Gottfried Wilhelm Leibniz was a German polymath active as a mathematician, philosopher, scientist and diplomat who invented calculus in addition to many other branches of mathematics and statistics. Leibniz has been called the "last universal genius" due to his knowledge and skills in different fields and because such people became less common during the Industrial Revolution and spread of specialized labor after his lifetime. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science by devising a cataloguing system whilst working at the Herzog August Library in Wolfenbüttel, Germany, that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to a wide range of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German.
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
Hermann Günther Grassmann was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. His work preceded and exceeded the concept which is now known as a vector space. He introduced the Grassmannian, the space which parameterizes all k-dimensional linear subspaces of an n-dimensional vector space V. In linguistics he helped free language history and structure from each other.
A binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary string of eight bits can represent any of 256 possible values and can, therefore, represent a wide variety of different items.
Religious philosophy is philosophical thinking that is influenced and directed as a consequence of teachings from a particular religion. It can be done objectively, but it may also be done as a persuasion tool by believers in that faith. Religious philosophy is concerned with the nature of religion, theories of salvation, and conceptions of god, gods, and/or the divine.
Thomas Harriot, also spelled Harriott, Hariot or Heriot, was an English astronomer, mathematician, ethnographer and translator to whom the theory of refraction is attributed. Thomas Harriot was also recognized for his contributions in navigational techniques, working closely with John White to create advanced maps for navigation. While Harriot worked extensively on numerous papers on the subjects of astronomy, mathematics and navigation, he remains obscure because he published little of it, namely only The Briefe and True Report of the New Found Land of Virginia (1588). This book includes descriptions of English settlements and financial issues in Virginia at the time. He is sometimes credited with the introduction of the potato to the British Isles. Harriot invented binary notation and arithmetic several decades before Gottfried Wilhelm Leibniz, but this remained unknown until the 1920's. He was also the first person to make a drawing of the Moon through a telescope, on 5 August 1609, about four months before Galileo Galilei.
Early modern philosophy The early modern era of philosophy was a progressive movement of Western thought, exploring through theories and discourse such topics as mind and matter, is a period in the history of philosophy that overlaps with the beginning of the period known as modern philosophy. It succeeded in the medieval era of philosophy. Early modern philosophy is usually thought to have occurred between the 16th and 18th centuries, though some philosophers and historians may put this period slightly earlier. During this time, influential philosophers included Descartes, Locke, Hume, and Kant, all of whom contributed to the current understanding of philosophy.
A centered nonagonal number is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal number for n layers is given by the formula
Universal science is a branch of metaphysics. In the work of Gottfried Wilhelm Leibniz, the universal science is the true logic. The idea of establishing a universal science originated in the seventeenth century with philosophers Francis Bacon and Rene Descartes. Bacon and Descartes conceptualized universal science as a unified approach to collect scientific information similar to encyclopedias of universal knowledge but were unsuccessful. Leibniz extended their ideas to use logic as an "index" to order universal scientific and mathematical information as an operational system with a universal language. Plato's system of idealism, formulated using the teachings of Socrates, is a predecessor to the concept of universal science and influenced Leibniz' s views against materialism in favor of logic. It emphasizes on the first principles which appear to be the reasoning behind everything, emerging and being in state with everything. This mode of reasoning had a supporting influence on great scientists such as Boole, Frege, Cantor, Hilbert, Gödel, and Turing. All of these great minds shared a similar dream, vision or belief in a future where universal computing would eventually change everything.
A Roman dodecahedron or Gallo-Roman dodecahedron is a small hollow object made of copper alloy which has been cast into a regular dodecahedral shape: twelve flat pentagonal faces. Each face has a circular hole of varying diameter in the middle, the holes connecting to the hollow center, and each corner has a protruding knob. Roman dodecahedra date from the 2nd to 4th centuries AD and their purpose remains unknown. They rarely show signs of wear, and do not have any inscribed numbers or letters.
Carl Bernard Pomerance is an American number theorist. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number has at least seven distinct prime factors. He joined the faculty at the University of Georgia, becoming full professor in 1982. He subsequently worked at Lucent Technologies for a number of years, and then became a distinguished Professor at Dartmouth College.
In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron has a right-angle corner, then the square of the area of the face opposite the right-angle corner is the sum of the squares of the areas of the other three faces:
Fritz Alexander Ernst Noether was a Jewish German mathematician who emigrated from Nazi Germany to the Soviet Union. He was later executed by the NKVD.
The problem in number theory known as "Fermat's Last Theorem" has repeatedly received attention in fiction and popular culture. It was proved by Andrew Wiles in 1994.
Dirk van Dalen is a Dutch mathematician and historian of science.
Pollock's conjectures are closely related conjectures in additive number theory. They were first stated in 1850 by Sir Frederick Pollock, better known as a lawyer and politician, but also a contributor of papers on mathematics to the Royal Society. These conjectures are a partial extension of the Fermat polygonal number theorem to three-dimensional figurate numbers, also called polyhedral numbers.
Feminist metaphysics aims to question how inquiries and answers in the field of metaphysics have supported sexism. Feminist metaphysics overlaps with fields such as the philosophy of mind and philosophy of self. Feminist metaphysicians such as Sally Haslanger, Ásta, and Judith Butler have sought to explain the nature of gender in the interest of advancing feminist goals.
Adolf Weiler (1851–1916) was a Swiss mathematician.
In differential geometry, the Tait–Kneser theorem states that, if a smooth plane curve has monotonic curvature, then the osculating circles of the curve are disjoint and nested within each other. The logarithmic spiral or the pictured Archimedean spiral provide examples of curves whose curvature is monotonic for the entire curve. This monotonicity cannot happen for a simple closed curve but for such curves the theorem can be applied to the arcs of the curves between its vertices.
Julia Antonovna Rozanska was a Soviet topologist. After studying under Pavel Aleksandrov, she was an associate professor at Moscow State University. She was a member of the Moscow Mathematical Society. She attended the First International Topological Conference, Moscow, 1935.
