Instruct: Given a question, retrieve relevant documents that answer the question.
Query: Who invented Boolean logic?
The syllogistic logic developed by Aristotle predominated in the West until the mid-19th century, when interest in the foundations of mathematics stimulated the development of symbolic logic (now called mathematical logic). In 1854, George Boole published "An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities", introducing symbolic logic and the principles of what is now known as Boolean logic. In 1879, Gottlob Frege published "Begriffsschrift", which inaugurated modern logic with the invention of quantifier notation. From 1910 to 1913, Alfred North Whitehead and Bertrand Russell published "Principia Mathematica" on the foundations of mathematics, attempting to derive mathematical truths from axioms and inference rules in symbolic logic. In 1931, Gödel raised serious problems with the foundationalist program and logic ceased to focus on such issues.
In the late 1980s, Berners-Lee, then a scientist at CERN, invented the World Wide Web to meet the demand for simple and immediate information-sharing among physicists working at CERN and different universities or institutes all over the world.
Circa 1797, Count Rumford (born Benjamin Thompson) showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824. By 1860, as formalized in the works of those such as Rudolf Clausius and William Thomson, two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist Josiah Willard Gibbs, in his memoir "Graphical Methods in the Thermodynamics of Fluids", clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.
It was invented between the 1st and 4th centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the 9th century. Influential were the books of Muḥammad ibn Mūsā al-Khwārizmī ("On the Calculation with Hindu Numerals", ) and Al-Kindi ("On the Use of the Hindu Numerals", ). The system later spread to medieval Europe by the High Middle Ages.
In 1946, John Mauchly made the first mention of binary search as part of the Moore School Lectures, a seminal and foundational college course in computing. In 1957, William Wesley Peterson published the first method for interpolation search. Every published binary search algorithm worked only for arrays whose length is one less than a power of two until 1960, when Derrick Henry Lehmer published a binary search algorithm that worked on all arrays. In 1962, Hermann Bottenbruch presented an ALGOL 60 implementation of binary search that placed the comparison for equality at the end, increasing the average number of iterations by one, but reducing to one the number of comparisons per iteration. The uniform binary search was developed by A. K. Chandra of Stanford University in 1971. In 1986, Bernard Chazelle and Leonidas J. Guibas introduced fractional cascading as a method to solve numerous search problems in computational geometry.
Euclid (; – "Eukleídēs", ; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His "Elements" is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the "Elements", Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor.
TTL was invented in 1961 by James L. Buie of TRW, which declared it, "particularly suited to the newly developing integrated circuit design technology." The original name for TTL was "transistor-coupled transistor logic" (TCTL). The first commercial integrated-circuit TTL devices were manufactured by Sylvania in 1963, called the Sylvania Universal High-Level Logic family (SUHL). The Sylvania parts were used in the controls of the Phoenix missile. TTL became popular with electronic systems designers after Texas Instruments introduced the 5400 series of ICs, with military temperature range, in 1964 and the later 7400 series, specified over a narrower range and with inexpensive plastic packages, in 1966.
Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. Pythagoras established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers. Although he was preceded by the Babylonians and the Chinese, the Neopythagorean mathematician Nicomachus (60–120 AD) provided one of the earliest Greco-Roman multiplication tables, whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the British Museum). The association of the Neopythagoreans with the Western invention of the multiplication table is evident in its later Medieval name: the "mensa Pythagorica".
The chip design started in April 1970, when Federico Faggin joined Intel, and was completed under his leadership in January 1971. The first commercial sale of the fully operational 4004 occurred in March 1971 to Busicom Corp. of Japan for which it was originally designed and built as a custom chip. In mid-November of the same year, with the prophetic ad "Announcing a new era in integrated electronics", the 4004 was made commercially available to the general market. The 4004 was the first commercially available monolithic processor, fully integrated in one small chip. Such a feat of integration was made possible by the use of the then-new silicon gate technology for integrated circuits, originally developed by Faggin (with Tom Klein) at Fairchild Semiconductor in 1968, which allowed twice the number of random-logic transistors and an increase in speed by a factor of five compared to the incumbent MOS aluminum gate technology. Faggin also invented the bootstrap load with silicon gate and the “buried contact”, improving speed and circuit density compared with aluminum gate.
Since the 18th century, women have developed scientific computations, including Nicole-Reine Lepaute's prediction of Halley's Comet, and Maria Mitchell's computation of the motion of Venus. The first algorithm intended to be executed by a computer was designed by Ada Lovelace who was a pioneer in the field. Grace Hopper was the first person to design a compiler for a programming language. Throughout the 19th and early-20th century, and up to World War II, programming was predominantly done by women; significant examples include the Harvard Computers, codebreaking at Bletchley Park and engineering at NASA.
The logicist project received a near-fatal setback with the discovery of a paradox in 1901 by Bertrand Russell. This proved Frege's naive set theory led to a contradiction. Frege's theory contained the axiom that for any formal criterion, there is a set of all objects that meet the criterion. Russell showed that a set containing exactly the sets that are not members of themselves would contradict its own definition (if it is not a member of itself, it is a member of itself, and if it is a member of itself, it is not). This contradiction is now known as Russell's paradox. One important method of resolving this paradox was proposed by Ernst Zermelo. Zermelo set theory was the first axiomatic set theory. It was developed into the now-canonical Zermelo–Fraenkel set theory (ZF). Russell's paradox symbolically is as follows:
Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of "reasoning" about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it stems from the Greek word formula_1 or ‘episteme’ meaning knowledge. Epistemology is nevertheless more concerned with analyzing the very "nature" and "scope" of knowledge, addressing questions such as “What is the definition of knowledge?” or “How is knowledge acquired?”. In fact, epistemic logic grew out of epistemology in the Middle Ages thanks to the efforts of Burley and Ockham. The formal work, based on modal logic, that inaugurated contemporary research into epistemic logic dates back only to 1962 and is due to Hintikka. It then sparked in the 1960s discussions about the principles of knowledge and belief and many axioms for these notions were proposed and discussed. For example, the interaction axioms formula_2 and formula_3 are often considered to be intuitive principles: if an agent Knows formula_4 then (s)he also Believes formula_4, or if an agent Believes formula_4, then (s)he Knows that (s)he Believes formula_4. More recently, these kinds of philosophical theories were taken up by researchers in economics, artificial intelligence and theoretical computer science where reasoning about knowledge is a central topic. Due to the new setting in which epistemic logic was used, new perspectives and new features such as computability issues were then added to the research agenda of epistemic logic.
In 1714 Dutch scientist and inventor Daniel Gabriel Fahrenheit invented the first reliable thermometer, using mercury instead of alcohol and water mixtures. In 1724 he proposed a temperature scale which now (slightly adjusted) bears his name. He could do this because he manufactured thermometers, using mercury (which has a high coefficient of expansion) for the first time and the quality of his production could provide a finer scale and greater reproducibility, leading to its general adoption. In 1742, Anders Celsius (1701–1744) proposed a scale with zero at the boiling point and 100 degrees at the freezing point of water, though the scale which now bears his name has them the other way around. French entomologist René Antoine Ferchault de Réaumur invented an alcohol thermometer and temperature scale in 1730 that ultimately proved to be less reliable than Fahrenheit's mercury thermometer.
The transistor is the fundamental building block of modern electronic devices, and is ubiquitous in modern electronic systems. Julius Edgar Lilienfeld patented a field-effect transistor in 1926 but it was not possible to actually construct a working device at that time. The first practically implemented device was a point-contact transistor invented in 1947 by American physicists John Bardeen, Walter Brattain, and William Shockley. The transistor revolutionized the field of electronics, and paved the way for smaller and cheaper radios, calculators, and computers, among other things. The transistor is on the list of IEEE milestones in electronics, and Bardeen, Brattain, and Shockley shared the 1956 Nobel Prize in Physics for their achievement.
The World Wide Web, also known as the WWW and the Web, is an information space where documents and other web resources are identified by Uniform Resource Locators (URLs), interlinked by hypertext links, and accessible via the Internet. English scientist Tim Berners-Lee invented the World Wide Web in 1989. He wrote the first web browser in 1990 while employed at CERN near Geneva, Switzerland. The browser was released outside CERN in 1991, first to other research institutions starting in January 1991 and to the general public on the Internet in August 1991.
The word "algorithm" itself derives from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized "Algoritmi". A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem (decision problem) posed by David Hilbert in 1928. Later formalizations were framed as attempts to define "effective calculability" or "effective method". Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939.
Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. He is also notable for being the inaugural holder of the prestigious Lucasian Professorship of Mathematics, a post later held by his student, Isaac Newton who also went on to develop calculus in its modern form.
Although Greek mathematician and engineer Heron of Alexandria is noted as the first to have conceived these numbers, Rafael Bombelli first set down the rules for multiplication of complex numbers in 1572. The concept had appeared in print earlier, for instance in work by Gerolamo Cardano. At the time imaginary numbers, as well as negative numbers, were poorly understood and regarded by some as fictitious or useless, much as zero once was. Many other mathematicians were slow to adopt the use of imaginary numbers, including René Descartes, who wrote about them in his "La Géométrie", where the term "imaginary" was used and meant to be derogatory. The use of imaginary numbers was not widely accepted until the work of Leonhard Euler (1707–1783) and Carl Friedrich Gauss (1777–1855). The geometric significance of complex numbers as points in a plane was first described by Caspar Wessel (1745–1818).
Eventually communication reached an electronic state, and the telegraph was invented. Harrison Dyar, who sent electrical sparks through chemically treated paper tape to burn dots and dashes, invented the first telegraph in the USA. The telegraph was the first piece of equipment that allowed users to send electronic messages. A more developed version came from Samuel Morse, whose telegraph printed code on tape and was operated using a keypad and an earpiece. The pattern of communication soon became known as Morse code.
About 20 years later, John Ambrose Fleming (scientific adviser to the Marconi Company
and former Edison employee) realized that the Edison effect could be used as a radio detector. Fleming patented the first true thermionic diode, the Fleming valve, in Britain on November 16, 1904 (followed by in November 1905).
The world’s first transistor computer was built at the University of Manchester in November 1953. The computer was built by Richard Grimsdale, then a research student in the Department of Electrical Engineering and later a Professor of Electronic Engineering at Sussex University. The machine used point-contact transistors, made in small quantities by STC and Mullard. These consisted of a single crystal of germanium with two fine wires, resembling the crystal and cat’s whisker of the 1920s. These transistors had the useful property that a single transistor could possess two stable states. ... The development of the machine was severely hampered by the unreliability of the transistors, which consumed 150 watts.
Foster's Ph.D. dissertation and his first few papers were in the area of mathematical logic. Starting from this point, he soon focused his interest on the related theory of Boolean algebras and Boolean rings, and was thus led from logic to algebra. He extensively studied the role of duality in Boolean theory and subsequently developed a theory of n-ality for certain rings which played for n-valued logics the role of Boolean rings vis-a-vis Boolean algebras. The late Benjamin Bernstein of the Berkeley mathematics faculty was his collaborator in some of this research. This work culminated in his seminal paper “The theory of Boolean-like rings” appearing in 1946.
Attempts of formal treatment of mathematics had started with Leibniz and Lambert (1728–1777), and continued with works by algebraists such as George Peacock (1791–1858).
Systematic mathematical treatments of logic came with the British mathematician George Boole (1847) who devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1 and logical combinations (conjunction, disjunction, implication and negation) are operations similar to the addition and multiplication of integers. Additionally, De Morgan published his laws in 1847. Logic thus became a branch of mathematics. Boolean algebra is the starting point of mathematical logic and has important applications in computer science.
In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra in this setting, and he introduced switching algebra as a way to analyze and design circuits by algebraic means in terms of logic gates. Shannon already had at his disposal the abstract mathematical apparatus, thus he cast his switching algebra as the two-element Boolean algebra. In circuit engineering settings today, there is little need to consider other Boolean algebras, thus "switching algebra" and "Boolean algebra" are often used interchangeably. Efficient implementation of Boolean functions is a fundamental problem in the design of combinational logic circuits. Modern electronic design automation tools for VLSI circuits often rely on an efficient representation of Boolean functions known as (reduced ordered) binary decision diagrams (BDD) for logic synthesis and formal verification.
The mathematical structure of modal logic, namely Boolean algebras augmented with unary operations (often called modal algebras), began to emerge with J. C. C. McKinsey's 1941 proof that "S2" and "S4" are decidable, and reached full flower in the work of Alfred Tarski and his student Bjarni Jónsson (Jónsson and Tarski 1951–52). This work revealed that "S4" and "S5" are models of interior algebra, a proper extension of Boolean algebra originally designed to capture the properties of the interior and closure operators of topology. Texts on modal logic typically do little more than mention its connections with the study of Boolean algebras and topology. For a thorough survey of the history of formal modal logic and of the associated mathematics, see Robert Goldblatt (2006).