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🔗 Biography 🔗 Computing 🔗 Mathematics 🔗 Military history 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 Military history/Military science, technology, and theory 🔗 Physics 🔗 Economics 🔗 Philosophy 🔗 Philosophy/Logic 🔗 Biography/science and academia 🔗 Philosophy/Philosophy of science 🔗 Philosophy/Contemporary philosophy 🔗 Military history/Military biography 🔗 Biography/military biography 🔗 History of Science 🔗 Computing/Computer science 🔗 Philosophy/Philosophers 🔗 Education 🔗 Hungary 🔗 Military history/World War II 🔗 Military history/Cold War 🔗 Physics/History 🔗 Physics/Biographies 🔗 Game theory 🔗 Eastern Europe

John von Neumann (; Hungarian: Neumann János Lajos, pronounced [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. Von Neumann was generally regarded as the foremost mathematician of his time and said to be "the last representative of the great mathematicians"; who integrated both pure and applied sciences.

He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, representation theory, operator algebras, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.

He was a pioneer of the application of operator theory to quantum mechanics in the development of functional analysis, and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer.

He published over 150 papers in his life: about 60 in pure mathematics, 60 in applied mathematics, 20 in physics, and the remainder on special mathematical subjects or non-mathematical ones. His last work, an unfinished manuscript written while he was in hospital, was later published in book form as The Computer and the Brain.

His analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a short list of facts about his life he submitted to the National Academy of Sciences, he stated, "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen in 1926, and subsequently in Berlin in 1927–1929. Also, my work on various forms of operator theory, Berlin 1930 and Princeton 1935–1939; on the ergodic theorem, Princeton, 1931–1932."

During World War II, von Neumann worked on the Manhattan Project with theoretical physicist Edward Teller, mathematician Stanisław Ulam and others, problem solving key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb. He developed the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon, and coined the term "kiloton" (of TNT), as a measure of the explosive force generated.

After the war, he served on the General Advisory Committee of the United States Atomic Energy Commission, and consulted for a number of organizations, including the United States Air Force, the Army's Ballistic Research Laboratory, the Armed Forces Special Weapons Project, and the Lawrence Livermore National Laboratory. As a Hungarian émigré, concerned that the Soviets would achieve nuclear superiority, he designed and promoted the policy of mutually assured destruction to limit the arms race.

🔗 Mathematics 🔗 History of Science

Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, yet many mathematical problems, both major and minor, still remain unsolved. These unsolved problems occur in multiple domains, including physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph, group, model, number, set and Ramsey theories, dynamical systems, partial differential equations, and more. Some problems may belong to more than one discipline of mathematics and be studied using techniques from different areas. Prizes are often awarded for the solution to a long-standing problem, and lists of unsolved problems (such as the list of Millennium Prize Problems) receive considerable attention.

🔗 Psychology 🔗 Linguistics 🔗 History of Science 🔗 Linguistics/Applied Linguistics 🔗 Portugal 🔗 Galicia

Saudade (European Portuguese: [sɐwˈðaðɨ] ; Brazilian Portuguese: [sawˈdadʒi] ; Galician: [sawˈðaðɪ]; Northeast Brazil: [sawˈdadi]). (English: ; plural saudades) in Portuguese and Galician is an emotional state of melancholic or profoundly nostalgic longing for a beloved yet absent someone or something. It derives from the Latin word for solitude. It is often associated with a repressed understanding that one might never encounter the object of longing ever again. It is a recollection of feelings, experiences, places, or events, often elusive, that cause a sense of separation from the exciting, pleasant, or joyous sensations they once caused. Duarte Nunes Leão defines saudade as, "Memory of something with a desire for it". In Brazil, the day of saudade is officially celebrated on 30 January. It is not a widely acknowledged day in Portugal.

🔗 London 🔗 British Museum 🔗 Classical Greece and Rome 🔗 History of Science 🔗 Archaeology 🔗 Visual arts 🔗 Glass

The Lycurgus Cup is a 4th-century Roman glass cage cup made of a dichroic glass, which shows a different colour depending on whether or not light is passing through it: red when lit from behind and green when lit from in front. It is the only complete Roman glass object made from this type of glass, and the one exhibiting the most impressive change in colour; it has been described as "the most spectacular glass of the period, fittingly decorated, which we know to have existed".

The cup is also a very rare example of a complete Roman cage-cup, or diatretum, where the glass has been painstakingly cut and ground back to leave only a decorative "cage" at the original surface-level. Many parts of the cage have been completely undercut. Most cage-cups have a cage with a geometric abstract design, but here there is a composition with figures, showing the mythical King Lycurgus, who (depending on the version) tried to kill Ambrosia, a follower of the god Dionysus (Bacchus to the Romans). She was transformed into a vine that twined around the enraged king and restrained him, eventually killing him. Dionysus and two followers are shown taunting the king. The cup is the "only well-preserved figural example" of a cage cup.

The dichroic effect is achieved by making the glass with tiny proportions of nanoparticles of gold and silver dispersed in colloidal form throughout the glass material. The process used remains unclear, and it is likely that it was not well understood or controlled by the makers, and was probably discovered by accidental "contamination" with minutely ground gold and silver dust. The glass-makers may not even have known that gold was involved, as the quantities involved are so tiny; they may have come from a small proportion of gold in any silver added (most Roman silver contains small proportions of gold), or from traces of gold or gold leaf left by accident in the workshop, as residue on tools, or from other work. The very few other surviving fragments of Roman dichroic glass vary considerably in their two colours.

🔗 Biography 🔗 Mathematics 🔗 Philosophy 🔗 Philosophy/Social and political philosophy 🔗 Biography/science and academia 🔗 History of Science 🔗 Middle Ages 🔗 Middle Ages/History 🔗 Philosophy/Philosophers 🔗 Philosophy/Medieval philosophy

Nicole Oresme (French: [nikɔl ɔʁɛm]; c. 1320–1325 – 11 July 1382), also known as Nicolas Oresme, Nicholas Oresme, or Nicolas d'Oresme, was a French philosopher of the later Middle Ages. He wrote influential works on economics, mathematics, physics, astrology, astronomy, philosophy, and theology; was Bishop of Lisieux, a translator, a counselor of King Charles V of France, and one of the most original thinkers of 14th-century Europe.

🔗 Biography 🔗 Mathematics 🔗 Environment 🔗 Iran 🔗 Biography/science and academia 🔗 Astronomy 🔗 Geography 🔗 History of Science 🔗 Astrology 🔗 Middle Ages 🔗 Islam 🔗 Middle Ages/History 🔗 Central Asia 🔗 Maps 🔗 Iraq 🔗 Biography/Core biographies 🔗 Islam/Muslim scholars

Muḥammad ibn Mūsā al-Khwārizmī (Persian: Muḥammad Khwārizmī محمد بن موسی خوارزمی‎; c. 780 – c. 850), Arabized as al-Khwarizmi with al- and formerly Latinized as Algorithmi, was a Persian polymath who produced works in mathematics, astronomy, and geography. Around 820 CE he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad.

Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813–833 CE) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The term algebra itself comes from the title of his book (specifically the word al-jabr meaning "completion" or "rejoining"). His name gave rise to the terms algorism and algorithm. His name is also the origin of (Spanish) guarismo and of (Portuguese) algarismo, both meaning digit.

In the 12th century, Latin translations of his textbook on arithmetic (Algorithmo de Numero Indorum) which codified the various Indian numerals, introduced the decimal positional number system to the Western world. The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities.

In addition to his best-known works, he revised Ptolemy's Geography, listing the longitudes and latitudes of various cities and localities. He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial. He also made important contributions to trigonometry, producing accurate sine and cosine tables, and the first table of tangents.

🔗 Astronomy 🔗 History of Science 🔗 Astronomy/Astronomical objects 🔗 Astronomy/Solar System

Vulcan was a theorized planet that some pre-20th century astronomers thought existed in an orbit between Mercury and the Sun. Speculation about, and even purported observations of, intermercurial bodies or planets date back to the beginning of the 17th century. The case for their probable existence was bolstered by the support of the French mathematician Urbain Le Verrier, who had predicted the existence of Neptune using disturbances in the orbit of Uranus. By 1859 he had confirmed unexplained peculiarities in Mercury's orbit and predicted that they had to be the result of the gravitational influence of another unknown nearby planet or series of asteroids. A French amateur astronomer's report that he had observed an object passing in front of the Sun that same year led Le Verrier to announce that the long sought after planet, which he gave the name Vulcan, had been discovered at last.

Many searches were conducted for Vulcan over the following decades, but despite several claimed observations, its existence could not be confirmed. The need for the planet as an explanation for Mercury's orbital peculiarities was later rendered unnecessary when Einstein's 1915 theory of general relativity showed that Mercury's departure from an orbit predicted by Newtonian physics was explained by effects arising from the curvature of spacetime caused by the Sun's mass.

🔗 Biography 🔗 Mathematics 🔗 Religion 🔗 Physics 🔗 London 🔗 Philosophy 🔗 England 🔗 Biography/science and academia 🔗 Astronomy 🔗 Philosophy/Philosophy of science 🔗 History of Science 🔗 Philosophy/Philosophers 🔗 Biography/politics and government 🔗 Philosophy/Metaphysics 🔗 Physics/Biographies 🔗 Christianity 🔗 Christianity/theology 🔗 Lincolnshire 🔗 Anglicanism

Isaac Newton (4 January 1643 – 31 March 1727) was considered an insightful and erudite theologian by his Protestant contemporaries. He wrote many works that would now be classified as occult studies, and he wrote religious tracts that dealt with the literal interpretation of the Bible. He kept his heretical beliefs private.

Newton's conception of the physical world provided a model of the natural world that would reinforce stability and harmony in the civic world. Newton saw a monotheistic God as the masterful creator whose existence could not be denied in the face of the grandeur of all creation. Although born into an Anglican family, and a devout but unorthodox Christian, by his thirties Newton held a Christian faith that, had it been made public, would not have been considered orthodox by mainstream Christians. Scholars now consider him a Nontrinitarian Arian.

He may have been influenced by Socinian christology.

🔗 Religion 🔗 Biology 🔗 History of Science 🔗 Science 🔗 Evolutionary biology 🔗 Molecular Biology 🔗 Creationism 🔗 Tree of Life 🔗 Molecular Biology/Genetics

Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes that are passed on from parent to offspring during reproduction. Different characteristics tend to exist within any given population as a result of mutation, genetic recombination and other sources of genetic variation. Evolution occurs when evolutionary processes such as natural selection (including sexual selection) and genetic drift act on this variation, resulting in certain characteristics becoming more common or rare within a population. The evolutionary pressures that determine whether a characteristic would be common or rare within a population constantly change, resulting in a change in heritable characteristics arising over successive generations. It is this process of evolution that has given rise to biodiversity at every level of biological organisation, including the levels of species, individual organisms and molecules.

The theory of evolution by natural selection was conceived independently by Charles Darwin and Alfred Russel Wallace in the mid-19th century and was set out in detail in Darwin's book On the Origin of Species. Evolution by natural selection was first demonstrated by the observation that more offspring are often produced than can possibly survive. This is followed by three observable facts about living organisms: (1) traits vary among individuals with respect to their morphology, physiology and behaviour (phenotypic variation), (2) different traits confer different rates of survival and reproduction (differential fitness) and (3) traits can be passed from generation to generation (heritability of fitness). Thus, in successive generations members of a population are more likely to be replaced by the progenies of parents with favourable characteristics that have enabled them to survive and reproduce in their respective environments. In the early 20th century, other competing ideas of evolution such as mutationism and orthogenesis were refuted as the modern synthesis reconciled Darwinian evolution with classical genetics, which established adaptive evolution as being caused by natural selection acting on Mendelian genetic variation.

All life on Earth shares a last universal common ancestor (LUCA) that lived approximately 3.5–3.8 billion years ago. The fossil record includes a progression from early biogenic graphite, to microbial mat fossils, to fossilised multicellular organisms. Existing patterns of biodiversity have been shaped by repeated formations of new species (speciation), changes within species (anagenesis) and loss of species (extinction) throughout the evolutionary history of life on Earth. Morphological and biochemical traits are more similar among species that share a more recent common ancestor, and can be used to reconstruct phylogenetic trees.

Evolutionary biologists have continued to study various aspects of evolution by forming and testing hypotheses as well as constructing theories based on evidence from the field or laboratory and on data generated by the methods of mathematical and theoretical biology. Their discoveries have influenced not just the development of biology but numerous other scientific and industrial fields, including agriculture, medicine, and computer science.

🔗 Physics 🔗 History of Science

The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century to early 20th century classical physics that an ideal black body at thermal equilibrium would emit an unbounded quantity of energy as wavelength decreased into the ultraviolet range.^: 6–7 The term "ultraviolet catastrophe" was first used in 1911 by Paul Ehrenfest, but the concept originated with the 1900 statistical derivation of the Rayleigh–Jeans law.

The phrase refers to the fact that the empirically derived Rayleigh–Jeans law, which accurately predicted experimental results at large wavelengths, failed to do so for short wavelengths. (See the image for further elaboration.) As the theory diverged from empirical observations when these frequencies reached the ultraviolet region of the electromagnetic spectrum, there was a problem. This problem was later found to be due to a property of quanta as proposed by Max Planck: There could be no fraction of a discrete energy package already carrying minimal energy.

Since the first use of this term, it has also been used for other predictions of a similar nature, as in quantum electrodynamics and such cases as ultraviolet divergence.