, physicist and engineer, jurist and diplomat, historian and librarian, and much more, in one person. As a councillor at noble houses, he even was indirectly involved in European politics.

His imagination went as far as postulating lifelong aims like collecting all human knowledge, looking for a lingua universalis or developing the calculus differentialis et integralis. In philosophy, he is most remembered for optimism, i.e., his conclusion that our universe is, in a restricted sense, the best possible one God could have made. He was, along with René Descartes and Baruch Spinoza, one of the three great 17th century rationalists, but his philosophy also both looks back to the Scholastic tradition and anticipates modern logic and analysis.

Leibniz has influenced the development of mathematics decisively; he had the gift to collect knowledge of his time, select the important bits, generalise and develop them further in new theories. In this way, he independently developed the calculus differentialis et integralis in a consistent manner; including the fundamental theorem, the 'dx notation' and the integral sign, showing his ingenious sense for an easy notation and formal symbolic logic which is fundamental to modern mathematics. Additonally he had an extrodinary talent for designing calculating machines on the basis of his discovery, the binary system. Another important piece of mathematical work undertaken by Leibniz was his work on dynamics. He criticised Descartes' ideas of mechanics and examined what are effectively foundations of modern physics . Although he sometimes lacked the patience or the will to develop the ideas conceived by his wide-ranging imagination, it now appears that he also was a pioneer in combinatorics, mathematical logic and topology, beeing way ahead of contemporaries, but due to his fragmentary publications beeing difficult to access for fellow mathematicians.

His contributions to this vast array of subjects are scattered in journals and in tens of thousands of letters and unpublished manuscripts. To date, there is no complete edition of Leibniz's writings available (although the Leibniz Society is working on it), and a complete account of his accomplishments is not yet possible. During his whole lifetime Leibniz traveled through Europe and exchanged views with internationally renowned scientists, and put much energy in promting scientific societies. Finally, in 1700 he persuaded the later king of prussia, Frederick I., to install the academy of sciences in Berlin following the english and french examples, setting standards for the German Science Community of these days – Leibniz, of course became its first president, and Frederick is quoted to have said that even if all members of the academy would dissappear, with his knowledge, Leibniz could run the academy of sciences on his own.

Ingo Witzke