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
Computability and problems with Set theory | Math History | NJ Wildberger
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of the 20th century, and the Formalist approach to resolving these difficulties. This program of Hilbert was seriously disrupted by Godel's conclusions about Inconsistency of formal systems. Nevertheles
From playlist MathHistory: A course in the History of Mathematics
What's so wrong with the Axiom of Choice ?
One of the Zermelo- Fraenkel axioms, called axiom of choice, is remarkably controversial. It links to linear algebra and several paradoxes- find out what is so strange about it ! (00:22) - Math objects as sets (00:54) - What axioms we use ? (01:30) - Understanding axiom of choice (03:2
From playlist Something you did not know...
Cantor's theorem, formally proven
In this video we're going to give an explicit proof of Cantor's theorem and also go a little deeper in understanding the offending set in the famous diagonal construction employed here. https://en.wikipedia.org/wiki/Cantor%27s_theorem https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argu
From playlist Logic
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
Cantor's Theorem - A Classic Proof [ No surjection between Power Set and Set itself ]
GET 15% OFF EVERYTHING! THIS IS EPIC! https://teespring.com/stores/papaflammy?pr=PAPAFLAMMY Help me create more free content! =) https://www.patreon.com/mathable AC Playlist: https://www.youtube.com/watch?v=jmD1CWzHjzU&list=PLN2B6ZNu6xmdvtm_DdFUaHIK_VB84hG_m Let us prove Cantor's Theore
From playlist Theory and Proofs
Professor Adrian Moore journeys through philosophical thought on infinity over the last two and a half thousand years. This comes from a BBC radio series. For a good introduction to the philosophy of mathematics, check out: https://www.youtube.com/watch?v=UhX1ouUjDHE 00:00 Horror of the I
From playlist Logic & Philosophy of Mathematics
Why infinite sets don't exist | Arithmetic and Geometry Math Foundations 16 | N J Wildberger
Historically mathematicians have been careful to avoid treating `infinite sets'. After G. Cantor's work in the late 1800's, the position changed dramatically. Here I start the uphill battle to convince you that talking about`infinite sets' is just that---talk, not mathematics. The paradoxe
From playlist Math Foundations
A road to the infinities: Some topics in set theory by Sujata Ghosh
PROGRAM : SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS ORGANIZERS : Siva Athreya and Anita Naolekar DATE : 13 May 2019 to 24 May 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The summer school is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech.
From playlist Summer School for Women in Mathematics and Statistics 2019
Infinity: The Science of Endless
"The infinite! No other question has ever moved so profoundly the spirit of man," said David Hilbert, one of the most influential mathematicians of the 19th century. A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity stil
From playlist Explore the World Science Festival
Topology Without Tears - Video 2b - Infinite Set Theory
This is part (b) of Video 2, the second in a series of videos supplementing the online book "Topology Without Tears" which is available at no cost from www.topologywithouttears.net
From playlist Topology Without Tears
Umberto Bottazzini, The immense sea of the infinite - 10 aprile 2019
https://www.sns.it/it/evento/the-immense-sea-of-the-infinite Umberto Bottazzini (Università degli Studi di Milano) The immense sea of the infinite Abstract In a celebrated talk Hilbert stated that the infinite was nowhere to be found in the real, external world. Yet from time immemorial
From playlist Colloqui della Classe di Scienze
Zero to Infinity | Full Documentary | NOVA | PBS
Discover how the concepts of zero and infinity revolutionized mathematics. Official Website: https://to.pbs.org/3tkPFTx | #novapbs Zero and infinity. These seemingly opposite, obvious, and indispensable concepts are relatively recent human inventions. Discover the surprising story of h
From playlist Full episodes I NOVA
MAE5790-23 Fractals and the geometry of strange attractors
Analogy to making pastry. The geometry underlying chaos: Stretching, folding, and reinjection of phase space. The same process generates the fractal microstructure of strange attractors. Rössler attractor. Visualizing a strange attractor as an "infinite complex of surfaces" (in the words o
From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
The weirdest paradox in statistics (and machine learning)
🌏 AD: Get Exclusive NordVPN deal here ➼ https://nordvpn.com/mathemaniac. It's risk-free with Nord's 30-day money-back guarantee! ✌ Second channel video: https://www.youtube.com/watch?v=3ne9yghOtw8 Stein's paradox is of fundamental importance in modern statistics, introducing concepts of
From playlist Novel topics (not in usual math curricula)
"Counting Past Infinity" in All Spatial Dimensions
In this video, I explain the history behind infinity and briefly cover infinitesimals to construct infinite spatial dimensions. Sometimes I think more about my videos after posting them, these are my Post-Thoughts: * I originally had designed this video as follows: null set = 0th Dimens
From playlist Summer of Math Exposition Youtube Videos
"UNSOLVABLE" Logic Puzzle: How Old Is The Priest?
Thanks to Peter for sending me this problem! This is a really fun one and I encourage you to work it out. A priest and a cantor have a conversation about the product and sum of three visitors. After a few exchanges, the cantor figures out the visitors ages. But wait, how old is the priest?
From playlist Logic Puzzles And Riddles
Set Theory (Part 2a): Russell's Paradox
Please feel free to leave comments/questions on the video below! In this video, I briefly speak about the Russell paradox and why ZFC avoids this paradox when discussing pathological sets. One should hopefully see why it is that this paradox is disastrous for the naive set theory adopted
From playlist Set Theory by Mathoma
The Road to Gödel's Incompleteness Theorems - Juliette Kennedy
Friends Lunch with a Member Topic: The Road to Gödel's Incompleteness Theorems Speaker: Juliette Kennedy Date: November 22, 2019
From playlist Friends of the Institute