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
What is the Fundamental theorem of Algebra, really? | Abstract Algebra Math Foundations 217
Here we give restatements of the Fundamental theorems of Algebra (I) and (II) that we critiqued in our last video, so that they are now at least meaningful and correct statements, at least to the best of our knowledge. The key is to abstain from any prior assumptions about our understandin
From playlist Math Foundations
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Definitions, specification and interpretation | Arithmetic and Geometry Math Foundations 44
We discuss important meta-issues regarding definitions and specification in mathematics. We also introduce the idea that mathematical definitions, expressions, formulas or theorems may support a variety of possible interpretations. Examples use our previous definitions from elementary ge
From playlist Math Foundations
SketchySVD - Joel Tropp, California Institute of Technology
This workshop - organised under the auspices of the Isaac Newton Institute on “Approximation, sampling and compression in data science” — brings together leading researchers in the general fields of mathematics, statistics, computer science and engineering. About the event The workshop ai
From playlist Mathematics of data: Structured representations for sensing, approximation and learning
The problem with `functions' | Arithmetic and Geometry Math Foundations 42a
[First of two parts] Here we address a core logical problem with modern mathematics--the usual definition of a `function' does not contain precise enough bounds on the nature of the rules or procedures (or computer programs) allowed. Here we discuss the difficulty in the context of funct
From playlist Math Foundations
Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w
From playlist Mathematics
History of Science and Technology Q&A (April 6, 2022)
Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram If you missed the original livestream of
From playlist Stephen Wolfram Ask Me Anything About Science & Technology
What exactly is a circle? | Arithmetic and Geometry Math Foundations 28 | N J Wildberger
Moving beyond points and lines, circles are the next geometrical objects we encounter. Here we address the question of how best to introduce this important notion, strictly in the setting of rational numbers, and without metaphysical waffling about `infinite sets.' This lecture is part of
From playlist Math Foundations
Complex polynomials and their factors | Linear Algebra MATH1141 | N J Wildberger
We look at the arithmetic of complex polynomials, prove both the Factor theorem and the Remainder theorem, and discuss the contentious "Fundamental theorem of Algebra" from a computational perspective. ************************ Screenshot PDFs for my videos are available at the website htt
From playlist Higher Linear Algebra
Lee Smolin Public Lecture: Time Reborn
What is time? Is our perception of time passing an illusion which hides a deeper, timeless reality? Or is it real, indeed, the most real aspect of our experience of the world? Perimeter Institute Faculty member Lee Smolin examines these and other timely questions from his book Time Reborn
From playlist Public Lecture Series
The Role of Theory in Science - David Gross
Speaker : David Gross (KITP, Santa Barbara) Date and Time : 28 Dec 2009, 05:30 PM Venue : J. N. Tata Auditorium, IISc, Bangalore On the occasion of the inauguration of the International Centre for Theoretical Sciences, TIFR, I shall share some of my observations and conclusions as to the
From playlist Public Lectures
After Math: Reasoning, Proving, and Computing in the Postwar United States - Stephanie Dick
More videos on http://video.ias.edu
From playlist Historical Studies
Lucien Hardy on quantum gravity and (apparent) paradoxes
Lucien Hardy is a theoretical physicist working at the intersection of the two pillars of modern physics – general relativity and quantum mechanics – in the quest for a single unifying theory: quantum gravity. Hardy joins co-hosts Lauren and Colin for a conversation about the puzzles that
From playlist Conversations at the Perimeter
Neil Turok Public Lecture: The Astonishing Simplicity of Everything
On Oct. 7, 2015, Perimeter Institute Director Neil Turok opened the 2015/16 season of the PI Public Lecture Series with a talk about the remarkable simplicity that underlies nature. Turok discussed how this simplicity at the largest and tiniest scales of the universe is pointing toward ne
From playlist Public Lecture Series
Uncovering 80 Years of Research into the Near and Middle East at IAS - Sabine Schmidtke
https://www.ias.edu/events/friends-publiclecture-schmidtke More videos on https://video.ias.edu
From playlist Friends of the Institute
The man who invented calculus: the life and work of Madhava (Lecture 1) by P P Divakaran
MADHAVA LECTURES THE MAN WHO INVENTED CALCULUS: THE LIFE AND WORK OF MADHAVA SPEAKER: P P Divakaran (formerly Professor of Physics at TIFR-Mumbai) DATE: 11 February 2020, 16:00 VENUE: ICTS-TIFR, Bengaluru Lecture 1: Tuesday, February 11, 2020 at 16:00 Lecture 2: Thursday, February 13
From playlist Madhava Lectures
Milner Award Lecture 2015: Reactive, real-time and hybrid computer systems
Listen to a world expert on computer science speak about advances in reactive, real-time, and hybrid computer systems. Milner Award Lecture 2015 delivered by Professor Thomas Henzinger, Institute of Science and Technology, at the Royal Society, London, on 18 November 2015. https://royal
From playlist Latest talks and lectures
Extended Fundamental Theorem of Calculus
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Extended Fundamental Theorem of Calculus. You can use this instead of the First Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus. - Formula - Proof sketch of the formula - Six Examples
From playlist Calculus
Michael R. Douglas - How will we do mathematics in 2030?
Abstract: We make the case that over the coming decade, computer assisted reasoning will become far more widely used in the mathematical sciences. This includes interactive and automatic theorem verification, symbolic algebra, and emerging technologies such as formal knowledge repositories
From playlist 2nd workshop Nokia-IHES / AI: what's next?