Branches of Mathematics

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• .name
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• 
  

• 
  Cumberland River
  The Cumberland River is a waterway in the Southern United States. It is 688 miles (1,107 km) long. It starts out as three separate forks that join in Harlan County, KY. Martins Fork starts in Hensley Settlement (Kentucky) on Brush Mountain in Bell County, KY and snakes its way north through the mountains to Baxter, KY. Clover Fork starts on Black Mountain (Kentucky) in Holmes Mill, KY, near the Virginia border, and flows west paralleling Kentucky Route 38 until it reaches Harlan, KY. Originally, Clover Fork flowed through downtown Harlan and merged with Martin's Fork at the intersection of Kentucky Route 38 and US Route 421. However, as part of a flood control project in 1992, the Clover Fork was diverted through a tunnel under Little Black Mountain, emerging in Baxter, KY where it joined with Martins Fork. Poor Fork starts as a small stream on Pine Mountain (Appalachian Mountains) in Letcher County, KY near Flat Gap, VA. It flows southwest paralleling Pine Mountain until it merges with the other two forks in Baxter, KY. From there, the wider river continues flowing west through the mountains of Kentucky to Cumberland Falls.
  
  wn.com/Cumberland_River
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  Egypt
  Egypt ⁱ/ˈiːdʒɪpt/ (Arabic: مصر, Miṣr, Egyptian Arabic: [mɑsˤɾ] ; Coptic: Ⲭⲏⲙⲓ, Kīmi ; Sahidic Coptic: ⲕⲏⲙⲉ, Kēme), officially the Arab Republic of Egypt, Arabic:  جمهوريّة مصر العربيّة (help·info), is a country mainly in North Africa, with the Sinai Peninsula forming a land bridge in Southwest Asia. Egypt is thus a transcontinental country, and a major power in Africa, the Mediterranean Basin, the Middle East and the Muslim world. Covering an area of about 1,010,000 square kilometers (390,000 sq mi), Egypt is bordered by the Mediterranean Sea to the north, the Gaza Strip and Israel to the northeast, the Red Sea to the east, Sudan to the south and Libya to the west.
  Egypt is one of the most populous countries in Africa and the Middle East. The great majority of its over 81 million people live near the banks of the Nile River, in an area of about 40,000 square kilometers (15,000 sq mi), where the only arable land is found. The large areas of the Sahara Desert are sparsely inhabited. About half of Egypt's residents live in urban areas, with most spread across the densely populated centres of greater Cairo, Alexandria and other major cities in the Nile Delta.
  
  wn.com/Egypt
• 
  Israel
  Coordinates: 31°N 35°E / 31°N 35°E / 31; 35
  Israel, officially the State of Israel ( /ˈɪzriːəl/ or  /ˈɪzreɪəl/; Hebrew: מְדִינַת יִשְׂרָאֵל‎, Medīnat Yisrā'el, IPA: [me̞diˈnät jisʁäˈʔe̞l] ( listen); Arabic: دَوْلَة إِسْرَائِيل‎, Dawlat Isrāʼīl, IPA: [dawlat ʔisraːˈʔiːl]), is a parliamentary republic in the Middle East, along the eastern shore of the Mediterranean Sea. It borders Lebanon in the north, Syria in the northeast, Jordan and the West Bank in the east, Egypt and the Gaza Strip on the southwest, and the Gulf of Aqaba in the Red Sea to the south, and it contains geographically diverse features within its relatively small area. Israel is defined as a Jewish and Democratic State in its Basic Laws and is the world's only Jewish-majority state.
  Following the adoption of a resolution by the General Assembly of the United Nations on 29 November 1947 recommending the adoption and implementation of the United Nations plan to partition Palestine, on 14 May 1948 David Ben-Gurion, the Executive Head of the World Zionist Organization and president of the Jewish Agency for Palestine, declared the establishment of a Jewish state in Eretz Israel, to be known as the State of Israel, a state independent from the British Mandate for Palestine. Neighboring Arab states invaded the next day in support of the Palestinian Arabs. Israel has since fought several wars with neighboring Arab states, in the course of which it has occupied the West Bank, Sinai Peninsula, Gaza Strip and the Golan Heights. Portions of these territories, including east Jerusalem, have been annexed by Israel, but the border with the neighboring West Bank has not yet been permanently defined.^{[neutrality is disputed]} Israel has signed peace treaties with Egypt and Jordan, but efforts to resolve the Israeli–Palestinian conflict have so far not resulted in peace.
  
  wn.com/Israel
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  Manhattan
  Manhattan (/mænˈhætən/) is the most densely populated and the oldest of the five boroughs of New York City. Located primarily on the island of Manhattan at the mouth of the Hudson River, the boundaries of the borough are identical to those of New York County, an original county of the U.S. state of New York. The borough and county consist of Manhattan Island and several small adjacent islands: Roosevelt Island, Randall's Island, Wards Island, Governors Island, Liberty Island, part of Ellis Island,Mill Rock, and U Thant Island; as well as Marble Hill, a very small area on the mainland bordering the Bronx. The original city of New York began at the southern end of Manhattan, expanded northward, and then between 1874 and 1898, annexed land from surrounding counties.
  The New York County is the most densely populated county in the United States, and one of the most densely populated areas in the world, with a 2010 population of 1,585,873 living in a land area of 22.96 square miles (59.5 km²), or 69,464 residents per square mile (26,924/km²), more dense than any individual American city. It is also one of the wealthiest counties in the United States, with a 2005 per capita income above $100,000. Manhattan is the third-largest of New York's five boroughs in population, and its smallest borough in land area.
  
  wn.com/Manhattan
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  Ontario
  Ontario /ɒnˈtɛərioʊ/ is one of the provinces of Canada, located in east-central Canada. It is Canada's most populous province or territory and fourth largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa.
  Ontario is bordered by the province of Manitoba to the west, Hudson Bay to the north, Quebec to the east, and to the south by the U.S. states of Minnesota, Michigan (portions to the west), New York (portions to the east), Ohio and Pennsylvania. All but a small part of Ontario's 2,700 km (1,677 mi) border with the United States follow inland waterways: from the west at Lake of the Woods, eastward along the major rivers and lakes of the Great Lakes/St. Lawrence River drainage system. These are the Rainy River, the Pigeon River, Lake Superior, the St. Mary's River, Lake Huron, the St. Clair River, Lake St. Clair, the Detroit River, Lake Erie, the Niagara River, Lake Ontario, and along the St. Lawrence River from Kingston, Ontario to the Quebec boundary just east of Cornwall, Ontario.
  
  wn.com/Ontario
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  San Francisco
  San Francisco (/ˌsæn frənˈsɪskoʊ/), officially the City and County of San Francisco, is the financial, cultural, and transportation center of the San Francisco Bay Area, a region of 7.6 million people which includes San Jose and Oakland. The only consolidated city-county in California, it encompasses a land area of about 46.9 square miles (121 km²) on the northern end of the San Francisco Peninsula, giving it a density of about 17,179 people per square mile (6,632 people per km²). It is the most densely settled large city (population greater than 200,000) in the state of California and the second-most densely populated large city in the United States after New York City. San Francisco is the fourth most populous city in California and the 13th most populous city in the United States, with a population of 805,235 as of the 2010 Census. The San Francisco-Oakland-Fremont metropolitan area has a population of 4,335,391.
  In 1776, colonists from Spain established a fort at the Golden Gate and a mission named for Francis of Assisi a few miles away. The California Gold Rush of 1849 propelled the city into a period of rapid growth, increasing the population in one year from 1,000 to 25,000, and thus transforming it into the largest city on the West Coast at the time. After three-quarters of the city was destroyed by the 1906 earthquake and fire, San Francisco was quickly rebuilt, hosting the Panama-Pacific International Exposition nine years later. During World War II, San Francisco was the port of embarkation for service members shipping out to the Pacific Theater. After the war, the confluence of returning servicemen, massive immigration, liberalizing attitudes, and other factors led to the Summer of Love and the gay rights movement, cementing San Francisco as a center of liberal activism in the United States.
  
  wn.com/San_Francisco

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  Abraham
  Abraham (Hebrew:  אַבְרָהָם (help·info), Modern: Avraham, Tiberian: ʼAḇrāhām, Ashkenazi Avrohom or Avruhom, Arabic: إبراهيم‎ Ibrāhīm, Ge'ez: አብርሃም ʼAbrəham, Greek: Aβραάμ, Russian: Авраам), whose birth name was Abram, is the eponym of the Abrahamic religions, among which are Judaism, Christianity and Islam. According to both the Hebrew Bible and the Qur'an, through his sons Ishmael and Isaac, Abraham is the forefather of many tribes, namely the Ishmaelites, Israelites, Midianites and Edomites. Abraham was a descendant of Noah's son, Shem. Christians believe that Jesus was a descendant of Abraham through Isaac, and Muslims believe that Muhammad was a descendant of Abraham through Ishmael. Abraham is notable for his advocation and promotion of monotheism.
  The Book of Genesis narrative that records the life of Abraham presents his role as one that could only be fulfilled through a monotheistic covenant established between him and God. The Qur'an has stories about Abraham and his offspring that are similar to the Bible's. In Islam, Abraham is recognised as a prophet, patriarch and messenger, archetype of the perfect Muslim, and reformer of the Kaaba.
  
  wn.com/Abraham
• Alan Ross Anderson
  Alan Ross Anderson (1925 – 1973) was an American logician and professor of philosophy at Yale University and the University of Pittsburgh.
  A frequent collaborator with Nuel Belnap, Anderson was instrumental in the development of relevance logic and deontic logic.
  Anderson died of cancer in 1973.
  Anderson believed that the conclusion of a valid inference ought to have something to do with (i.e. be relevant to) the premises. Formally, he captured this "relevance condition" with the principle that
  As simple as this idea appears, implementing it in a formal system requires a radical departure from the semantics of classical logic. Anderson and Belnap (with contributions from J. Michael Dunn, Kit Fine, Alasdair Urquhart, Robert K. Meyer, Anil Gupta (logician), and others) explored the formal consequences of the relevance condition in great detail in their influential Entailment books (see references below), which are the most frequently cited works in the field of relevance logic.
  Anderson and Belnap were quick to observe that the concept of relevance had been central to logic since Aristotle, but had been unduly neglected since Gottlob Frege and George Boole laid the foundations for what would come to be known, somewhat ironically, as "classical" logic. (For an example of classical logic's failure to satisfy the relevance condition, see the article on the principle of explosion.)
  
  wn.com/Alan_Ross_Anderson
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  Alan Turing
  Alan Mathison Turing, OBE, FRS ( /ˈtjʊərɪŋ/ TEWR-ing; 23 June 1912 – 7 June 1954), was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a significant role in the creation of the modern computer. Turing is widely considered to be the father of computer science and artificial intelligence.
  During the Second World War, Turing worked for the Government Code and Cypher School (GCCS) at Bletchley Park, Britain's codebreaking centre. For a time he was head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine.
  After the war he worked at the National Physical Laboratory, where he created one of the first designs for a stored-program computer, the ACE. In 1948 Turing joined Max Newman's Computing Laboratory at Manchester University, where he assisted in the development of the Manchester computers and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis, and he predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, which were first observed in the 1960s.
  
  wn.com/Alan_Turing
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  Alexander Bain
  Alexander Bain (11 June 1818 – 18 September 1903) was a Scottish philosopher and educationalist in the British school of empiricism who was a prominent and innovative figure in the fields of psychology, linguistics, logic, moral philosophy and education reform. He founded Mind, the first ever journal of psychology and analytical philosophy, and was the leading figure in establishing and applying applying the scientific method to psychology. Bain was the inaugural Regius Chair in Logic and Professor of Logic at the University of Aberdeen, where he also held Professorships in Moral Philosophy and English Literature and was twice elected Lord Rector of the University of Aberdeen.
  Alexander Bain was born in Aberdeen, Scotland to George Bain, a weaver and veteran soldier, and Margaret Paul. At age eleven he left school to work as a weaver hence the description of him as Weevir, rex philosophorum. He also took to lectures at the Mechanics' Institutes of Aberdeen and the Aberdeen Public Library.
  
  wn.com/Alexander_Bain
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  Alfred Tarski
  Alfred Tarski (January 14, 1901 – October 26, 1983) was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of California, Berkeley, from 1942 until his death.
  A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.
  His biographers Anita and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models."
  Alfred Tarski was born Alfred Teitelbaum (Polish spelling: "Tajtelbaum"), to parents who were Polish Jews in comfortable circumstances. He first manifested his mathematical abilities while in secondary school, at Warsaw's Szkoła Mazowiecka. Nevertheless, he entered the University of Warsaw in 1918 intending to study biology.
  
  wn.com/Alfred_Tarski
• Alonzo Church
  Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, Church–Turing thesis, solving the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem.
  Alonzo Church was born on June 14, 1903 in Washington, D.C. where his father, Samuel Robbins Church, was the judge of the Municipal Court for the District of Columbia. The family later moved to Virginia after his father lost this position because of failing eyesight. With help from his uncle, also named Alonzo Church, he was able to attend the Ridgefield School for Boys in Ridgefield, Connecticut. After graduating from Ridgefield in 1920, Church attended Princeton University where he was an exceptional student, publishing his first paper, on Lorentz transformations, and graduating in 1924 with a degree in mathematics. He stayed at Princeton, earning a Ph.D. in mathematics in three years under Oswald Veblen.
  
  wn.com/Alonzo_Church
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  Aristotle
  Aristotle (Ancient Greek: Ἀριστοτέλης, Aristotélēs) (384 BC – 322 BC) was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology. Together with Plato and Socrates (Plato's teacher), Aristotle is one of the most important founding figures in Western philosophy. Aristotle's writings were the first to create a comprehensive system of Western philosophy, encompassing morality, aesthetics, logic, science, politics, and metaphysics.
  Aristotle's views on the physical sciences profoundly shaped medieval scholarship, and their influence extended well into the Renaissance, although they were ultimately replaced by Newtonian physics. In the zoological sciences, some of his observations were confirmed to be accurate only in the 19th century. His works contain the earliest known formal study of logic, which was incorporated in the late 19th century into modern formal logic. In metaphysics, Aristotelianism had a profound influence on philosophical and theological thinking in the Islamic and Jewish traditions in the Middle Ages, and it continues to influence Christian theology, especially the scholastic tradition of the Catholic Church. His ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotle's philosophy continue to be the object of active academic study today. Though Aristotle wrote many elegant treatises and dialogues (Cicero described his literary style as "a river of gold"), it is thought that the majority of his writings are now lost and only about one-third of the original works have survived.
  
  wn.com/Aristotle
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  Augustus De Morgan
  Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous. The crater De Morgan on the Moon is named after him.
  Augustus De Morgan was born in 1806. His father was Col. Augustus De Morgan, who held various appointments in the service of the East India Company. His mother descended from James Dodson, who computed a table of anti-logarithms, that is, the numbers corresponding to exact logarithms. Augustus De Morgan became blind in one eye a month or two after he was born. The family moved to England when Augustus was seven months old. As his father and grandfather had both been born in India, De Morgan used to say that he was neither English, nor Scottish, nor Irish, but a Briton "unattached", using the technical term applied to an undergraduate of Oxford or Cambridge who is not a member of any one of the Colleges.
  When De Morgan was ten years old, his father died. Mrs. De Morgan resided at various places in the southwest of England, and her son received his elementary education at various schools of no great account. His mathematical talents went unnoticed until he was fourteen, when a family-friend discovered him making an elaborate drawing of a figure in Euclid with ruler and compasses. She explained the aim of Euclid to Augustus, and gave him an initiation into demonstration.
  
  wn.com/Augustus_De_Morgan
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  Averroes
  ʾAbū l-Walīd Muḥammad bin ʾAḥmad bin Rušd (Arabic: أبو الوليد محمد بن احمد بن رشد‎), better known just as Ibn Rushd (Arabic: ابن رشد‎), and in European literature as Averroes ( /əˈvɛroʊ.iːz/; April 14, 1126 – December 10, 1198), was an Andalusian Muslim polymath; a master of Aristotelian philosophy, Islamic philosophy, Islamic theology, Maliki law and jurisprudence, logic, psychology, politics, Arabic music theory, and the sciences of medicine, astronomy, geography, mathematics, physics and celestial mechanics. He was born in Córdoba, Al Andalus, modern-day Spain, and died in Marrakesh, Morocco. His school of philosophy is known as Averroism.
  Ibn Rushd was a defender of Aristotelian philosophy against claims from the influential Islamic theologian Ghazali who attacked philosophy so it would not become an affront to the teachings of Islam.
  Averroes' name is also seen as Averroës, Averroès or Averrhoës, indicating that the "o" and the "e" form separate syllables. Averroes is a Latinisation of a Hebrew transcription of the Arab name Ibn Rushd.
  
  wn.com/Averroes
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  Avicenna
  Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā (Persian پورسينا Pur Sina [ˈpuːr ˈsiːnɑː] "son of Sina"; c. 980, Afshana near Bukhara– 1037, Hamadan, Iran), commonly known as Ibn Sīnā or by his Latinized name Avicenna, was a Persianpolymath, who wrote almost 450 treatises on a wide range of subjects, of which around 240 have survived. In particular, 150 of his surviving treatises concentrate on philosophy and 40 of them concentrate on medicine.
  His most famous works are The Book of Healing, a vast philosophical and scientific encyclopaedia, and The Canon of Medicine, which was a standard medical text at many medieval universities. The Canon of Medicine was used as a text-book in the universities of Montpellier and Leuven as late as 1650. Ibn Sīnā's Canon of Medicine provides a complete system of medicine according to the principles of Galen (and Hippocrates).
  His corpus also includes writing on philosophy, astronomy, alchemy, geology, psychology, Islamic theology, logic, mathematics, physics, as well as poetry. He is regarded as the most famous and influential polymath of the Islamic Golden Age.
  
  wn.com/Avicenna
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  Bertrand Russell
  Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these in any profound sense. He was born in Monmouthshire, into one of the most prominent aristocratic families in Britain.
  Russell led the British "revolt against idealism" in the early 20th century. He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege and his friend Ludwig Wittgenstein, and is widely held to be one of the 20th century's premier logicians. He co-authored, with A. N. Whitehead, Principia Mathematica, an attempt to ground mathematics on logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy." His work has had a considerable influence on logic, mathematics, set theory, linguistics, computer science (see type theory and type system), and philosophy, especially philosophy of language, epistemology, and metaphysics.
  
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  Chrysippus
  Chrysippus of Soli (Ancient Greek: Χρύσιππος ὁ Σολεύς, Chrysippos ho Soleus; c. 279 BC – c. 206 BC) was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of Cleanthes in the Stoic school. When Cleanthes died, around 230 BC, Chrysippus became the third head of the school. A prolific writer, Chrysippus expanded the fundamental doctrines of Zeno of Citium, the founder of the school, which earned him the title of Second Founder of Stoicism.
  Chrysippus excelled in logic, the theory of knowledge, ethics and physics. He created an original system of propositional logic in order to better understand the workings of the universe and role of humanity within it. He adhered to a deterministic view of fate, but nevertheless sought a role for personal freedom in thought and action. Ethics, he taught, depended on understanding the nature of the universe, and he taught a therapy of extirpating the unruly passions which depress and crush the soul. He initiated the success of Stoicism as one of the most influential philosophical movements for centuries in the Greek and Roman world.
  
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  David
  David (Hebrew: דָּוִד, דָּוִיד, Modern David Tiberian Dāwîḏ; ISO 259-3 Dawid; Strong's Daveed; beloved; Arabic: داوود‎ or داود‎ Dāwūd) was, according to the Hebrew Bible, the second king of the United Kingdom of Israel and, according to the Gospel of Matthew and the Gospel of Luke, an ancestor of Jesus. David is seen as a major Prophet in Islamic traditions. His life is conventionally dated to c. 1040–970 BC, his reign over Judah c. 1010–1003 BC,^{[citation needed]} and his reign over the United Kingdom of Israel c. 1003–970 BC.^{[citation needed]} The Books of Samuel, 1 Kings, and 1 Chronicles are the only sources of information on David, although the Tel Dan stele records "House of David", which some take as confirmation of the existence in the mid-9th century BC of a Judean royal dynasty called the "House of David".
  David is very important to Jewish, Christian and Islamic doctrine and culture. In Judaism, David, or David HaMelekh, is the King of Israel, and the Jewish people. Jewish tradition maintains that a direct descendant of David will be the Messiah. In Islam, he is known as Dawud, considered to be a prophet and the king of a nation. He is depicted as a righteous king, though not without faults, as well as an acclaimed warrior, musician, and poet, traditionally credited for composing many of the psalms contained in the Book of Psalms.
  
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  David Hilbert
  David Hilbert, FRS (German pronunciation: [ˈdaːvɪt ˈhɪlbɐt]; January 23, 1862 – February 14, 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
  Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.
  Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.
  
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  Duns Scotus
  John (Johannes, Ioannes) Duns Scotus, O.F.M. (c. 1256 – November 18, 1308) was one of the more important theologians and philosophers of the High Middle Ages. He was given the medieval accolade Doctor Subtilis (Subtle Doctor) for his penetrating and subtle manner of thought.
  Scotus has had considerable influence on Roman Catholic thought. The doctrines for which he is best known are the "univocity of being," that existence is the most abstract concept we have, applicable to everything that exists; the formal distinction, a way of distinguishing between different aspects of the same thing; and the idea of haecceity, the property supposed to be in each individual thing that makes it an individual. Scotus also developed a complex argument for the existence of God, and argued for the Immaculate conception of Mary.
  Little is known of Scotus' life. He was probably born in 1265, probably at Duns, in Berwickshire, Scotland. In 1291 he was ordained as a priest in Northampton, England. A note in Codex 66 of Merton College, Oxford, records that Scotus "flourished at Cambridge, Oxford and Paris. He began lecturing on Peter Lombard's Sentences at the prestigious University of Paris in the Autumn of 1302. Later in that academic year, however, he was expelled from the University of Paris for siding with then Pope Boniface VIII in his feud with Philip the Fair of France, over the taxation of church property.
  
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  Ernst Schröder
  Ernst Schröder (25 November 1841, Mannheim, Baden, Germany – 16 June 1902, Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic (a term he may have invented), by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce. He is best known for his monumental Vorlesungen über die Algebra der Logik (Lectures on the algebra of logic), in 3 volumes, which prepared the way for the emergence of mathematical logic as a separate discipline in the twentieth century by systematizing the various systems of formal logic of the day.
  Schröder learned mathematics at Heidelberg, Königsberg, and Zürich, under Hesse, Kirchhoff, and Franz Neumann. After teaching school for a few years, he moved to the Technische Hochschule Darmstadt in 1874. Two years later, he took up a chair in mathematics at the Polytechnische Schule in Karlsruhe, where he spent the remainder of his life. He never married.
  
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  Ernst Zermelo
  Ernst Friedrich Ferdinand Zermelo (German: [ʦɛrˈmeːlo]; 1871–1953) was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy.^{[citation needed]} He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.
  He graduated from Berlin's Luisenstädtisches Gymnasium in 1889. He then studied mathematics, physics and philosophy at the universities of Berlin, Halle and Freiburg. He finished his doctorate in 1894 at the University of Berlin, awarded for a dissertation on the calculus of variations (Untersuchungen zur Variationsrechnung). Zermelo remained at the University of Berlin, where he was appointed assistant to Planck, under whose guidance he began to study hydrodynamics. In 1897, Zermelo went to Göttingen, at that time the leading centre for mathematical research in the world, where he completed his habilitation thesis in 1899.
  In 1910, Zermelo left Göttingen upon being appointed to the chair of mathematics at Zurich University, which he resigned in 1916. He was appointed to an honorary chair at Freiburg im Breisgau in 1926, which he resigned in 1935 because he disapproved of Hitler's regime. At the end of World War II and at his request, Zermelo was reinstated to his honorary position in Freiburg.
  
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  Eve
  Eve (Hebrew: חַוָּה‎, Ḥawwāh in Classical Hebrew, Khavah in Modern Israeli Hebrew, Arabic: حواء‎, Syriac: ܚܘܐ ) was, according to the creation myth of Abrahamic religions, the first woman created by God, in the Genesis creation narrative.
  In the Bible, Eve (Hebrew: חַוָּה, Ḥawwāh; Arabic: حواء‎, Hawwa'; Ge'ez: ሕይዋን Hiywan; "living one" or "source of life", related to ḥāyâ, "to live"; ultimately from the Semitic root ḥyw; Greek: Εὕα, heúā) is Adam's wife. Her name occurs only four times; the first being Genesis 3:20: "And Adam called his wife's name Ḥawwāh; because she was the mother of all living" (a title previously held by the Babylonian creatrix Tiamat). In Vulgate she appears as "Hava" in the Old Testament, but "Eva" in the New Testament. The name may actually be derived from that of the Hurrian Goddess Kheba, who was shown in the Amarna Letters to be worshipped in Jerusalem during the Late Bronze Age. It has been suggested that the name Kheba may derive from Kubau, a woman who reigned as the first king of the Third Dynasty of Kish Another name of Asherah in the first millennium BCE was Chawat, Hawwah in Aramaic, (Eve in English).
  
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  Georg Cantor
  Georg Ferdinand Ludwig Philipp Cantor ( /ˈkæntɔr/ KAN-tor; German: [ɡeˈɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware.
  
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  George Boole
  George Boole ( /ˈbuːl/; 2 November 1815 – 8 December 1864) was an English-born mathematician and logician. His work was in the fields of differential equations and algebraic logic, and he is now best known as the author of The Laws of Thought. As the inventor of the prototype of what is now called Boolean logic, which became the basis of the modern digital computer, Boole is regarded in hindsight as a founder of the field of computer science. Boole said,
  ... no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise ... those universal laws of thought which are the basis of all reasoning ...
  George Boole's father, John Boole (1779–1848), was a tradesman in Lincoln and gave him lessons. He had an elementary school education, but little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin; which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages. At age 16 Boole took up a junior teaching position in Doncaster, at Heigham's School, being at this point the breadwinner for his parents and three younger siblings. He taught also in Liverpool, briefly.
  
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• George Boolos
  George Stephen Boolos (September 4, 1940, New York City – May 27, 1996) was a philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
  Boolos graduated from Princeton University in 1961 with an A.B. in mathematics. Oxford University awarded him the B.Phil in 1963. In 1966, he obtained the first Ph.D. in philosophy ever awarded by the Massachusetts Institute of Technology, under the direction of Hilary Putnam. After teaching three years at Columbia University, he returned to MIT in 1969, where he spent the rest of his career until his death from cancer.
  A charismatic speaker well known for his clarity and wit, he once delivered a lecture (1994b) giving an account of Gödel's second incompleteness theorem, employing only words of one syllable. At the end of his viva, Hilary Putnam asked him, "And tell us, Mr. Boolos, what does the analytical hierarchy have to do with the real world?" Without hesitating Boolos replied, "It's part of it".
  An expert on puzzles of all kinds, in 1993 Boolos reached the London Regional Final of The Times crossword competition. His score was one of the highest ever recorded by an American. He wrote a paper on "the hardest logic puzzle ever"—one of many puzzles created by Raymond Smullyan.
  
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  Gerhard Gentzen
  Gerhard Karl Erich Gentzen (November 24, 1909, Greifswald, Germany – August 4, 1945, Prague, Czechoslovakia) was a German mathematician and logician. He had his major contributions in the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died in 1945 after the Second World War, because he was deprived of food after being arrested in Prague.
  Gentzen was a student of Paul Bernays at the University of Göttingen. Bernays was fired as "non-Aryan" in April 1933 and therefore Hermann Weyl formally acted as his supervisor. At great risk to his career Gentzen kept in contact with Bernays until the beginning of the Second World War. In November 1933, he joined the Sturmabteilung to pass the state exam for teachers.^{[citation needed]} In 1935, he corresponded with Abraham Fraenkel from Jerusalem and was implicated by the Nazi teachers' union as one who "keeps contacts to the Chosen People." In 1935 and 1936, Hermann Weyl, head of the Göttingen mathematics department in 1933 until his resignation under Nazi pressure, made strong efforts to bring him to the Institute for Advanced Study in Princeton.
  
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  Giuseppe Peano
  Giuseppe Peano (Italian pronunciation: [dʒuˈzɛppe peˈaːno]; 27 August 1858 – 20 April 1932) was an Italian mathematician, whose work was of philosophical value. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin.
  Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Piedmont, Italy. He attended the Liceo classico Cavour in Turin, and enrolled at the University of Turin in 1876, graduating in 1880 with high honours, after which the University employed him to assist first Enrico D'Ovidio, and then Angelo Genocchi, the Chair of Infinitesimal calculus. Due to Genocchi's poor health, Peano took over the teaching of the infinitesimal calculus course within 2 years. His first major work, a textbook on calculus, was published in 1884 and was credited to Genocchi. A few years later, Peano published his first book dealing with mathematical logic. Here the modern symbols for the union and intersection of sets appeared for the first time.
  
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  Gottlob Frege
  Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925, pronounced [ˈɡɔtloːp ˈfreːɡə ]) was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on the philosophy of language and mathematics. While he was mainly ignored by the intellectual world when he published his writings, Giuseppe Peano (1858–1932) and Bertrand Russell (1872–1970) introduced his work to later generations of logicians and philosophers.
  Frege was born in 1848 in Wismar, in the state of Mecklenburg-Schwerin (the modern German federal state Mecklenburg-Vorpommern). His father Carl (Karl) Alexander Frege (3 August 1809 – 30 November 1866) was the co-founder and headmaster of a girls' high school until his death. After Carl's death, the school was led by Frege's mother Auguste Wilhelmine Sophie Frege (née Bialloblotzky, 12 January 1815 – 14 October 1898).
  
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• Haskell Curry
  Haskell Brooks Curry (September 12, 1900 – September 1, 1982) was an American mathematician and logician. Curry is best known for his work in combinatory logic; while the initial concept of combinatory logic was based on a single paper by Moses Schönfinkel, much of the development was done by Curry. Curry is also known for Curry's paradox and the Curry–Howard correspondence. There are three programming languages named after him, Haskell, Brooks and Curry, as well as the concept of currying, a technique used for transforming functions in mathematics and computer science.
  Curry was born on September 12, 1900, in Millis, Massachusetts, to Samuel Silas Curry and Anna Baright Curry, who ran a school for elocution. He entered Harvard University in 1916 to study medicine but switched to mathematics before graduating in 1920. After two years of graduate work in electrical engineering at MIT, he returned to Harvard to study physics, earning a MA in 1924. Curry's interest in mathematical logic started during this period when he was introduced to the Principia Mathematica, the attempt by Alfred North Whitehead and Bertrand Russell to ground mathematics in symbolic logic. Remaining at Harvard, Curry pursued a Ph.D. in mathematics. While he was directed by George Birkhoff to work on differential equations, his interests continued to shift to logic. In 1927, while an instructor at Princeton University, he discovered the work of Moses Schönfinkel in combinatory logic. Schönfinkel's work had anticipated much of Curry's own research, and as a consequence, he moved to Göttingen where he could work with Heinrich Behmann and Paul Bernays, who were familiar with Schönfinkel's work. Curry was supervised by David Hilbert and worked closely with Bernays, receiving a Ph.D. in 1930 with a dissertation on combinatory logic.
  
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  Hilary Putnam
  Hilary Whitehall Putnam (born July 31, 1926) is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science. He is known for his willingness to apply an equal degree of scrutiny to his own philosophical positions as to those of others, subjecting each position to rigorous analysis until he exposes its flaws. As a result, he has acquired a reputation for frequently changing his own position. Putnam is currently Cogan University Professor Emeritus at Harvard University.
  In philosophy of mind, Putnam is known for his argument against the type-identity of mental and physical states based on his hypothesis of the multiple realizability of the mental, and for the concept of functionalism, an influential theory regarding the mind-body problem. In philosophy of language, along with Saul Kripke and others, he developed the causal theory of reference, and formulated an original theory of meaning, inventing the notion of semantic externalism based on a famous thought experiment called Twin Earth.
  
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  Isaac Asimov
  Isaac Asimov (/ˈaɪzək ˈæzɨməv/ EYE-zək AZ-i-məv; born Isaak Yudovich Ozimov, Russian: Исаак Юдович Озимов; Yiddish: אייזיק יודאָוויטש אסימאוו; c. January 2, 1920 – April 6, 1992) was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000 letters and postcards. His works have been published in all ten major categories of the Dewey Decimal System (although his only work in the 100s—which covers philosophy and psychology—was a foreword for The Humanist Way).
  Asimov is widely considered a master of hard science fiction and, along with Robert A. Heinlein and Arthur C. Clarke, he was considered one of the "Big Three" science fiction writers during his lifetime. Asimov's most famous work is the Foundation Series; his other major series are the Galactic Empire series and the Robot series, both of which he later tied into the same fictional universe as the Foundation Series to create a unified "future history" for his stories much like those pioneered by Robert A. Heinlein and previously produced by Cordwainer Smith and Poul Anderson. He wrote many short stories, among them "Nightfall", which in 1964 was voted by the Science Fiction Writers of America the best short science fiction story of all time. Asimov wrote the Lucky Starr series of juvenile science-fiction novels using the pen name Paul French.
  
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  Jesse
  Jesse ( /ˈdʒɛs.iː/), Eshai or Yishai, (Hebrew: יִשַׁי, Modern Yishay Tiberian Yīšáy, meaning "God exists" or "God's gift"; Arabic: يَسَّى‎ Yassa; Greek: Ἰεσσαί Iessai; Latin: Isai, Jesse) is the father of the David, who became the king of the Israelites. His son David is sometimes called simply "Son of Jesse" (Ben Yishai).
  Jesse was the son of Obed and the grandson of Ruth and of Boaz. He lived in Bethlehem, in Judah, and was of the Tribe of Judah, he was a farmer, breeder and owner of sheep. He was a prominent resident of the town of Bethlehem. Jesse is important in Judaism because he was the father of the most famous king of Israel. He is important in Christianity, in part because he is in the Old Testament and mentioned in the genealogy of Jesus.
  Jesse is stated as having eight sons, including David the youngest. Among his grandchildren were the three sons of Zeruiah, Abishai, Joab and Ashashel. One day the prophet Samuel came to Bethlehem sent by God, to anoint the next king of Israel. Ostensibly, his visit to Bethlehem was to offer a sacrifice to God. He used that excuse because he was afraid that Saul might kill him if he suspected the true reason for his arrival in Bethlehem. Samuel offered a sacrifice with Jesse and then went to his house, where he sanctified him and his family. The prophet asked Jesse to present his sons, after seeing them, he realized that God has not chosen any of them. Then he said to Jesse if he had any other sons, Jesse told him that David the youngest was tending the flock. The prophet then asked for him, waited and when he came, God asked the prophet to anoint him as king over Israel.
  
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  Jesus
  Jesus ( /ˈdʒiːzəs/; Greek: Ἰησοῦς; 7–2 BC/BCE to 30–36 AD/CE), also referred to as Jesus Christ or simply Christ, is the central figure of Christianity and most Christian denominations venerate him as God the Son incarnated. In Islam, Jesus (in Arabic: عيسى‎ in Islamic usage, commonly transliterated as Isa) is considered one of God's important prophets.
  Most modern historians agree that Jesus existed and was a Jewish teacher from Galilee in Roman Judaea, who was baptized by John the Baptist, and was crucified in Jerusalem on the orders of the Roman Prefect, Pontius Pilate. Scholars have offered competing descriptions and portraits of Jesus, which at times share a number of overlapping attributes, such as a rabbi, a charismatic healer, the leader of an apocalyptic movement, a self-described Messiah, a sage and philosopher, or a social reformer who preached of the "Kingdom of God" as a means for personal and egalitarian social transformation. Scholars have correlated the New Testament accounts with non-Christian historical records to arrive at an estimated chronology of Jesus' life.
  
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• Jon Barwise
  Kenneth Jon Barwise (June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.
  Born in Independence, Missouri to Kenneth T. and Evelyn, he was a precocious child.
  A pupil of Solomon Feferman at Stanford University, Barwise started his research in infinitary logic. After positions as assistant professor at the Universities of Yale and Wisconsin, during which time his interests turned to natural language, he returned to Stanford in 1983 to direct the Center for the Study of Language and Information. He began teaching at Indiana University in 1990. He was elected a Fellow of the American Academy of Arts and Sciences in 1999.
  Barwise contended that, by being explicit about the context in which a proposition is made, the situation, many problems in the application of logic can be eliminated. He sought ... to understand meaning and inference within a general theory of information, one that takes us outside the realm of sentences and relations between sentences of any language, natural or formal. In particular, he claimed that such an approach resolved the liar paradox. He made use of Peter Aczel's non-well-founded set theory in understanding "vicious circles" of reasoning.
  
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  Kurt Gödel
  Kurt Friedrich Gödel (/ˈkɜrt ɡɜrdəl/; German pronunciation: [ˈkʊʁt ˈɡøːdəl] ( listen); April 28, 1906 – January 14, 1978) was an Austrian/American logician, mathematician, and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.
  Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
  
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• Leopold Löwenheim
  Leopold Löwenheim (26 June 1878 in Krefeld, Germany (also the birthplace of Max Zorn) – 5 May 1957 in Berlin) was a German mathematician, known for his work in mathematical logic. The Nazi regime forced him to retire because under the Nuremberg Laws he was considered only three quarters Aryan. In 1943 much of his work was destroyed during a bombing raid on Berlin. Nevertheless, he survived the Second World War, after which he resumed teaching mathematics.
  Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting point for model theory.
  Primary:
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  Ludwig Wittgenstein
  Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947. In his lifetime, he published just one book review, one article, a children's dictionary, and the 75-page Tractatus Logico-Philosophicus (1921). In 1999, his posthumously published Philosophical Investigations (1953) was ranked as the most important book of 20th-century philosophy, standing out as "...the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations".Bertrand Russell described him as "the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, and dominating".
  Born in Vienna into one of Europe's wealthiest families, he gave away his entire inheritance. Three of his brothers committed suicide, with Ludwig contemplating it too. He left academia several times: serving as an officer on the frontline during World War I, where he was decorated a number of times for his courage; teaching in schools in remote Austrian villages, where he encountered controversy for hitting children when they made mistakes in mathematics; and working during World War II as a hospital porter in London, where he told patients not to take the drugs they were prescribed, and where no-one knew he was one of the world's most famous philosophers. He described philosophy, however, as "the only work that gives me real satisfaction."
  
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• Paul Atreides
  Paul Atreides (/əˈtreɪdiːz/; later known as Paul Muad'Dib) is a fictional character in the Dune universe created by Frank Herbert. Paul is a prominent character in the first two novels in the series, Dune (1965) and Dune Messiah (1969), and returns in Children of Dune (1976). The character is brought back as two different gholas in the Brian Herbert/Kevin J. Anderson novels which conclude the original series, Hunters of Dune (2006) and Sandworms of Dune (2007).
  A primary theme of Dune and its sequels is Frank Herbert's warning about society's tendencies to "give over every decision-making capacity" to a charismatic leader. He said in 1979, "The bottom line of the Dune trilogy is: beware of heroes. Much better rely on your own judgment, and your own mistakes." Paul rises to leadership through military strategy and political maneuvering, but his superhuman powers and ability to fit himself into pre-existing religious infrastructure allow him to force himself upon mankind as their messiah. As "Muad'Dib," Paul becomes the central figure of a new religion, and reluctantly unleashes a bloody jihad in his name across the universe; Paul struggles with the potential idea of seizing divine control over his newly minted empire, only to finally escape from the burden of his destiny by placing it on his sister Alia and his offspring Leto II and Ghanima.
  
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• Paul Bernays
  Paul Isaac Bernays (17 October 1888, London – 18 September 1977, Zurich) was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator with, David Hilbert.
  Bernays spent his childhood in Berlin. Bernays attended the Köllner Gymnasium, 1895-1907. At the University of Berlin, he studied mathematics under Issai Schur, Edmund Landau, Ferdinand Georg Frobenius, and Friedrich Schottky; philosophy under Alois Riehl, Carl Stumpf and Ernst Cassirer; and physics under Max Planck. At the University of Göttingen, he studied mathematics under David Hilbert, Edmund Landau, Hermann Weyl, and Felix Klein; physics under Voigt and Max Born; and philosophy under Leonard Nelson.
  In 1912, the University of Berlin awarded him a Ph.D. in mathematics, for a thesis, supervised by Landau, on the analytic number theory of binary quadratic forms. That same year, the University of Zurich awarded him the Habilitation for a thesis on function theory and Picard's theorem. The examiner was Ernst Zermelo. Bernays was Privatdozent at the University of Zurich, 1912-17, where he came to know George Pólya.
  
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• Peter Geach
  Peter Thomas Geach, MA, FBA ( /ˈɡiːtʃ/; born 29 March 1916) is a British philosopher. His areas of interest are the history of philosophy, philosophical logic, and the theory of identity.
  Geach was educated at Balliol College, Oxford. He taught at Birmingham University (1951–1966) and from 1966 at the University of Leeds where he was Professor of Logic in the Department of Philosophy. Geach was given the title of Emeritus Professor of Logic on his retirement in 1981.
  Geach was elected a Fellow of the British Academy (FBA) in 1965.
  He has been awarded the papal cross "Pro Ecclesia et Pontifice" by the Holy See for his philosophical work.
  His early work includes the classic texts Mental Acts and Reference and Generality, the latter defending an essentially modern conception of reference against medieval theories of supposition.
  His Catholic perspective is integral to his philosophy. He is perhaps the founder of Analytical Thomism (though the current of thought running through his and Elizabeth Anscombe's work to the present day was only ostensibly so named forty years later by John Haldane), the aim of which is to synthesise Thomistic and Analytic approaches. He defends the Thomistic position that human beings are essentially rational animals, each one miraculously created. He dismisses Darwinistic attempts to regard reason as inessential to humanity, as "mere sophistry, laughable, or pitiable." He repudiates any capacity for language in animals as mere "association of manual signs with things or performances."
  
  wn.com/Peter_Geach
• Raymond Smullyan
  Raymond Merrill Smullyan (born May 25, 1919) is an American mathematician, concert pianist, logician, Taoist philosopher, and magician.
  Born in Far Rockaway, New York, his first career (like Persi Diaconis a generation later) was stage magic. He then earned a BSc from the University of Chicago in 1955 and his Ph.D. from Princeton University in 1959. He is one of many logicians to have studied under Alonzo Church.
  Born in Far Rockaway, New York, he showed musical talent, winning a gold medal in a piano competition when he was aged 12. The following year, his family moved to Manhattan and he attended Theodore Roosevelt High School in The Bronx as this school offered courses suited to his musical talents, but he left to study on his own as the school did not offer similar courses in mathematics.
  He attended several colleges, studying mathematics and music.
  While a Ph.D. student, Smullyan published a paper in the 1957 Journal of Symbolic Logic showing that Gödelian incompleteness held for formal systems considerably more elementary than that of Gödel's 1931 landmark paper. The contemporary understanding of Gödel's theorem dates from this paper. Smullyan later made a compelling case that much of the fascination with Gödel's theorem should be directed at Tarski's theorem, which is much easier to prove and equally disturbing philosophically. The culmination of Smullyan's lifelong reflection on the classic limitative theorems of mathematical logic is quite readable:
  
  wn.com/Raymond_Smullyan
• 
  Romanian name
  A name in Romanian consists of a given name (prenume) and a surname (nume or nume de familie). Surnames appear after given names in most Romanian contexts. However official documents invert the order, ostensibly for filing purposes. Correspondingly, some Romanians occasionally introduce themselves with their family names first, e.g. a student signing a test paper in school.
  Romanians have one, two or more given names, all being chosen by the child's parents. One of them, almost always the first, is used in daily life while the others are solely for official documents, such as birth, death and marriage certificates.
  Traditionally, most people were given names from the Romanian Orthodox calendar of saints. Common names of this type are Ion or Andrei for males and Maria or Elena for females. The prevalence of given names follows trends, with some names being popular in some years, and some considered definitely out-of-fashion. As an example, few children born since 1980 would bear the name Ion/Ioan, which is generally associated with the idea of an elderly man. However, such "old-fashioned" names are frequently used as second or third given names (middle names).
  
  wn.com/Romanian_name
• Rudolf Carnap
  Rudolf Carnap (May 18, 1891 – September 14, 1970) was an influential German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism.
  Carnap was born to a west German family that had been humble until his parents' generation. He began his formal education at the Barmen Gymnasium. From 1910 to 1914, he attended the University of Jena, intending to write a thesis in physics. But he also studied carefully Kant's Critique of Pure Reason during a course taught by Bruno Bauch, and was one of very few students to attend Gottlob Frege's courses in mathematical logic. After serving in the German army during World War I for three years, he was given permission to study physics at the University of Berlin, 1917–18, where Albert Einstein was a newly appointed professor. Carnap then attended the University of Jena, where he wrote a thesis defining an axiomatic theory of space and time. The physics department said it was too philosophical, and Bruno Bauch of the philosophy department said it was pure physics. Carnap then wrote another thesis, with Bauch's supervision, on the theory of space in a more orthodox Kantian style, and published as Der Raum (Space) in a supplemental issue of Kant-Studien (1922). In it he makes the clear distinction between formal, physical and perceptual (e.g., visual) spaces.
  
  wn.com/Rudolf_Carnap
• 
  Sarah
  Sarah or Sara ( /ˈsɛərə/;Hebrew: שָׂרָה, Modern Sara Tiberian Śārā ISO 259-3 Śarra; Latin: Sara; Arabic: سارة) was the wife of Abraham and the mother of Isaac as described in the Hebrew Bible and the Quran. Her name was originally Sarai. According to Genesis 17:15 God changed her name to Sarah as part of a covenant after Hagar bore Abraham his first son, Ishmael.
  The Hebrew name Sarah indicates a woman of high rank and is translated as "princess".
  Sarah was the wife of Abraham, as well as being his half-sister, the daughter of his father Terah (Genesis 20:12). The Talmud identifies Sarai with Iscah, daughter of Abraham's deceased brother Haran (Genesis 11:29), so that Sarah turns out to be the niece of Abraham and the sister of Lot and Milcah. She was also the mother-in-law of Rebecca, her successor. She was considered beautiful to the point that Abraham feared that when they were near more powerful rulers she would be taken away and given to another man. Twice he purposefully identified her as being only his sister so that he would be "treated well" for her sake. It is apparent that she remained attractive into her later years. Despite her great beauty, she was barren for an unknown reason. She was originally called "Sarai" which is translated "my princess." Later she was called "Sarah" i.e., princess." In Biblical times, the changing of one's name was significant and used to symbolize the binding of a covenant. In this case, God promised to put an end to her barrenness and give her a child (Isaac).
  
  wn.com/Sarah
• 
  Saul Kripke
  Saul Aaron Kripke (born November 13, 1940) is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center. Since the 1960s Kripke has been a central figure in a number of fields related to mathematical logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and set theory. Much of his work remains unpublished or exists only as tape-recordings and privately circulated manuscripts. Kripke was the recipient of the 2001 Schock Prize in Logic and Philosophy. A recent poll conducted among philosophers ranked Kripke among the top ten most important philosophers of the past 200 years.
  Kripke has made influential and original contributions to logic, especially modal logic, since he was a teenager. Unusual for a professional philosopher, his only degree is an undergraduate degree from Harvard, in mathematics. His work has profoundly influenced analytic philosophy, with his principal contribution being a semantics for modal logic, involving possible worlds as described in a system now called Kripke semantics. Another of his most important contributions is his argument that necessity is a 'metaphysical' notion, which should be separated from the epistemic notion of a priori, and that there are necessary a posteriori truths, such as "Water is H₂O." He has also contributed an original reading of Wittgenstein, referred to as "Kripkenstein." His most famous work is Naming and Necessity (1980).
  
  wn.com/Saul_Kripke
• Sindhi names
  The Sindhi family names are found in Sindh, Pakistan and among Sindhis in India.
  
  wn.com/Sindhi_names
• 
  Slavic names
  Given names originating from the Slavic languages are most popular in Slavic countries such as Belarus, Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic, Poland, Russia, Serbia, Slovakia, Slovenia, Ukraine, and others.
  In pre-Christian traditions, a child younger than 7–10 years old would bear a "substitutional name" (e.g. Niemój "not mine", Nielub "not loved"), whose purpose was to decrease the apparent importance of a child and protect him or her from the curiosity of evil powers. This practice probably derived from the existence of a high fatality rate for young children at that time. A child who survived 7–10 years was worthy of care and was granted adult status and a new adult name during the ritual of a first haircut.
  Generally traditional names were dominant until Slavic nations converted to Christianity (e.g. the Catholic Church, the Eastern Orthodox Church). For instance, the Council of Trent (1545–63) decided that every Catholic should have a Christian name instead of native one.
  
  wn.com/Slavic_names
• 
  Solomon
  Solomon (Hebrew: שְׁלֹמֹה, Modern Shlomo Tiberian Šəlōmō ISO 259-3 Šlomo; Arabic: سليمان‎ Sulaymān, also colloquially: Silimān; Greek: Σολομών Solomōn), according to the Book of Kings and the Book of Chronicles, a King of Israel and according to the Talmud one of the 48 prophets, is identified as the son of David, also called Jedidiah (Hebrew יְדִידְיָהּ) in 2 Samuel 12:25, and is described as the third king of the United Monarchy, and the final king before the northern Kingdom of Israel and the southern Kingdom of Judah split; following the split his patrilineal descendants ruled over Judah alone. In the Qur'an, he is considered as a major Prophet, known as Sulaiman, son of David.
  The Hebrew Bible credits Solomon as the builder of the First Temple in Jerusalem, and portrays him as great in wisdom, wealth, and power, but ultimately as a king whose sin, including idolatry and turning away from Yahweh, leads to the kingdom being torn in two during the reign of his son Rehoboam. Solomon is the subject of many other later references and legends.
  
  wn.com/Solomon
• 
  Stephen Cole Kleene
  Stephen Cole Kleene (January 5, 1909, Hartford, Connecticut, United States – January 25, 1994, Madison, Wisconsin) was an American mathematician who helped lay the foundations for theoretical computer science. One of many distinguished students of Alonzo Church, Kleene, along with Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory. Kleene's work grounds the study of which functions are computable. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixpoint theorem. He also invented regular expressions, and was a leading American advocate of mathematical intuitionism.
  Kleene pronounced his last name /ˈkleɪniː/ KLAY-nee. Commonplace mispronunciations include /ˈkliːniː/ and /ˈkliːn/. (His son, Ken Kleene, wrote: "As far as I am aware this pronunciation is incorrect in all known languages. I believe that this novel pronunciation was invented by my father.")^{[citation needed]}
  
  wn.com/Stephen_Cole_Kleene
• Thoralf Skolem
  Thoralf Albert Skolem (23 May 1887 – 23 March 1963) (Norwegian pronunciation: [ˈtuːɾɑlf ˈskuːləm]) was a Norwegian mathematician known mainly for his work on mathematical logic and set theory.
  Although Skolem's father was a primary school teacher, most of his extended family were farmers. Skolem attended secondary school in Kristiania (later renamed Oslo), passing the university entrance examinations in 1905. He then entered Det Kongelige Frederiks Universitet to study mathematics, also taking courses in physics, chemistry, zoology and botany.
  In 1909, he began working as an assistant to the physicist Kristian Birkeland, known for bombarding magnetized spheres with electrons and obtaining aurora-like effects; thus Skolem's first publications were physics papers written jointly with Birkeland. In 1913, Skolem passed the state examinations with distinction, and completed a dissertation titled Investigations on the Algebra of Logic. He also traveled with Birkeland to the Sudan to observe the zodiacal light. He spent the winter semester of 1915 at the University of Göttingen, at the time the leading research center in mathematical logic, metamathematics, and abstract algebra, fields in which Skolem eventually excelled. In 1916 he was appointed a research fellow at Det Kongelige Frederiks Universitet. In 1918, he became a Docent in Mathematics and was elected to the Norwegian Academy of Science and Letters.
  
  wn.com/Thoralf_Skolem
• Vladimir Harkonnen
  The Baron Vladimir Harkonnen is a fictional character and the main antagonist from the Dune universe created by Frank Herbert. He is primarily featured in the 1965 novel Dune and is also a prominent character in the Prelude to Dune prequel trilogy (1999-2001) by Brian Herbert and Kevin J. Anderson. The character is brought back as a ghola in the Herbert/Anderson sequels which conclude the original series, Hunters of Dune (2006) and Sandworms of Dune (2007).
  "Appendix IV: The Almanak en-Ashraf (Selected Excerpts of the Noble Houses)" in Dune says of him (in part):
  VLADIMIR HARKONNEN (10,110-10,193) Commonly referred to as Baron Harkonnen, his title is officially Siridar (planetary governor) Baron. Vladimir Harkonnen is the direct-line male descendant of the Bashar Abulurd Harkonnen who was banished for cowardice after the Battle of Corrin. The return of House Harkonnen to power generally is ascribed to adroit manipulation of the whale fur market and later consolidation with melange wealth from Arrakis.
  
  wn.com/Vladimir_Harkonnen
• 
  William of Ockham
  William of Ockham ( /ˈɒkəm/; also Occam, Hockham, or several other spellings; c. 1288 – c. 1348) was an English Franciscan friar and scholastic philosopher, who is believed to have been born in Ockham, a small village in Surrey. 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 fourteenth century. Although he is commonly known for Ockham's razor, the methodological principle that bears his name, William of Ockham also produced significant works on logic, physics, and theology. In the Church of England, his day of commemoration is 10 April.
  William of Ockham joined the Franciscan order at an early age. It is believed that he studied theology at the University of Oxford from 1309 to 1321, but never completed his master's degree (the usual undergraduate degree in those times). Because of this, he acquired the byname Venerabilis Inceptor, or "Worthy Beginner" (an inceptor was a student formally admitted to the ranks of teachers by the university authorities). He was also known as the Doctor Invincibilis or "Unconquerable Teacher."
  
  wn.com/William_of_Ockham
• 
  Yoshiyuki Tomino
  Yoshiyuki Tomino (富野 由悠季, Tomino Yoshiyuki^?, born 富野 喜幸 November 5, 1941) is a Japanese mecha anime creator, animator, director, screenwriter and novelist. He was born in Odawara, Kanagawa Prefecture, and studied at Nihon University's College of Art. He is best known for creating the Gundam anime franchise.
  Tomino, began his career in 1963 with Osamu Tezuka's company, Mushi Productions, scripting the storyboards and screenplay of the first Japanese television anime series, Tetsuwan Atomu (also known as Astro Boy). He later became one of the most important members of the anime studio Sunrise, going on to direct numerous anime through the 1970s, 1980s and 1990s. Tomino is perhaps best known for his transformation of the "Super Robot" mecha anime genre into the "Real Robot" genre with 1979's Mobile Suit Gundam, the first in the Gundam metaseries. He has also won numerous awards, including the "Best Director" award at the recent 2006 Tokyo International Anime Fair (for the 2005 film Mobile Suit Zeta Gundam: Heirs To The Stars). Two anime series directed by Tomino (Mobile Suit Gundam in 1979-80 and Space Runaway Ideon in 1980) won the Animage Anime Grand Prix award.
  
  wn.com/Yoshiyuki_Tomino

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