Mathematical logic | Metalogic | Proof theory
Proof theory is a major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also focuses on applications in computer science, linguistics, and philosophy. (Wikipedia).
Proof: What is it, and how does it work?
From playlist The Nature of Proof
Proofs by contradiction -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Introduction to Common Mathematical Proof Methods
This video introduces the common methods of mathematical proofs and provides a basic example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Geometry: Ch 5 - Proofs in Geometry (5 of 58) How to Proof Proofs
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is and how to proof proofs in geometry. Next video in this series can be seen at: https://youtu.be/xuWliQ6CHpw
From playlist GEOMETRY 5 - PROOFS IN GEOMETRY
Review of set theory -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
SImple proofs and their variations -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Proof: a³ - a is always divisible by 6 (2 of 2: Proof by exhaustion)
More resources available at www.misterwootube.com
From playlist The Nature of Proof
Introduction to Direct Proofs: If n is even, then n squared is even
This video introduces the mathematical proof method of direct proof provides an example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Inequality Proof: Summing Reciprocals of Squares (Experimental Silent Screencast)
via YouTube Capture
From playlist The Nature of Proof
Haniel Barbosa - Better SMT proofs for certifying compliance and correctness - IPAM at UCLA
Recorded 14 February 2023. Haniel Barbosa of Universidade Federal de Minas Gerais in Belo Horizonte presents "Better SMT proofs for certifying compliance and correctness" at IPAM's Machine Assisted Proofs Workshop. Abstract: SMT solvers can be hard to trust, since it generally means assumi
From playlist 2023 Machine Assisted Proofs Workshop
A Computer-Checked Proof that the Fundamental Group of the Circle is the Integers - Daniel Licata
Daniel Licata Carnegie Mellon University; Member, School of Mathematics November 26, 2012 This talk is designed for a general mathematical audience; no prior knowledge of type theory is presumed. One of the main goals for the special year on univalent foundations is the development of a l
From playlist Mathematics
Foundations S2 - Seminar 2 - The geometric part
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. This season the focus is on the proof of the Ax-Grothendieck theorem: an injective polynomial function from affine space (over the complex numbers) to itself is surjective. This week Will proved the the
From playlist Foundations seminar
Type theory and formalization of mathematics - Anders Mörtberg
Short Talks by Postdoctoral Members Anders Mörtberg - September 28, 2015 http://www.math.ias.edu/calendar/event/88254/1443464100/1443465000 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
Séminaire Bourbaki - 21/06/2014 - 3/4 - Thomas C. HALES
Developments in formal proofs A for mal proof is a proof that can be read and verified by computer, directly from the fundamental rules of logic and the foundational axioms of mathematics. The technology behind for mal proofs has been under development for decades and grew out of efforts i
From playlist Bourbaki - 21 juin 2014
Automated Theorem Proving and Axiomatic Mathematics
Jonathan Gorard
From playlist Wolfram Technology Conference 2019
Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine
(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des
From playlist Mathematics
On the Setoid Model of Type Theory - Erik Palmgren
Erik Palmgren University of Stockholm October 18, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Live CEOing Ep 178: Language Design in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Language Design in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design