To ignite fireA ferrocerium "flint" spark lighter in action
When struck against steel, a flint edge produces sparks. The hard flint edge shaves off a particle of the steel that exposes iron, which reacts with oxygen from the atmosphere and can ignite the proper tinder.
Prior to the wide availability of steel, rocks of pyrite (FeS2) would be used along with the flint...
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Thales of Miletus (/ˈθeɪliːz/ THAY-leez; Ancient Greek: Θαλῆς; c. 626/623 – c. 548/545 BC) was an Ancient Greek pre-Socratic philosopher from Miletus in Ionia, Asia Minor. Thales was one of the Seven Sages, founding figures of Ancient Greece.
Beginning in eighteenth-century historiography,[1]many came to regard him as the first philosopher in the Greek tradition, breaking from the prior use of mythology to explain the world and instead using natural philosophy. He is thus otherwise referred to as the first to have engaged in mathematics, science, and deductive reasoning.[2]
Thales's view that all of nature is based on the existence of a single ultimate substance, which he theorized to be water, was widely influential among the philosophers of his time. Thales thought the Earth floated on water.
In mathematics, Thales is the namesake of Thales's theorem, and the intercept theorem can also be referred to as Thales's theorem. Thales was said to have calculated the heights of the pyramids and the distance of ships from the shore. In science, Thales was an astronomer who reportedly predicted the weather and a solar eclipse. The discovery of the position of the constellation Ursa Major is also attributed to Thales, as well as the timings of the solstices and equinoxes. He was also an engineer, known for having allowed the Lydian army to cross the Halys River. Plutarch wrote that "at that time, Thales alone had raised philosophy from mere speculation to practice."[3]
Pythagoras of Samos[a] (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC)[b] was an ancient IonianGreek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle.
In antiquity, Pythagoras was credited with mathematical and scientific discoveries, such as the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He was reputedly the first man to call himself a philosopher ("lover of wisdom").[c] Historians debate whether Pythagoras made these discoveries and pronouncements, as some of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors, such as Hippasus and Philolaus.
Rearrangement proof of the Pythagorean theorem.In one rearrangement proof, two squares are used whose sides have a measure of and which contain four right triangles whose sides are a, b and c, with the hypotenuse being c. In the square on the right side, the triangles are placed such that the corners of the square correspond to the corners of the right angle in the triangles, forming a square in the center whose sides are length c. Each outer square has an area of (a + b)2 as well as 2ab + c2, with 2ab representing the total area of the four triangles. Within the big square on the left side, the four triangles are moved to form two similar rectangles with sides of length a and b. These rectangles in their new position have now delineated two new squares, one having side length a is formed in the bottom-left corner, and another square of side length b formed in the top-right corner. In this new position, this left side now has a square of area (a + b)2 as well as 2ab + a2 + b2. Since both squares have the area of (a + b)2 it follows that the other measure of the square area also equal each other such that 2ab + c2 = 2ab + a2 + b2. With the area of the four triangles removed from both side of the equation what remains is a2 + b2 = c2.
Leucippus (/luːˈsɪpəs/; Λεύκιππος, Leúkippos; fl. 5th century BCE) was a pre-Socratic Greek philosopher. He is traditionally credited as the founder of atomism, which he developed with his student Democritus. Leucippus divided the world into two entities: atoms, indivisible particles that make up all things, and the void, the nothingness that exists between the atoms. He developed his philosophy as a response to the Eleatics, who believed that all things are one and the void does not exist. Leucippus's ideas were influential in ancient and Renaissance philosophy. Leucippus was the first Western philosopher to develop the concept of atoms, but his ideas only bear a superficial resemblance to modern atomic theory.
Leucippus's atoms come in infinitely many forms and exist in constant motion, creating a deterministic world in which everything is caused by the collisions of atoms. Leucippus described the beginning of the cosmos as a vortex of atoms that formed the Earth, the Sun, the stars, and other celestial bodies. As Leucippus considered both atoms and the void to be infinite, he presumed that other worlds must exist as cosmoses are formed elsewhere. Leucippus and Democritus described the soul as an arrangement of spherical atoms, which are cycled through the body through respiration and create thought and sensory input.
The only records of Leucippus come from Aristotle and Theophrastus, ancient philosophers who lived after him, and little is known of his life. Most scholars agree that Leucippus existed, but some have questioned this, instead attributing his ideas purely to Democritus. Contemporary philosophers rarely distinguish their respective ideas. Two works are attributed to Leucippus (The Great World Systemand On Mind), but all of his writing has been lost with the exception of one sentence.
The thing I remember most of Democritus besides his Atomic theory, is that he was the "Laughing philosopher". I say that because he must have come up against fierce resistance especially from religionists. If you say that Atoms are everything, in a sense you omit the Gods. And I, being the founder-framer of the Plutonium Atom Totality have had to adopt the Democritus reaction to critics--- laughing my way outright in any discussion.
Democritus (/dɪˈmɒkrɪtəs/, dim-OCK-rit-əs; Greek: Δημόκριτος, Dēmókritos, meaning "chosen of the people"; c. 460 – c. 370 BC) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe.[2] Democritus wrote extensively on a wide variety of topics.[3]
None of Democritus' original work has survived, except through second-hand references. Many of these references come from Aristotle, who viewed him as an important rival in the field of natural philosophy.[4] He was known in antiquity as the ‘laughing philosopher’ because of his emphasis on the value of cheerfulness.[5]
Although many anecdotes about Democritus' life survive, their authenticity cannot be verified and modern scholars doubt their accuracy.[6]
According to Aristotle, Democritus was born in Abdera, on the coast of Thrace.[7][6] He was a polymath and prolific writer, producing nearly eighty treatises on subjects such as poetry, harmony, military tactics, and Babylonian theology. Some called him a Milesian, and the name of his father too is stated differently.[8] His birth year was fixed by Apollodorus in the first year of the 80th Olympiad, or 460 BC, while Thrasyllus had referred it to as the 3rd year of the 77th Olympiad.[9] Democritus had called himself forty years younger than Anaxagoras. His father, Hegesistratus,--or as others called him Damasippus or Athenocritus,--was possessed of so large a property, that he was able to receive and treat Xerxes on his march through Abdera.[10]
Democritus spent the inheritance left to him by his father on travels to distant countries, which he undertook to satisfy his extraordinary thirst for knowledge. He travelled over a great part of Asia, and, as some state, he even reached India and Aethiopia.[11] We know that he wrote on Babylon and Meroe; he must also have visited Egypt, and Diodorus Siculus[12] even states, that he lived there for a period of five years. He himself declared,[13] that among his contemporaries none had made greater journeys, seen more countries, and made the acquaintance of more men distinguished in every kind of science than himself. Among the last he mentions in particular the Egyptian mathematicians (ἀρπεδονάπται ; comp. Sturz, de Dialect. Maced. p. 98), whose knowledge he praises, without, however, regarding himself inferior to them. Theophrastus, too, spoke of him as a man who had seen many countries.[14] It was his desire to acquire an extensive knowledge of nature that led him into distant countries at a time when travelling was the principal means of acquiring an intellectual and scientific culture; and after returning to his native land he occupied himself only with philosophical investigations, especially such as related to natural history.[15]
Socrates (/ˈsɒkrətiːz/;[2] Ancient Greek: Σωκράτης, romanized: Sōkrátēs; c. 470 – 399 BC) was an ancient Greek philosopher from Classical Athens, perhaps the first Western moral philosopher, and a major inspiration on his student Plato, who largely founded the tradition of Western philosophy.[3] An enigmatic figure, Socrates authored no texts and is known mainly through the posthumous accounts of classical writers, particularly his students Plato and Xenophon. These accounts are written as dialogues, in which Socrates and his interlocutors examine a subject in the style of question and answer; they gave rise to the Socratic dialogue literary genre. Contradictory accounts of Socrates make a reconstruction of his philosophy nearly impossible, a situation known as the Socratic problem. Socrates was a polarizing figure in Athenian society. In 399 BC, he was accused of impiety and corrupting the youth. After a trial that lasted a day, he was sentenced to death. As related by Plato, he was put to death by administration of poison after refusing offers from allies to help him escape.
Plato's dialogues are among the most comprehensive accounts of Socrates to survive from antiquity. They demonstrate the Socratic approach to areas of philosophy including epistemology and ethics. The Platonic Socrates lends his name to the concept of the Socratic method, and also to Socratic irony. The Socratic method of questioning, or elenchus, takes shape in dialogue using short questions and answers, epitomized by those Platonic texts in which Socrates and his interlocutors examine various aspects of an issue or an abstract meaning, usually relating to one of the virtues, and find themselves at an impasse, unable to define what they thought they understood. Socrates frequently proclaims his ignorance, saying that he is only sure that he does not know.
Socrates exerted a strong influence on philosophers in later antiquity and has continued to do so in the modern era. He was studied by medieval and Islamic scholars and played an important role in the thought of the Italian Renaissance, particularly within the humanist movement. Interest in him continued unabated, as reflected in the works of Søren Kierkegaard and Friedrich Nietzsche. Depictions of Socrates in art, literature, and popular culture have made him a widely known figure in the Western philosophical tradition.
Philosophical work
Era
Ancient Greek philosophy
Notable students
Aristotle
Main interests
Epistemology, Metaphysics
Political philosophy, Ethics
Notable works
Notable ideasPlato (/ˈpleɪtoʊ/ PLAY-toe; Greek: Πλάτων, Plátōn; born c. 428–423 BC, died 348/347 BC) was an ancient Greek philosopher of Classical Athens who is most commonly considered the foundational thinker of the Western philosophical tradition.[1] An innovator of the literary dialogue and dialectic forms, Plato influenced all the major areas of theoretical philosophy and practical philosophy, and was the founder of the Platonic Academy, a philosophical school in Athenswhere Plato taught the collection of philosophical theories that would later become known as Platonism.
Plato's most famous contribution is his Theory of Forms (or Ideas), which aims to solve what is now known as the problem of universals. He was influenced by the pre-Socratic thinkers Pythagoras, Heraclitus, and Parmenides, although much of what is known about them is derived from Plato himself.
Along with his teacher Socrates, and his student Aristotle, Plato is a central figure in the history of Western philosophy. Plato's complete works are believed to have survived for over 2,400 years—unlike that of nearly all of his contemporaries.[2] Although their popularity has fluctuated, they have consistently been read and studied through the ages.[3] Through Platonism's outgrowth Neoplatonism, he also influenced Christian philosophy, and both Jewish and Islamic philosophy. In modern times, Alfred North Whitehead said: "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato."[4]
LifePlato was born between 428 and 423 BC[5][6] into an aristocratic and influential Athenian family
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Aristotle[A] (Attic Greek: Ἀριστοτέλης, romanized: Aristotélēs;[B] 384–322 BC) was an ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, and the arts. As the founder of the Peripatetic school of philosophy in the Lyceum in Athens, he began the wider Aristotelian tradition that followed, which set the groundwork for the development of modern science.
Little is known about Aristotle's life. He was born in the city of Stagira in northern Greece during the Classical period. His father, Nicomachus, died when Aristotle was a child, and he was brought up by a guardian. At around eighteen years old, he joined Plato's Academyin Athens and remained there until the age of thirty seven (c. 347 BC). Shortly after Plato died, Aristotle left Athens and, at the request of Philip II of Macedon, tutored his son Alexander the Great beginning in 343 BC. He established a library in the Lyceum, which helped him to produce many of his hundreds of books on papyrus scrolls.
Though Aristotle wrote many treatises and dialogues for publication, only around a third of his original output has survived, none of it intended for publication. Aristotle provided a complex synthesis of the various philosophies existing prior to him. His teachings and methods of inquiry have had a significant impact across the world, and remain a subject of contemporary philosophical discussion.
Aristotle's views
Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης; fl. 300BC) was an ancient Greek mathematician active as a geometer and logician.[2] Considered the "father of geometry",[3] he is chiefly known for the Elementstreatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.
Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissancescholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria.
In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour. In addition to the Elements, Euclid wrote a central early text in the optics field, Optics, and lesser-known works including Data and Phaenomena. Euclid's authorship of On Divisions of Figures and Catoptrics has been questioned. He is thought to have written many lost works.

Aristarchus of Samos (/ˌærɪˈstɑːrkəs/; Ancient Greek: Ἀρίσταρχος ὁ Σάμιος, Aristarkhos ho Samios; c. 310 – c. 230 BC) was an ancient Greek astronomerand mathematician who presented the first known heliocentric model that placed the Sun at the center of the universe, with the Earth revolving around the Sun once a year and rotating about its axis once a day. He also supported the theory of Anaxagoras that the Sun was just another star.[2]
Born in Samos in approximately 310 BC, Aristarchus likely moved to Alexandria and became a student of Strato of Lampsacus, who later became the head of the Peripatetic school in Greece. According to Ptolemy, Aristarchus observed the summer solstice of 280 BC.[3]Vitruvius writes that Aristarchus built two different sundials: one a flat disc; and one hemispherical.[4]Aristarchus estimated the sizes of the Sun and Moon as compared to Earth, and the distances from the Earth to the Sun and to the Moon. His estimate that the Sun was 7 times larger than Earth (it's actually 109 times, in diameter) brought about the further insight that the Sun's greater size made it the most natural central point of the universe, as opposed to Earth.
Aristarchus was influenced by the concept presented by Philolaus of Croton (c. 470 – 385 BC) of a fire at the center of the universe (i.e. by contemporary understanding, at the center of the Earth). Aristarchus recast this "central fire" as the Sun, and he arranged the other planets in their correct order of distance around the Sun.[5]
Like Anaxagoras before him, Aristarchus suspected that the stars were just other bodies like the Sun, albeit farther away from Earth. His astronomical ideas were often rejected in favor of the geocentrictheories of Aristotle and Ptolemy. Nicolaus Copernicus knew that Aristarchus had a 'moving Earth' theory, although it is unlikely that Copernicus was aware that it was a heliocentric theory.[7][8]
The original text has been lost, but a reference in a book by Archimedes, entitled The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli), describes a work in which Aristarchus advanced the heliocentric model as an alternative hypothesis to geocentrism:
Aristarchus proposed that the fixed stars were extremely distant, and because ancient cosmology placed them all on a single celestial sphere, the modern concept of stellar parallax did not apply to his model. He placed the stars at a great distance so that their apparent positions relative to each other would remain constant throughout Earth's motion. Aristarchus reconciled this issue by postulating that the stars were other suns that are very far away,[2] far enough that the parallax was not observable. This implied a universe much larger than had been believed.
It is a common misconception that the heliocentric view was considered sacrilegious by the contemporaries of Aristarchus.[10] Lucio Russo traces this to Gilles Ménage's printing of a passage from Plutarch's On the Apparent Face in the Orb of the Moon, in which Aristarchus jokes with Cleanthes, who is head of the Stoics, a sun worshipper, and opposed to heliocentrism.[10] In the manuscript of Plutarch's text, Aristarchus says Cleanthes should be charged with impiety.[10]Ménage's version, published shortly after the trials of Galileo and Giordano Bruno, transposes an accusative and nominative so that it is Aristarchus who is purported to be impious.[10] The resulting misconception of an isolated and persecuted Aristarchus is still promulgated.[10][11]
According to Plutarch, while Aristarchus postulated heliocentrism only as a hypothesis, Seleucus of Seleucia, a Hellenistic astronomer who lived a century after Aristarchus, maintained it as a definite opinion and gave a demonstration of it,[12] but no full record of the demonstration has been found. In his Naturalis Historia, Pliny the Elder later wondered whether errors in the predictions about the heavens could be attributed to a displacement of the Earth from its central position.[13] Pliny[14] and Seneca[15] referred to the retrograde motion of some planets as an apparent (unreal) phenomenon, which is an implication of heliocentrism rather than geocentrism. Still, no stellar parallax was observed, and Plato, Aristotle, and Ptolemy preferred the geocentric model that was believed throughout the Middle Ages.
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Avicenna
Ibn Sinaابن سیناModern portrait of Ibn Sina, National Library of Medicine (1952)
Born
c. 980Afshana, Transoxiana, Samanid Empire
Died
22 June 1037 (aged 56–57)[1]
Monuments
Avicenna Mausoleum
Other namesSharaf al-Mulk (شرف الملك)Hujjat al-Haq (حجة الحق)
al-Sheikh al-Ra'is (الشيخ الرئيس)
Bu Alī Sīnā (بو علی سینا)
Philosophical work
Era
Islamic Golden Age
Region
Middle Eastern philosophy
School
Aristotelianism, Avicennism
Main interests
Notable worksThis article contains special characters.Without proper rendering support, you may see question marks, boxes, or other symbols.
William of Ockham or Occam OFM (/ˈɒkəm/ OK-əm; Latin: Gulielmus Occamus;[11][12] c. 1287 – 9/10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and theologian, who was born in Ockham, a small village in Surrey.[13] He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of the 14th century. He is widely known for Occam's razor, the methodological principle that bears his name, and also produced significant works on logic, physics and theology. Ockham is remembered in the Church of England with a commemoration corresponding to the commonly ascribed date of his death on 10 April.[14]
In scholasticism, William of Ockham advocated reform in both method and content, the aim of which was simplification. Ockham incorporated much of the work of some previous theologians, especially Duns Scotus. From Duns Scotus, Ockham derived his view of divine omnipotence, his view of grace and justification, much of his epistemology and ethical convictions.[25] However, he also reacted to and against Scotus in the areas of predestination, penance, his understanding of universals, his formal distinction ex parte rei (that is, "as applied to created things"), and his view of parsimony which became known as Occam's razor.
One important contribution that he made to modern science and modern intellectual culture was efficient reasoning with the principle of parsimony in explanation and theory building that came to be known as Occam's razor. This maxim, as interpreted by Bertrand Russell,[30] states that if one can explain a phenomenon without assuming this or that hypothetical entity, there is no ground for assuming it, i.e. that one should always opt for an explanation in terms of the fewest possible causes, factors, or variables. He turned this into a concern for ontological parsimony; the principle says that one should not multiply entities beyond necessity—Entia non sunt multiplicanda sine necessitate—although this well-known formulation of the principle is not to be found in any of Ockham's extant writings.[31] He formulates it as: "For nothing ought to be posited without a reason given, unless it is self-evident
George Boole (/buːl/ BOOL; 2 November 1815 – 8 December 1864) was an English autodidact, mathematician, philosopher and logician who served as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought (1854), which contains Boolean algebra. Boolean logic, essential to computer programming, is credited with helping to lay the foundations for the Information Age.[4][5][6]
Boole was the son of a shoemaker. He received a primary school education and learned Latin and modern languages through various means. At 16, he began teaching to support his family. He established his own school at 19 and later ran a boarding school in Lincoln. Boole was an active member of local societies and collaborated with fellow mathematicians. In 1849, he was appointed the first professor of mathematics at Queen's College, Cork (now University College Cork) in Ireland, where he met his future wife, Mary Everest. He continued his involvement in social causes and maintained connections with Lincoln. In 1864, Boole died due to fever-induced pleural effusion after developing pneumonia.
Boole published around 50 articles and several separate publications in his lifetime. Some of his key works include a paper on early invariant theory and "The Mathematical Analysis of Logic", which introduced symbolic logic. Boole also wrote two systematic treatises: "Treatise on Differential Equations" and "Treatise on the Calculus of Finite Differences". He contributed to the theory of linear differential equations and the study of the sum of residues of a rational function. In 1847, Boole developed Boolean algebra, a fundamental concept in binary logic, which laid the groundwork for the algebra of logic tradition and forms the foundation of digital circuit design and modern computer science. Boole also attempted to discover a general method in probabilities, focusing on determining the consequent probability of events logically connected to given probabilities.
Boole's work was expanded upon by various scholars, such as Charles Sanders Peirce and William Stanley Jevons. Boole's ideas later gained practical applications when Claude Shannon and Victor Shestakov employed Boolean algebra to optimize the design of electromechanical relay systems, leading to the development of modern electronic digital computers. His contributions to mathematics earned him various honours, including the Royal Society's first gold prize for mathematics, the Keith Medal, and honorary degrees from the Universities of Dublin and Oxford. University College Cork celebrated the 200th anniversary of Boole's birth in 2015, highlighting his significant impact on the digital age.
William Stanley Jevons FRS (/ˈdʒɛvənz/;[2] 1 September 1835 – 13 August 1882) was an English economist and logician.
Irving Fisher described Jevons's book The Theory of Political Economy (1871) as the start of the mathematical method in economics.[3] It made the case that economics, as a science concerned with quantities, is necessarily mathematical.[4] In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons' work, along with similar discoveries made by Carl Menger in Vienna (1871) and by Léon Walras in Switzerland (1874), marked the opening of a new period in the history of economic thought. Jevons's contribution to the marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time.
Jevons broke off his studies of the natural sciences in London in 1854 to work as an assayer in Sydney, where he acquired an interest in political economy. Returning to the UK in 1859, he issued a "Notice of a General Mathematical Theory of Political Economy" in 1862, outlining the marginal utility theory of value, and published A Serious Fall in the Value of Gold in 1863. For Jevons, the utility or value to a consumer of an additional unit of a product is inversely related to the number of units of that product he already owns, at least beyond some critical quantity.
Jevons received public recognition for his work on The Coal Question (1865), in which he called attention to the gradual exhaustion of Britain's coal supplies and also put forth the view that increases in energy production efficiency leads to more, not less, consumption.[5]: 7f, 161f This view is known today as the Jevons paradox, named after him. Due to this particular work, Jevons is regarded today as the first economist of some standing to develop an 'ecological' perspective on the economy.[6]: 295f [7]: 147 [5]: 2
The most important of his works on logic and scientific methods is his Principles of Science (1874),[8]as well as The Theory of Political Economy (1871) and The State in Relation to Labour (1882). Among his inventions was the logic piano, a mechanical computer.
Friedrich Ludwig Gottlob Frege (/ˈfreɪɡə/;[7] German:[ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano(1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be one of the greatest logicians since Aristotle, and one of the most profound philosophers of mathematics ever.[8]
His contributions include the development of modern logic in the Begriffsschrift and work in the foundations of mathematics. His book the Foundations of Arithmeticis the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical papers "On Sense and Reference" and "The Thought" are also widely cited. The former argues for two different types of meaningand descriptivism. In Foundations and "The Thought", Frege argues for Platonism against psychologism or formalism, concerning numbers and propositionsrespectively.
James Clerk Maxwell FRS FRSE (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician[1] who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism achieved the second great unification in physics,[2] where the first one had been realised by Isaac Newton. Maxwell was also key in the creation of statistical mechanics.
Maxwell graduated from Trinity College, Cambridge, in 1854, where he earned distinction in mathematics and the Smith’s Prize. He remained at Cambridge briefly, publishing early mathematical work and investigations into optics, particularly the principles of colour combination and colour-blindness. He later held the Chair of Natural Philosophy at Marischal College, where he studied the rings of Saturn and correctly proposed that they were composed of numerous small particles,[3] work that earned him the Adams Prize in 1859. During this time he married Katherine Mary Dewar, who assisted him in his laboratory work. From 1860 to 1865, he served as the Professor of Natural Philosophy at King’s College London, where he developed his theory of electromagnetic fields. His publication of "A Dynamical Theory of the Electromagnetic Field" in 1865 demonstrated that electric and magnetic fieldstravel through space as waves moving at the speed of light, proposing that light is an undulation in the same medium that is the cause of electric and magnetic phenomena.[4] His unification of light and electrical phenomena led to his prediction of the existence of radio waves.
Maxwell was the first to derive the Maxwell–Boltzmann distribution, a statistical means of describing aspects of the kinetic theory of gases, which he worked on sporadically throughout his career.[5] He presented the first durable colour photograph in 1861, and showed that any colour can be produced with a mixture of any three primary colours, those being red, green, and blue, the basis for colour television.[6] He worked on analysing the rigidity of rod-and-joint frameworks (trusses) like those in many bridges. He devised modern dimensional analysis and helped to establish the CGS system of measurement. He was the first to understand chaos, and the first to emphasize the butterfly effect. His 1863 paper On Governors serves as an important foundation for control theory and cybernetics, and was also the earliest mathematical analysis on control systems.[7][8] In 1867, he proposed the thought experiment known as Maxwell's demon, which challenges how information affects entropy in thermodynamics. In his seminal 1867 paper On the Dynamical Theory of Gases he introduced the Maxwell model for describing the behavior of a viscoelastic material and originated the Maxwell-Cattaneo equation for describing the transport of heat in a medium.
In 1871, Maxwell returned to Cambridge as the first Cavendish Professor of Physics, overseeing the construction of the Cavendish Laboratory. As a result of his work he is regarded as a founder of the modern field of electrical engineering.[6] His discoveries helped usher in the era of modern physics, laying the foundations for such fields as relativity, also being the one to introduce the term into physics,[9] and quantum mechanics.[10][11]
Pierre Curie[a] (15 May 1859 – 19 April 1906) was a French physicist and chemist, and a pioneer in crystallography and magnetism. He shared one half of the 1903 Nobel Prize in Physics with his wife, Marie Curie, for their work on radioactivity.[3] With their win, the Curies became the first married couple to win a Nobel Prize, launching the Curie family legacy of five Nobel Prizes.
Paul Adrien Maurice Dirac (/dɪˈræk/ dih-RAK;[3] 8 August 1902 – 20 October 1984) was a British theoretical physicist who is considered to be one of the founders of quantum mechanics.[4][5] Dirac laid the foundations for both quantum electrodynamics and quantum field theory, coining the former term.[6][7][8][9] He was the Lucasian Professor of Mathematics at the University of Cambridge from 1932 to 1969, and a professor of physics at Florida State University from 1970 to 1984. Dirac shared the 1933 Nobel Prize in Physicswith Erwin Schrödinger "for the discovery of new productive forms of atomic theory."[10]
Dirac graduated from the University of Bristol with a First Class HonoursBachelor of Science degree in electrical engineering in 1921, and a first class honours Bachelor of Arts degree in mathematics in 1923.[11] Dirac then graduated from St John's College, Cambridge, with a Ph.D. in physics in 1926, writing the first ever thesis on quantum mechanics.[12]
He formulated the Dirac equation, one of the most important results in physics, in 1928.[7] It connected special relativity and quantum mechanics and predicted the existence of antimatter.[13] He wrote a famous paper in 1931,[14]which further predicted the existence of antimatter.[15][16][13] Dirac also contributed greatly to the reconciliation of general relativity with quantum mechanics. He contributed to Fermi–Dirac statistics, which describes the behaviour of fermions, particles with half-integer spin. His 1930 monograph, The Principles of Quantum Mechanics, is one of the most influential texts on the subject.[17] He and Schrödinger tied for eighth in a Physics World poll of the greatest physicists of all time.[18]
In 1987, Abdus Salam declared that "Dirac was undoubtedly one of the greatest physicists of this or any century ... No man except Einstein has had such a decisive influence, in so short a time, on the course of physics in this century."[19] In 1995, Stephen Hawking stated that "Dirac has done more than anyone this century, with the exception of Einstein, to advance physics and change our picture of the universe"[20] while Stanley Deser remarked that "We all stand on Dirac's shoulders."[21]
Dirac was born on 8 August 1902 at his parents' home in Bristol, England,[22]and grew up in the Bishopston area of the city.[23][24] His father, Charles Adrien Ladislas Dirac, was an immigrant from Saint-Maurice, Switzerland, of French descent,[25] who worked in Bristol as a French teacher. His mother, Florence Hannah Holten, was born to a Cornish Methodist family in Liskeard, Cornwall.[26][27] She was named after Florence Nightingale by her father, a ship's captain, who had met Nightingale while he was a soldier during the Crimean War.[28] His mother moved to Bristol as a young woman, where she worked as a librarian at the Bristol Central Library; despite this she still considered her identity to be Cornish rather than English.[29] Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, and an older brother, Reginald Charles Félix, known as Felix,[30][31] who died by suicide in March 1925.[32] Dirac later recalled: "My parents were terribly distressed. I didn't know they cared so much ... I never knew that parents were supposed to care for their children, but from then on I knew."[33]
Charles and the children were officially Swiss nationals until they became naturalised on 22 October 1919.[34] Dirac's father was strict and authoritarian, although he disapproved of corporal punishment.[35] Dirac had a strained relationship with his father, so much so that after his father's death, Dirac wrote, "I feel much freer now, and I am my own man." Charles forced his children to speak to him only in French so that they might learn the language. When Dirac found that he could not express what he wanted to say in French, he chose to remain silent.[36][37]
John Stewart Bell FRS[2] (28 July 1928 – 1 October 1990)[3] was a physicistfrom Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories.[4][5][6][7][8]
In 2022, the Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger for work on Bell inequalities and the experimental validation of Bell's theorem.[9]
Bell was born in Belfast, Northern Ireland to a working class family. Due to financial hardship, neither parent and none of his three older siblings completed high school, typically dropping out of school by age 14 to work.[10]When he was 11 years old, he decided to be a scientist, and encouraged by his mother, at 16 he graduated from Belfast Technical High School.[10] Then in an exceptionally rare occurrence for someone of his background, Bell attended the Queen's University of Belfast, where, in 1948, he obtained a bachelor's degree in experimental physics and, a year later, a bachelor's degree in mathematical physics.[10] He went on to complete a PhD in physics at the University of Birmingham in 1956, specialising in nuclear physics and quantum field theory. In 1954, he married Mary Ross, also a physicist, whom he had met while working on accelerator physics at Malvern, UK.[11]: 139 Bell became a vegetarian in his teen years.[12] According to his wife, Bell was an atheist.[13]
Bell's career began with the UK Atomic Energy Research Establishment, near Harwell, Oxfordshire, known as AERE or Harwell Laboratory. In 1960, he moved to work for the European Organization for Nuclear Research (CERN, Conseil Européen pour la Recherche Nucléaire), in Geneva, Switzerland.[14]There he worked almost exclusively on theoretical particle physics and on accelerator design, but found time to pursue a major avocation, investigating the foundations of quantum theory. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1987.[15] Also of significance during his career, Bell, together with John Bradbury Sykes, M. J. Kearsley, and W. H. Reid, translated several volumes of the ten-volume Course of Theoretical Physics of Lev Landau and Evgeny Lifshitz, making these works available to an English-speaking audience in translation, all of which remain in print.
Bell was a proponent of pilot wave theory.[16] In 1987, inspired by Ghirardi–Rimini–Weber theory, he also advocated collapse theories.[17] He said about the interpretation of quantum mechanics: "Well, you see, I don't really know. For me it's not something where I have a solution to sell!"[18]