November 11, 1675: Gottfried Leibniz does some math. He was born in Leipzig in the Holy Roman Empire in 1646 and was interested both in mathematics and philosophy. His father was a Professor of Moral Philosophy at the University of Leipzig but died when his son was just six. Leibniz’s mother took over raising the boy and her influence greatly shaped his later philosophical processes. Young Gottfried inherited his father’s library which was vast and all-encompassing. While his formal schooling was limited to a small canon of authorities, his voracious consumption of his private library led to a far more liberal and wide-ranging education and gave him access to advanced philosophical and theological thought than was available to most men before moving on to university work. Since most of the works were written in Latin, Leibniz became proficient in the dead language.
He entered the University of Leipzig at the age of 15 and earned his Bachelor’s degree in 1662 and his Master’s degree in philosophy in 1664. He went on to write several papers and dissertations on his subject of study and earned a Bachelor’s of Law in 1665. In 1666 at age 20, he wrote his first book. He was hoping to earn a Doctorate of Law, but the University refused to grant him such, probably due to his youth. Whatever the reason, the young man was miffed and left town and enrolled in the University of Altdorf, submitted his thesis, and earned a Doctorate of Law there in 1666. He turned down a teaching post and got a job as a secretary to an alchemical society in Nuremberg. He didn’t know much on the subject when he started, but soon taught himself and his reputation grew.
His philosophical endeavors took up his young adulthood and he came later to mathematics. Although the idea of function was implicit in both trigonometric and logarithmic tables of the time, Leibniz was the first to employ it explicitly. He not only used it for the calculus, but also in geometric concepts, although these uses were lost later. He is thought to have developed the calculus independent of Isaac Newton but the issue was hotly debated by both men as well as others in the mathematical community of the day. Leibniz went on to work with topology as well as other matters of science such as physics and geology (before it was even invented). The polymath had an astonishing range in his areas of interest and his ability to understand the world around him.
On this day, Leibniz (according to his notebooks) first used integral calculus. He was looking for the area of the graph of a function y = ƒ(x). Included in his notes were some new ways to encode the mathematical process such as integral sign ∫ representing an elongated S. He chose this sign based on the Latin summa and he used a d for differentials again based on Latin for differentia. While he did not publish anything until 1684, his notations are still used today and the product rule of differential calculus is still called Leibniz’s law. This is not the only law based on his use of the calculus, as the Leibniz integral rule is based on his dictum as to the proper time to differentiate under the integral sign.
Music is the pleasure the human mind experiences from counting without being aware that it is counting.
Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof.
I hold that the mark of a genuine idea is that its possibility can be proved, either a priori by conceiving its cause or reason, or a posteriori when experience teaches us that it is in fact in nature.
The ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God. – all from Gottfried Leibniz
Also on this day: The War to End All Wars – In 1918, World War I ended.
This Isn’t the Hudson – In 1620, the Mayflower Compact was signed.
Mum’s the Word – In 1790, chrysanthemums were introduced into England.
Cold – In 1930, Einstein’s refrigerator was patented.
Fun at School – In 1750, the Flat Hat Club formed.