Though Newton had been the first to derive calculus as a mathematical approach, Leibniz was the first one to widely disseminate the concept throughout Europe. This was perhaps the most conclusive evidence that Newton and Leibniz were both independent developers of calculus. Newton’s timeline displays more evidence of inventing calculus because of his refusal to use theories or concepts to prove his answers, while Leibniz furthered other mathematician’s ideas to collaborate and bring together theorems for the application of calculus. The history of calculus developed as a result of sequential events, including many inventions and innovations, which led to forward thinking in the development of the mathematical system.
In this essay, published in 1738, Voltaire explains the philosophies of not only Newton, but in a large part Descartes because of his contributions in the fields of geometry. In Voltaire's concise explanation of Newton's and other philosophers' paradigms related in the fields of astronomy and physics, he employs geometry through diagrams and pictures and proves his statements with calculus. Voltaire in fact mentions that this essay is for the people who have the desire to teach themselves, and makes the intent of the book as a textbook. In 25 chapters, and every bit of 357 pages, as well as six pages of definitions, Voltaire explains Newton's discoveries in the field of optics, the rainbow spectrum and colors, musical notes, the Laws of Attraction, disproving the philosophy of Descarte's cause of gravity and structure of light, and proving Newton's new paradigm, or Philosophy as Voltaire would have called it. Voltaire in a sense created the idea that Newton's principles were a new philosophy and acknowledged the possibility for errors.
The Abbasid dynasty was well reigned throughout the ninth century. Two important characters were Harun el-Rashed (786-809) and his son, al-Ma'mun (813-833) "who founded an astronomical observation and created a foundation for translating classical Greek works. "(p.171) Since Arabs conquered many of the rich provinces from the old Roman Empire they themselves were also becoming very wealthy with Baghdad as the trade center for the Middle East and Europe. Unfortunately for the empire there was at some point an awful fight between two brothers for the succession to the caliphate. This obviously hurt the Abbasids because they lost many monuments and people lost property.
Islam and Science The 6th century Islamic empire inherited the scientific tradition of late antiquity. They preserved it, elaborated it, and finally, passed it to Europe (Science: The Islamic Legacy 3). At this early date, the Islamic dynasty of the Umayyads showed a great interest in science. The Dark Ages for Europeans were centuries of philosophical and scientific discovery and development for Muslim scholars. The Arabs at the time assimilated the ancient wisdom of Persia and the classical heritage of Greece, as well as adapting their own ways of thinking (Hitti 363).
From about the 11th Century Adelard of Bath, then later Fibonacci, brought this Islamic mathematics and its knowledge of Greek mathematics back into Europe. Major progress in mathematics in Europe began again at the beginning of the 16th Century with Pacioli, then Cardan, Tartaglia and Ferrari with the algebraic solution of cubic and quartic equations. Copernicus and Galileo revolutionised the applications of mathematics to the study of the universe. The progress in algebra had a major psychologic... ... middle of paper ... ...ever have taken place without logs. Then the world changed.
It is so important for modern people to look back on the contributions of this amazing society and to ponder what can be learned from them and their inventions. Today’s society and mathematical understanding would not be nearly as advanced if it had not been for the Babylonians. The people of today are forever indebted to them. Their achievements in mathematics are astounding to modern minds because we assume that such mathematical concepts are more modern in origin. But the proof is there, on those tablets, the ones baked in the Sun.
While Europe was experiencing the Dark Ages, Islam was experiencing a time of intense philosophical and scientific achievements. The Islamic empire in the eight century preserved and elaborated scientific tradition. They assimilated ancient wisdom and adapted it to their own needs and thinking. Islamic civilization expanded society as a whole and made great contributions in many fields, such as science, math, medicine, theology, and architecture. Without the contributions made by the Islamic culture, the Renaissance Era would not have been the same.
Rene Descartes was a famous French mathematician, scientist and philosopher. He was arguably the first major philosopher in the modern era to make a serious effort to defeat skepticism. His views about knowledge and certainty, as well as his views about the relationship between mind and body have been very influential over the last three centuries. Descartes was born at La Haye (now called Descartes), and educated at the Jesuit College of La Flèche between 1606 and 1614. Descartes later claimed that his education gave him little of substance and that only mathematics had given him certain knowledge.
Helena M. Pycior’s essay “At the Intersection of Mathematics and Humor: Lewis Carroll’s Alices and Symbolical Algebra” attempts to explain Carroll’s wit through concepts in Symbolical Algebra (which is today more commonly known as simply Symbolic Algebra or included in the related subject, Abstract Algebra). The first section of the essay begins with a rather detailed history of the development of Symbolical Algebra, and outlines some of the concepts the subject addresses. Pycior deals very little with Carroll in the first two-thirds of the article, focusing instead on George Peacock, Augustus De Morgan, and William Frend, all of whom were accomplished mathematicians. Eventually Pycior connects Carroll to the others by pointing out their common interests and influences. George Peacock was the mathematician who first “chose to redefine algebra as a science dealing with undefined signs and symbols, governed by laws of the mathematician’s making.” (Pycior 152) This redefinition was necessary, because in the years leading up ... ... middle of paper ... ...bjects of scrutiny in abstract algebra and linguistics, respectively.
WE limit the series, we make it finite by imposing boundaries on it and by instituting “rules of membership”: “A series of all the real numbers up to and including 1000” . Such a series has no continuation (after the number 1000). But, then, the very concept of continuation is arbitrary. Any point can qualify as an end (or as a beginning). Are the statements: “There is an end”, “There is no continuation” and “There is a beginning” – equivalent?