Kate Jordan
Footnote 18
MAT 266
Naala Brewer
5/5/07
Newton and Leibniz: A Background and Contrast
The ideas and principles of calculus have peppered the mathematical world for centuries. Greeks such as Archimedes and Eudoxus toyed with the essential concepts behind integration as far back as the 4th century B.C.. But calculus as a separate genus of mathematics did not emerge until the 17th century A.D., when such geniuses as Isaac Newton and Gottfried Wilhelm Leibniz untangled such concepts as derivation and integration and brought forward the elegant form of mathematics we employ today.
Born on Christmas Day, 1642, Isaac Newton passed a childhood that was, as far as is known, unremarkable. Entering Cambridge University in 1661, he graduated with a B.A. four years later and eventually took over as Lucasian Professor in 1669, a position he held for twenty-eight years. He was thus greatly connected to the university for much of his life. But ironically, it was during a forced absence from Cambridge, which closed from 1665 through 1666 due to the plague, that he accomplished some of his most famous achievements. From the summer of 1664 through 1666, Newton returned to his home in Lincolnshire and began a serious study of mathematics that resulted in three of his greatest contributions to scientific knowledge, namely the nature of light, gravitational theory and calculus. But, until Principia Mathematica of 1687 and Opticks of 1704, which expanded upon his findings in mechanics and optics, his discovery in the realm of pure mathematics, calculus, remained almost entirely unpublished and hidden from the academic world. Even then, very little was published on solely mathematics. Though Newton complied and organized the results of his research in calculus in 1666 in a manuscript now called “The October 1666 Tract on Fluxions,” this compilation remained largely unseen by the academic world. So thus, while Newton discovered calculus and its complexities as early as 1666, his findings, hidden from view, were, to the rest of the world, as if they had never existed.
In 1646, a few years after the arrival of Newton into the world, there was born another future genius, Gottfried Wilhelm Leibniz. Entering the university at Leipzig at the age of fifteen, graduating with a bachelor’s degree at seventeen, writing a brilliant thesis on law at twenty, and receiving a doctorate in philosophy at twenty-one, he distinguished himself as something extraordinary from the beginning. At twenty-six he was sent to Paris on an errand of diplomacy, and it was during his four years there that he conducted his first serious study of mathematics. In his studies he not only developed his own version of calculus but also created a calculating machine and began what would become a lifelong search for a symbolic logic and universal mathematical language. Leibniz published many of his discoveries in the journal Acta Eruditorum in 1684 and 1686, making his brilliant mathematics available and accessible to many.
In the years after Leibniz published his own conception of calculus, many of Newton’s accused him of working from Newton’s 1666 manuscripts and publishing his own calculus without acknowledgement of Newton’s influence. Unfortunately, these accusations developed into actual charges, and the Royal Society of London, of which Newton was the president and Leibniz a member, appointed a commission to resolve the matter. In 1712, the commission ruled that Leibniz was guilty of plagiarism, a decision that appeared to have less to do with mathematics than an academic rivalry between England and the rest of Europe. The debate of who truly invented calculus seemed not a fight for knowledge or even justice, but for a misplaced national pride. The beautiful analytical methods to which Leibniz so tightly held, as well as his search for basic techniques that can be applied to certain kinds of problems, complimented beautifully Newton’s focus on the intricacies of a particular problem and the discovery of concrete solutions. The mathematical inventions of these two gentlemen are evidence not of plagiarism and credit-stealing, but of two brilliant minds unearthing mathematical principles and each approaching them from unique and mutually advantageous perspectives. Calculus as we know it today would not be the same were it not for the overwhelming contributions of both Newton and Leibniz.
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