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
A Beautiful Proof of Ptolemy's Theorem.
Ptolemy's Theorem seems more esoteric than the Pythagorean Theorem, but it's just as cool. In fact, the Pythagorean Theorem follows directly from it. Ptolemy used this theorem in his astronomical work. Google for the historical details. Thanks to this video for the idea of this visual
From playlist Mathy Videos
Symmetries show up everywhere in physics. But what is a symmetry? While the symmetries of shapes can be interesting, a lot of times, we are more interested in symmetries of space or symmetries of spacetime. To describe these, we need to build "invariants" which give a mathematical represen
From playlist Relativity
Here I prove the Heine-Borel Theorem, one of the most fundamental theorems in analysis. It says that in R^n, all boxes must be compact. The proof itself is very neat, and uses a bisection-type argument. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHG
From playlist Topology
The Predictive Power Of Symmetry
From a bee’s hexagonal honeycomb to the elliptical paths of planets, symmetry has long been recognized as a vital quality of nature. Einstein saw symmetry hidden in the fabric of space and time. The brilliant Emmy Noether proved that symmetry is the mathematical flower of deeply rooted phy
From playlist Science Shorts and Explainers
SummerSchool "Arithmetic geometry" Tschinkel - Introduction | 2006
lecture notes: https://drive.google.com/file/d/1VLucSK53-iLrVUbPAanNZ6Lb7nAAgaQ1/view?usp=sharing Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry" survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the Univer
From playlist Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry"
Viviani's Theorem: "Proof" Without Words
Link: https://www.geogebra.org/m/BXUrfwxj
From playlist Geometry: Challenge Problems
Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon
From playlist Math Foundations
Albert Einstein, Holograms and Quantum Gravity
In the latest campaign to reconcile Einstein’s theory of gravity with quantum mechanics, many physicists are studying how a higher dimensional space that includes gravity arises like a hologram from a lower dimensional particle theory. Read about the second episode of the new season here:
From playlist In Theory
5 Fairy Tales That Were Way Darker Than You Realized as a Kid | What the Stuff?!
The older versions of popular fairy tales often get into some surprisingly mature themes: murder, mutilation, revenge. Learn the gory details in this video. 10 Fairy Tales That Were Way Darker Than You Realized as a Kid http://people.howstuffworks.com/10-dark-fairy-tales.htm Subscribe ht
From playlist What the Stuff?!
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 2
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
How Old is the Oldest Fairy Tale?
We know folklore goes back hundreds of years, but thanks to a new study using biological research methods, we now know it’s even older than that. Learn more at HowStuffWorks.com: http://people.howstuffworks.com/10-da... Share on Facebook: https://goo.gl/KpLq1f Share on Twitter: https://g
From playlist How Lauren Vogelbaum Works
"Numerical evidence for the Bruinier-Yang conjecture" Kristin Lauter, Microsoft Research [2011]
Kristin Lauter, Microsoft Research Wednesday Nov 9, 2011 11:00 - 11:40 Numerical evidence for the Bruinier-Yang conjecture and comparison with denominators of Igusa class polynomials Women in Numbers Conference Video taken from: http://www.birs.ca/events/2011/5-day-workshops/11w5075/vide
From playlist Mathematics
Pierre Colmez - Flânerie dans le programme de Fontaine
Je proposerai une promenade orientée et partiale à travers l'oeuvre de Fontaine.
From playlist The Paris-London Number Theory Seminar, Oct. 2019
General Relativity & Mathematical Reality
Yet another anecdote that (in my opinion) suggest that mathematics is the basis of our reality: Inside Einstein's Mind — PBS Nova In this brief clip explaining the beauty of Einstein's equation for General Relativity, Professor Robbert Dijkgraaf of Princeton's Institute for Advanced Study
From playlist Gravity
TYP102 - Language Reconstruction
This E-Lecture discusses the main principles of language reconstruction. Its main topics are: proto-languages, the comparative method, and cognate comparison. Using many examples from the VLC Language Index, the methods of reconstructing former languages receive vivid support.
From playlist VLC300 - Applied Linguistics
Recent developments in knot contact homology - Lenny Ng
Princeton/IAS Symplectic Geometry Seminar Topic: Recent developments in knot contact homology Speaker: Lenny Ng, Duke University Date: December 11, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
This E-Lecture deals with the development from Indo-European to Old English with special emphasis on the grouping of English into the branches of Indo-European. The focus is historical rather than linguistic. However, in order to understand the linguistic principles underlying this develop
From playlist VLC203 - The History of English
6 Surprising Banned Books | What the Stuff?!
Many books throughout history have been banned for their "questionable content," but these 6 will really surprise you. Subscribe http://bit.ly/1AWgeM7 Twitter https://twitter.com/HowStuffWorks Facebook https://www.facebook.com/HowStuffWorks Google+ https://plus.google.com/+howstuffworks W
From playlist What the Stuff?!
The Maths of General Relativity (7/8) - The Einstein equation
In this series, we build together the theory of general relativity. This seventh video focuses on the Einstein equation, the key ingredient of the theory which allows us to relate our mathematical model to the physical world. For more videos, subscribe to the YouTube channel : https://www
From playlist The Maths of General Relativity