In the philosophy of mathematics, intuitionism, or neointuitionism, is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.
In mathematical logic, Russell's paradox is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. The paradox had already been discovered independently in 1899 by the German mathematician Ernst Zermelo. However, Zermelo did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other academics at the University of Göttingen. At the end of the 1890s, Georg Cantor – considered the founder of modern set theory – had already realized that his theory would lead to a contradiction, as he told Hilbert and Richard Dedekind by letter.
Friedrich Ludwig Gottlob Frege 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 the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.
Classical logic or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy.
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic". An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics.
In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano.
Christos Dimitriou Papakyriakopoulos, commonly known as Papa, was a Greek mathematician specializing in geometric topology.
Apostolos K. Doxiadis is a Greek writer. He is best known for his international bestsellers Uncle Petros and Goldbach's Conjecture (2000) and Logicomix (2009).
Athens College is a co-educational private preparatory school in Psychiko, Greece, a suburb of Athens, part of the Hellenic-American Educational Foundation which also includes Psychico College, although both schools are usually referred to as "Athens College". It was established in 1925. Among the school's founders and big donors had been Emmanuel Benakis, namesake of the Benaki Museum of Athens, as well as the school's main building, and Stephanos Deltas who the school’s athletic facilities were named by. Instruction is in both Greek and English, while also including french lessons 2 hours a week.
Christos Charilaos Papadimitriou is a Greek theoretical computer scientist and the Donovan Family Professor of Computer Science at Columbia University.
Uncle Petros and Goldbach's Conjecture is a 1992 novel by Greek author Apostolos Doxiadis. It concerns a young man's interaction with his reclusive uncle, who sought to prove a famous unsolved mathematics problem, called Goldbach's Conjecture, that every even number greater than two is the sum of two primes. The novel discusses mathematical problems and some recent history of mathematics.
In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess." According to formalism, the truths expressed in logic and mathematics are not about numbers, sets, or triangles or any other coextensive subject matter — in fact, they aren't "about" anything at all. Rather, mathematical statements are syntactic forms whose shapes and locations have no meaning unless they are given an interpretation. In contrast to mathematical realism, logicism, or intuitionism, formalism's contours are less defined due to broad approaches that can be categorized as formalist.
Anatolia College (Greek: Κολλέγιο Ανατόλια, pronounced[koˈleʝioanaˈtolia], also known as the American College, is a private, non-profit, educational institution located in Pylaia, a suburb of Thessaloniki, Greece. The school has five subdivisions: Anatolia Elementary School, Anatolia High School, Pinewood International School, CTY Greece and ACT, the tertiary division of the institution.
Constantinos Daskalakis is a Greek theoretical computer scientist. He is a professor at MIT's Electrical Engineering and Computer Science department and a member of the MIT Computer Science and Artificial Intelligence Laboratory. He was awarded the Rolf Nevanlinna Prize and the Grace Murray Hopper Award in 2018.
Stathis K. Zachos is a mathematician, logician and theoretical computer scientist.
The mathematical concept of a function dates from the 17th century in connection with the development of the calculus; for example, the slope of a graph at a point was regarded as a function of the x-coordinate of the point. Functions were not explicitly considered in antiquity, but some precursors of the concept can perhaps be seen in the work of medieval philosophers and mathematicians such as Oresme.
The type theory was initially created to avoid paradoxes in a variety of formal logics and rewrite systems. Later, type theory referred to a class of formal systems, some of which can serve as alternatives to naive set theory as a foundation for all mathematics.
Andrew David Irvine, FSCC is a Canadian academic who teaches at the University of British Columbia. He holds a PhD in philosophy from Sydney University and is a professor of philosophy and mathematics at UBC Okanagan. He has served as vice-chair of the UBC Board of Governors, as head of the UBCO Department of Economics, Philosophy and Political Science, as president of the British Columbia Civil Liberties Association, and as a member of the board of directors of the Society for Academic Freedom and Scholarship. An advocate of traditional democratic civil liberties, Irvine has written about the importance of the rule of law for both modern and ancient democracies. He has held visiting positions at several Canadian and American universities and has been recognized as one of British Columbia's most influential public intellectuals.
Alecos Papadatos is a Greek comic book writer and illustrator, best known as the artist of Logicomix, a graphic novel written by Apostolos Doxiadis and Christos Papadimitriou. Logicomix was the No. 1 New York Times Best Seller Paperback Graphic Book of October 18, 2009.
