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
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
Problems with the Calculus | Math History | NJ Wildberger
We discuss some of the controversy and debate generated by the 17th century work on Calculus. Newton and Leibniz's ideas were not universally accepted as making sense, despite the impressive, even spectacular achievements that the new theory was able to demonstrate. In this lecture we di
From playlist MathHistory: A course in the History of Mathematics
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
Alister McGrath - Atheism's Best Arguments?
Free access Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Atheism fields two kinds of arguments denying the existence of God: arguments that refute so-called 'proofs' of God's existence and arguments that affirmatively support the truth claims of atheism. This first see
From playlist Atheism's Best Arguments? - CTT Interview Series
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
(Part 1) The Palamite Controversy: A Thomistic Analysis by Fr. Peter Totleben, O.P.
A reading of the introduction and chapter 1 (The history of the Palamite controversy) of "The Palamite Controversy: A Thomistic Analysis" by Peter Totleben, O.P. https://www.academia.edu/35580908/The_Palamite_Controversy_A_Thomistic_Analysis
From playlist Palamas and Thomism
Real Analysis Ep 6: Countable vs uncountable
Episode 6 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about countable and uncountable sets, Cantor's theorem, and the continuum hypothesis. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/c
From playlist Math 3371 (Real analysis) Fall 2020
NUMBERS: "∞" infinity, The ladder of Heaven | Five numbers that changed the world | Cool Math
NUMBERS - secrets of Math. Mathematics is shrouded behind a veil and does not easily reveal itself. Students resort to rote memorization of math formulas to solve problems in a boring exercise of the mind that is also repetitive. However, if you knew the history of mathematics, the way the
From playlist Civilization
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
"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
Infinite Sets and Foundations (Joel David Hamkins) | Ep. 17
Joel David Hamkins is a Professor of Logic with appointments in Philosophy and Mathematics at Oxford University. His main interest is in set theory. We discuss the field of set theory: what it can say about infinite sets and which issues are unresolved, and the relation of set theory to ph
From playlist Daniel Rubin Show, Full episodes
Real Analysis Ep 5: Cardinality
Episode 5 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is cardinality of sets. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://faculty.fairfiel
From playlist Math 3371 (Real analysis) Fall 2020
Fundamentals of Mathematics - Lecture 28: Left and Right Inverses and the Axiom of Choice
Course Page: https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton UVM
From playlist Fundamentals of Mathematics
Number theory and algebra in Asia (a) | Math History | NJ Wildberger
After the later Alexandrian mathematicians Ptolemy and Diophantus, Greek mathematics went into decline and the focus shifted eastward. This lecture discusses some aspects of Chinese, Indian and Arab mathematics, in particular the interest in number theory: Pell's equation, the Chinese rema
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...
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
Metric Spaces - Lectures 11 & 12: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 6th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Number theory and algebra in Asia (b) | Math History | NJ Wildberger
After the later Alexandrian mathematicians Ptolemy and Diophantus, Greek mathematics went into decline and the focus shifted eastward. This lecture discusses some aspects of Chinese, Indian and Arab mathematics, in particular the interest in number theory (Pell's equation, the Chinese rema
From playlist MathHistory: A course in the History of Mathematics