Set theory | Mathematical concepts
In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory, relations between primitive notions are restricted by axioms. Some authors refer to the latter as "defining" primitive notions by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress (per the regress problem). For example, in contemporary geometry, point, line, and contains are some primitive notions. Instead of attempting to define them, their interplay is ruled (in Hilbert's axiom system) by axioms like "For every two points there exists a line that contains them both". (Wikipedia).
Teach Astronomy - Revolutions in Science and the Arts
http://www.teachastronomy.com/ Too often science is treated in isolation from other human pursuits. However the broad history of ideas from the time of Copernicus to the time of Newton parallels a similar evolution in the arts in Europe at that time period. The popular cliché goes that s
From playlist 03. Concepts and History of Astronomy and Physics
We Need a Bigger Definition of Creativity
► Please Subscribe to My Channel Here - http://bit.ly/spencervideos When you the word “creative,” you might think of a painter or a playwright or an author or a photographer or a filmmaker or a chef. In other words, you might think of people who make things. I think it’s what we mean wh
From playlist What Is Creativity?
The route to our best, most genius-like thoughts is not to be afraid of our stranger-sounding insights and hunches. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/qmKUmL Join our mailing list: http://bit.ly/2e0TQNJ Or visit us in person at our London H
From playlist SELF
Nature of Genius 133 Geography
From playlist The Nature of Genius
Nature of Genius 322 PolyMaths
From playlist The Nature of Genius
What is Science? by Pierre Hohenberg (New York University)
28 December 2016, 16:00 to 17:00 VENUE ICTS campus, Bengaluru In this talk we propose a new definition of science based on the distinction between the activity of scientists and the product of that activity: the former is denoted (lower-case) science and the latter (upper-case) Science. Th
From playlist DISTINGUISHED LECTURES
Nietzsche’s concept of the Superman is one of the most exciting and yet weird aspects of his thought. What did he really mean by this unusual word? Please subscribe here: http://tinyurl.com/o28mut7 Find out more by reading our book "Life lessons from Nietzsche" : http://www.theschooloflife
From playlist WESTERN PHILOSOPHY
Teach Astronomy - Early Greek Ideas
http://www.teachastronomy.com/ The early Greek philosophers had none of the tools of modern science. They did not have the machines with which to probe the atom. They did not have telescopes. They didn't have modern technology of any kind, and yet with logic and mathematics they were ab
From playlist 02. Ancient Astronomy and Celestial Phenomena
SHM - 16/01/15 - Constructivismes en mathématiques - Thierry Coquand
Thierry Coquand (Université de Gothenburg), « Théorie des types et mathématiques constructives »
From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques
The order of an integer modulo n Number Theory 16
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From playlist Number Theory
The order of an integer modulo n -- Number Theory 16
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From playlist Number Theory v2
Séminaire Bourbaki - 21/06/2014 - 4/4 - Thierry COQUAND
Théorie des types dépendants et axiome d'univalence Cet exposé sera une introduction à la théorie des types dépendants et à l'axiome d'univalence. Cette théorie est une alternative à la théorie des ensembles comme fondement des mathématiques. Guidé par une interprétation d'un type comme u
From playlist Bourbaki - 21 juin 2014
CTNT 2018 - "L-functions and the Riemann Hypothesis" (Lecture 2) by Keith Conrad
This is lecture 2 of a mini-course on "L-functions and the Riemann Hypothesis", taught by Keith Conrad, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - "L-functions and the Riemann Hypothesis" by Keith Conrad
Constructive Type Theory and Homotopy - Steve Awodey
Steve Awodey Institute for Advanced Study December 3, 2010 In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in
From playlist Mathematics
Foundations - Seminar 9 - Gödel's incompleteness theorem Part 1
Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Will Troiani starts the proof of Gödel's incompleteness theorem. You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video was filmed in Deprecati
From playlist Foundations seminar
CERIAS Security: Categories of Digital Forensic Investigation Techniques 2/6
Clip 2/6 Speaker: Brian Carrier · Purdue University This talk examines formal concepts of digital forensic investigations. To date, the field has had an applied focus and little theory exists to formally define analysis techniques and requirements. This work defines an extended finite
From playlist The CERIAS Security Seminars 2006
Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 5
Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of
From playlist Hypergeometric Functions, Character Sums and Applications
Birational Geometry and Orbifold Pairs :Arithmetic and hyperbolic... (Lecture 3) by Frederic Campana
PROGRAM : TOPICS IN BIRATIONAL GEOMETRY ORGANIZERS : Indranil Biswas and Mahan Mj DATE : 27 January 2020 to 31 January 2020 VENUE : Madhava Lecture Hall, ICTS Bangalore Birational geometry is one of the current research trends in fields of Algebraic Geometry and Analytic Geometry. It ca
From playlist Topics In Birational Geometry