Most paradoxes either stem from the misunderstanding of a topic, or aren't really paradoxes. However, here is a paradox that seems to contradict logic itself. What's going on here? And what does the liar paradox have to do with computer science? #some2
From playlist Summer of Math Exposition 2 videos
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy
Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. -- Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true.
From playlist New TED-Ed Originals
Viviani's Theorem: "Proof" Without Words
Link: https://www.geogebra.org/m/BXUrfwxj
From playlist Geometry: Challenge Problems
Relativity: how people get time dilation wrong
Einstein’s special theory of relativity is notorious for being easy to misuse, with the result that sometimes result in claims of paradoxes. When one digs more carefully into the theory, you find that no such paradoxes actually exist. In this video, Fermilab’s Dr. Don Lincoln describes a
From playlist Relativity
Newcomb's paradox | Famous Math Problems 7 | NJ Wildberger
Newcomb's paradox was first studied by American physicist William Newcomb, and popularized by articles by Robert Nozick and famously Martin Gardner in one of his 1974 Mathematical Games columns in Scientific American. The paradox involves notions of free will, determinism, choice, probabil
From playlist Famous Math Problems
Verifying The Unseen: Interactive Proofs for Label-Invariant Distribution Properties - Guy Rothblum
Computer Science/Discrete Mathematics Seminar I Topic: Verifying The Unseen: Interactive Proofs for Label-Invariant Distribution Properties Speaker: Guy Rothblum Affiliation: Weizmann Institute Date: October 4, 2021 Given i.i.d. samples drawn from an unknown distribution over a large do
From playlist Mathematics
The Abel lectures: László Lovász and Avi Wigderson
0:30 Introduction by the Abel Prize Committee Chair, Hans Munthe-Kaas 02:42 László Lovász: Continuous limits of finite structures 49:27 Questions and answers 1:00:31 Avi Wigderson: The Value of Errors in Proofs 1:41:24 Questions and answers 1:50:20 Final remarks by John Grue, Chair of the
From playlist Abel Lectures
Parallel Repetition of Two Prover Games: A Survey - Ran Raz
Ran Raz Weizmann Institute; Member, School of Mathematics October 8, 2012 I will give an introduction to the problem of parallel repetition of two-prover games and its applications and related results in theoretical computer science (the PCP theorem, hardness of approximation), mathemat
From playlist Mathematics
Nexus Trimester - Huijia Lin (University of California, Santa Barbara)
Zero Knowledge Huijia Lin (University of California, Santa Barbara) March 28, 2016 Abstract: Zero-knowledge protocols, introduced by Goldwasser, Micali, and Rackoff [STOC 1985], are fascinating constructs in cryptography: They provide the paradoxical guarantee that a player, the prover,
From playlist Nexus Trimester - 2016 - Secrecy and Privacy Theme
Introduction to Proof by Contradiction: sqrt(2) is irrational
This video introduces the mathematical proof method of proof by contradiction and provides an example of a proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
The Value of Errors in Proofs - Avi Wigderson
Members’ Seminar Topic: The Value of Errors in Proofs Speaker: Avi Wigderson Affiliation: Herbert H. Maass Professor, School of Mathematics Date: March 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
11/14/2019, Erich Kaltofen, North Carolina State University
Erich Kaltofen, North Carolina State University Title: Proof-of-work Certificates for High Complexity Computations for Linear Algebra Abstract: Computations done by high-power cloud servers such as a Google data center can yield outputs that are easy to verify, such as the factors of an
From playlist Fall 2019 Symbolic-Numeric Computing Seminar
John Harrison - Formalization and Automated Reasoning: A Personal and Historical Perspective
Recorded 13 February 2023. John Harrison of Amazon Web Services presents "Formalization and Automated Reasoning: A Personal and Historical Perspective" at IPAM's Machine Assisted Proofs Workshop. Abstract: In this talk I will try to first place the recent interest in machine-assisted proof
From playlist 2023 Machine Assisted Proofs Workshop
Even More Paradoxical: The Twin Paradox in Curved Spacetime
The Twin Paradox gets a stranger, even more mind-bending upgrade in General Relativity's world of curved spacetime. We explore the surprising and relatively unknown results to these new scenarios, while getting our toes wet in some of GR's conceptual frameworks. And finally, after several
From playlist Summer of Math Exposition Youtube Videos
Basic Methods: We define theorems and describe how to formally construct a proof. We note further rules of inference and show how the logical equivalence of reductio ad absurdum allows proof by contradiction.
From playlist Math Major Basics
Guy Rothblum : Privacy and Security via Randomized Methods - 4
Recording during the thematic meeting: «Nexus of Information and Computation Theories » theJanuary 28, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Nexus Trimester - 2016 -Tutorial Week at CIRM
Proof by Contradiction | Method & First Example
Proof by Contradiction is one of the most important proof methods. It is an indirect proof technique that works like this: You want to show a statement P is true. First assume the P is actually false. Then manipulate until you get a contradiction like 0=1. This means your assumption that P
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Verifier-on-a-Leash: new schemes for verifiable (...) - S. Jeffery - Main Conference - CEB T3 2017
Stacey Jeffery (CWI Amsterdam) / 15.12.2017 Title: Verifier-on-a-Leash: new schemes for verifiable delegated quantum computation, with quasilinear resources Abstract: The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevan
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Luca De Feo, Proving knowledge of isogenies, quaternions and signatures
VaNTAGe Seminar, November 15, 2022 License: CC-BY-NC-SA Links to some of the papers and cites mentioned in the talk: Couveignes (2006): https://eprint.iacr.org/2006/291 Fiat-Shamir (1986): https://doi.org/10.1007/3-540-47721-7_12 De Feo-Jao-Plût (2011): https://eprint.iacr.org/2011/506 B
From playlist New developments in isogeny-based cryptography