Unpredictability, Undecidability, and Uncomputability
Quite a number of mathematical theorems prove that the power of mathematics has its limits. But how relevant are these theorems for science? In this video I want to briefly summarize an essay that I just submitted to the essay contest of the Foundational Questions Institute. This year the
From playlist Philosophy of Science
A conversation between Mario Carneiro, Norman Megill and Stephen Wolfram
Stephen Wolfram plays the role of Salonnière in this new, on-going series of intellectual explorations with special guests. Watch all of the conversations here: https://wolfr.am/youtube-sw-conversations Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this
From playlist Conversations with Special Guests
Celebrating Emil Post & His "Intractable Problem" of Tag: 100 Years Later
100 years after combinators were first presented, Stephen Wolfram unveils the latest computational results along with some special guests. After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of Computational Irreducibility, and More: https://writings.stephenwolfram.com/202
From playlist Stephen Wolfram Livestreams
THIS 1936 Paper Theorized the FIRST Computer EVER, by Alan Turing
In 1936, Alan Turing wrote a paper that changed the course of history, titled "On Computable Numbers, with an Application to the Entscheidungsproblem", first introducing the Universal Turing Machine and laying the theoretical foundation of modern computing . It revolutionized the field of
From playlist Computer Science History Documentaries
Stanford Seminar - Preventing Successful Cyberattacks Using Strongly-typed Actors
Carl Hewitt MIT John Perry Stanford University UC Riverside June 17, 2021 Carl and John discuss how fundamental higher-order theories of mathematical structures of computer science are categorical meaning that they can be axiomatized up to a unique isomorphism thereby removing any ambi
From playlist Stanford EE380-Colloquium on Computer Systems - Seminar Series
After Math: Reasoning, Proving, and Computing in the Postwar United States - Stephanie Dick
More videos on http://video.ias.edu
From playlist Historical Studies
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
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Set Theory (Part 20): The Complex Numbers are Uncountably Infinite
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will establish a bijection between the complex numbers and the real numbers, showing that the complex numbers are also uncountably infinite. This will eventually mean that the cardinal
From playlist Set Theory by Mathoma
Why it took 379 pages to prove 1+1=2
Sign up to Brilliant to receive a 20% discount with this link! https://brilliant.org/upandatom/ Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collecti
From playlist Math
IMS Public Lecture : Waking Up from Leibniz' Dream: On the Unmechanizability of Truth
Denis Hirschfeldt, The University of Chicago, USA
From playlist Public Lectures
Crisis in the Foundation of Mathematics | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What if the foundation that all of mathematics is built upon isn't as firm as we thought it was? Note: The natural numbers sometimes include zero and sometimes don't -
From playlist An Infinite Playlist
Divisibility, Prime Numbers, and Prime Factorization
Now that we understand division, we can talk about divisibility. A number is divisible by another if their quotient is a whole number. The smaller number is a factor of the larger one, but are there numbers with no factors at all? There's some pretty surprising stuff in this one! Watch th
From playlist Mathematics (All Of It)
Pythagoras' theorem (b) | Math History | NJ Wildberger
Pythagoras' theorem is both the oldest and the most important non-trivial theorem in mathematics. This is the second part of the first lecture of a short course on the History of Mathematics, by N J Wildberger at UNSW (MATH3560 and GENS2005). We will follow John Stillwell's text Mathem
From playlist MathHistory: A course in the History of Mathematics
This one is famous! And super ancient. We aren't sure if old Pythag was the first to come up with it, but if not, he arrived at it independently of anyone prior, and his name is associated with it. It's quite nifty when you really think about it. Take a look! Watch the whole Mathematics p
From playlist Geometry
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
How to develop a proper theory of infinitesimals I | Famous Math Problems 22a | N J Wildberger
Infinitesimals have been contentious ingredients in quadrature and calculus for thousands of years. Our definition of the term starts with the Wikipedia entry, modified a bit to reduce the dependence on "real numbers", which is actually quite unnecessary--- but as a logical definition it i
From playlist Famous Math Problems
Wolfram Physics Project: Working Session Tuesday, Feb. 2, 2021 [Proofs and Metamathematics]
This is a Wolfram Physics Project working session about proofs and metamathematics. Begins at 3:22 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.
From playlist Wolfram Physics Project Livestream Archive
Wittgenstein's Games (A. C. Grayling)
Professor A. C. Grayling discusses the thought of Ludwig Wittgenstein and the intellectual context surrounding his life and work. Note, the audio has been slightly improved. I increased the volume and tried to reduce some of the cell phone interference that occasionally shows up. In any ca
From playlist Wittgenstein
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