During the Renaissance in Western Europe, a rediscovery and advancement of classical mathematics laid the foundation for the empiricism of the Science Revolution. One of the pillars of this intellectual reawakening in mathematics was the increased use of mathematical symbols that enabled scholars to more easily and accurately communicate with each other across geographical, national, and linguistic boarders. more
At the dawn of the 18th century scientific and Western theology was based on the concept of an unchanging, immutable God ruling a static universe. For theologians, Newtonian physics and the rise of mechanistic explanations of the natural world held forth the promise of a deeper understanding of the inner workings of the Cosmos and, accordingly, of the nature of God. During the course of the 18th century, however, there was a major conceptual rift between science and theology that was reflected in a growing scientific disregard for understanding based upon divine revelation and growing acceptance of an understanding of Nature based upon natural theology. By the end of the 18th century, experimentation had replaced scripture as the determinant authority in science. Enlightenment thinking, spurred by advances in the physical sciences, sent sweeping changes across the political and social landscape.
Throughout the 18th century English physicist Sir Isaac Newton's (1642-1727) Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) first published in 1687, dominated the intellectual landscape. Moreover, Newton actively wrote and modified his observations during the first quarter of the 18th century. In addition to the elaboration of physics and calculus, however, Newton also concerned himself with the relationship between science and theology. Without question, Newton was the culminating figure in the Scientific Revolution of the 16th and 17th centuries and the leading articulator of the mechanistic vision of the physical world initially put forth by French mathematician Rene Descartes (1596-1650). Within his own lifetime Newton saw the rise and triumph of Newtonian physics, and the widespread acceptance of a mechanistic concept regarding the workings of the universe among philosophers and scientists.
Newtonian laws -- and a well-functioning clockwork universe -- depended upon the deterministic effects of gravity, electricity, and magnetism. In such a universe matter was passive, moved about and controlled by "active principles". For Newton, who rejected the mainstream Trinitarian concepts of Christianity, the order and beauty found in the universe, was God. Newton argued that God set the Cosmos in motion, and to account for small differences between predicted and observed results, God actively intervened from time to time to reset or "restore" the mechanism.
Theologians and scientists were deeply concerned about the moral implications of a scientific theories that explained everything as the inevitable consequence of mechanical principles. Accordingly, much effort was expended to reconcile Newtonian physics -- and a clockwork universe -- with conventional theology to provide an on-going and active role for God. Objective evidence regarding the universe was often sifted through theological filters that evaluated whether a set of facts of theories tended to prove or disprove the existence of God. Ironically, it was this interplay between religion and science that led many to subsequently insist on a strong scientific objectivity that largely discounted religious subjectivity. more
During the European Dark Ages there was no coherent system of scientific or philosophical thought. Throughout Western Civilization, theological doctrine and dogma replaced the rational and logical inquiry of the ancient Greek scholars. During the 13th and 14th centuries, however, the rediscovery of Aristotle's (384-322 B.C.) philosophy, as preserved by Arabic scholars, renewed interest in the development of logic and scientific inquiry. The critical writings of St. Thomas Aquinas (1227-1274), Roger Bacon (1214-1294) and William Ockham (also spelled Occham, 1285-1347/49) regarding Aristotelian ideas ultimately laid the intellectual foundations for the 17th century Scientific Revolution by de-emphasizing the primacy of understanding based upon scriptural revelation or authority.
Although the origins of astronomy and cosmology predate the human written record, by the height of ancient Greek civilization the cause of natural phenomena was attributed to the collective whim of a pantheon of Gods. Although monotheistic in the same sense as was ancient Judaism, out of this pantheism (a theology that includes multiple Gods) arose the idea that there was an infinite being, Plato's (c. 428 - c.347 B.C.), "The One," and Aristotle's (384-322 B.C.) "prime mover.' Aristotle's influence over astronomy and cosmology was to extend for nearly two millennia and, as a set of philosophical and scientific explanations of the universe, Aristotle's assertions ultimately became integral to the tightly interwoven fabric of philosophy, science, and theology that came to dominate the late Medieval intellectual landscape. more
The content of the Moscow and Rhind Papyruses shed considerable light on the nature and extent of ancient Egyptian mathematics. Both papyri provide vivid documentary evidence of geometrical reasoning in the Egyptian Twelfth Dynasty and insight into the practical applications of mathematics prior to the more formal development of mathematical theory in ancient Greece. A careful analysis of the mathematical presentation and content of the two documents, however, limits the claims of Egyptian influence upon the later rise of theory in Greek mathematics.
The physical archaeological record leaves little doubt as to the use and influence of mathematics on ancient Egyptian culture. Temples and other cultural artifacts provide extensive evidence of mathematical reasoning that predates the existing documentary record. The arrangement of pillars and stones in temple monuments, such as those found at Karnak, are lasting tribute to the careful calculations of ancient priests and astronomers in their attempt to provide accurate calendars based upon the movements of the Sun.
Whatever the initial need for a written record, whether its first use was as a more portable means of recording and deciphering astronomical data, or whether the general rise of civilization provided a swelling and multifaceted need to record the methods of mathematical reasoning, the earliest existing documentary records embodied in the Moscow papyrus and the Rhind papyrus, disclose that the ancient Egyptians utilized considerable practical skill in the use and application of mathematics. (more)
Advances in 19th century concepts of electromagnetism moved rapidly from experimental novelties to prominent and practical applications. At the start of the century gas and oil lamps burned in homes, but by the end of the century electric light bulbs illuminated an increasing number of electrified homes. By mid-century (1865) a telegraph cable connected the United States and England. Yet, within a few decades, even this magnificent technological achievement was eclipsed by advancements in electromagnetic theory that spurred the discovery and development of the radio waves that sparked a 20th century communications revolution. So rapid were the advances in electromagnetism that by the end of the 19th century high-energy electromagnetic radiation in the form of x-rays was used to diagnose injury. The mathematical unification of 19th century experimental work in electromagnetism profoundly shaped the relativity and quantum theories of 20th century physics.
In the late 18th and 19th centuries philosophical and religious ideas led many scientists to accept the argument that seemingly separate forces of nature (e.g., electricity, magnetism, light, etc.) shared a common and fundamental source. In addition, profound philosophical and scientific questions posed by Issac Newton's Optics (published in 1704) regarding the nature of light still dominated the 19th century intellectual landscape. Accordingly, in addition to a search for a common source of all natural phenomena, an elusive "ether" through which light could pass was thought necessary to explain the wave-like behavior of light.
The discovery of the relationship between electricity and magnetism at the end of the 18th century and the beginning of the 19th century was hampered by a rift in the descriptions and models of nature used by mathematicians and experimentalists. To a significant extent, advances in electromagnetic theory during the 19th century mirrored unification of these approaches. The culmination of this merger coming with Scottish physicist James Clerk Maxwell's (1831-1879) development of a set of equations that accurately described electromagnetic phenomena better than any previous non-mathematical model.
The development of Maxwell's equations embodied the mathematical genius of the German mathematician Carl Fredrich Gauss (1777-1855), the reasonings and laboratory work of French scientist Andre Marie Ampere (1775-1836), the observations of Danish scientist Hans Christian Oersted (1777-1851), and a wealth of experimental evidence provided by English physicist and chemist Micheal Faraday (1791-1867). (more)
Nucleosynthesis is the process of building nuclei of atoms heavier than hydrogen. The Big Bang produced hydrogen, helium, and some lithium, but all later creation of higher weight atoms has occurred in the hearts of stars via nucleosynthesis. All elements heavier than hydrogen of which Earth and humans are made were forged in stellar interiors by nucleosynthesis.
Until the second half of the nineteenth century, astronomy was principally concerned with accurately describing the movements of planets and stars. Developments in the electromagnetic theory of light in the late nineteenth century along with the articulation of quantum and relativity theories in the early twentieth century, however, gave astronomers the tools they needed to probe the inner workings of the sun and other stars. In the first two-thirds of the century, astronomers and physicists unraveled the life cycles of most types of stars and reconciled the predictions of physical theory with astronomical observation. Insights into the birth and death of stars led to the stunning conclusion that Earth and all life upon it, including human beings, are in a direct and physical sense a product of stellar evolution. In astronomy, the term "evolution" is used to name the orderly process by which individual stars change as they age: stellar evolution is unrelated to biological evolution. more
Lerner KL. ** The Bohr Model of the Atom. Draft Copy. Part of a series of essays identifying and explaining theories essential to understanding modern scientific thought. Updated: 2010, 2012. Originally Published. 1999.Abstract
The Bohr model of atomic structure was developed by Danish physicist and Nobel laureate Niels Bohr (1885-1962). Published in 1913, Bohr's model improved the classical atomic models of physicists J. J. Thomson and Ernest Rutherford by incorporating quantum theory. While working on his doctoral dissertation at Copenhagen University, Bohr studied physicist Max Planck's quantum theory of radiation. After graduation, Bohr worked in England with Thomson and subsequently with Rutherford. During this time Bohr developed his model of atomic structure. (more)
Compared to their male counterparts, disproportionately fewer female students go on to take advanced or elective science at the secondary school level. Consequently, disproportionately fewer women pursue university degrees or careers in mathematics, science and engineering. Although more female students are taking elective secondary school math and science courses, these disproportions remain significant. Based on a comprehensive survey of research and field reports, this paper outlines and evaluates the theory and methodology behind attempts -- particularly those emphasizing reading and writing skills -- to meet the specific needs of female students and asserts that addressing gender inequity is a “win-win” for teachers who desire to enhance education for all students. (more)
Compared to their male counterparts, disproportionately fewer female students go on to take advanced or elective science at the secondary school level. Consequently, disproportionately fewer women pursue university degrees or careers in mathematics, science and engineering. Although more female students are taking elective secondary school math and science courses, these disproportions remain significant. Based on a comprehensive survey of research and field reports, this paper outlines and evaluates simple modifications to expository instruction-particularly those emphasizing reading and writing skills-that enable teachers to better meet the specific needs of female students. (more)