Unsolved problems in number theory | Figurate numbers | Additive number theory | Conjectures
Pollock's conjectures are two closely related unproven conjectures in additive number theory. They were first stated in 1850 by Sir Frederick Pollock, better known as a lawyer and politician, but also a contributor of papers on mathematics to the Royal Society. These conjectures are a partial extension of the Fermat polygonal number theorem to three-dimensional figurate numbers, also called polyhedral numbers. * Pollock tetrahedral numbers conjecture: Every positive integer is the sum of at most five tetrahedral numbers. The numbers that are not the sum of at most 4 tetrahedral numbers are given by the sequence 17, 27, 33, 52, 73, ..., (sequence in the OEIS) of 241 terms, with 343867 being almost certainly the last such number. * Pollock octahedral numbers conjecture: Every positive integer is the sum of at most seven octahedral numbers. This conjecture has been proven for all but finitely many positive integers. * Polyhedral numbers conjecture: Let m be the number of vertices of a platonic solid “regular n-hedron” (n is 4, 6, 8, 12, or 20), then every positive integer is the sum of at most m+1 n-hedral numbers. (i.e. every positive integer is the sum of at most 5 tetrahedral numbers, or the sum of at most 9 cube numbers, or the sum of at most 7 octahedral numbers, or the sum of at most 21 dodecahedral numbers, or the sum of at most 13 icosahedral numbers) (Wikipedia).
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 (compelling?) reason for the Riemann Hypothesis to be true #SOME2
A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.
From playlist Summer of Math Exposition 2 videos
From playlist Level 2 NCEA Physics
Robbins' formulas, the Bellows conjecture + polyhedra volumes|Rational Geometry Math Foundations 128
We discuss modern developments in the direction of our latest videos, namely formulas for areas of polygons in terms of the quadrances of the sides. We discuss work of Moebius, Bowman and Robbins on the areas of cyclic pentagons. There is also a rich story about 3 dimensional generalizati
From playlist Math Foundations
Why do some scientists believe that our universe is a hologram?
In this video, I explain why some scientists believe that our universe is a hologram and we really live in the 2-dimensional projection of a higher dimensional space. First, I explain just what physicists mean by the "holographic principle." The holographic principle says that the degrees
From playlist Physics
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
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
Geometry of Surface Group Representations by Mahan Mj
ICTS at Ten ORGANIZERS: Rajesh Gopakumar and Spenta R. Wadia DATE: 04 January 2018 to 06 January 2018 VENUE: International Centre for Theoretical Sciences, Bengaluru This is the tenth year of ICTS-TIFR since it came into existence on 2nd August 2007. ICTS has now grown to have more tha
From playlist ICTS at Ten
pp-adic versions of BSD - Florian Sprung
Florian Sprung Brown University; Member, School of Mathematics October 4, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Why science is NOT 'Just a Theory'
Have you ever heard ‘evolution’ dismissed as ‘just a theory’? Is a scientific theory no different to the theory that Elvis is still alive? Jim Al-Khalili puts the record straight. Subscribe for regular science videos: http://bit.ly/RiSubscRibe There’s an important difference between a sci
From playlist Ri Animations
Descent obstructions on constant curves over global (...) - Creutz - Workshop 2 - CEB T2 2019
Brendan Creutz (University of Canterbury) / 26.06.2019 Descent obstructions on constant curves over global function fields Let C and D be proper geometrically integral curves over a finite field and let K be the function field of D. I will discuss descent obstructions to the existence o
From playlist 2019 - T2 - Reinventing rational points
https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu
From playlist Mathematics
Can you give a feel for how the math of General Relativity allows for anti-gravity?
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From playlist Science Unplugged: General Relativity
Asymptotic invariants of locally symmetric spaces – Tsachik Gelander – ICM2018
Lie Theory and Generalizations Invited Lecture 7.4 Asymptotic invariants of locally symmetric spaces Tsachik Gelander Abstract: The complexity of a locally symmetric space M is controlled by its volume. This phenomena can be measured by studying the growth of topological, geometric, alge
From playlist Lie Theory and Generalizations
The Case for Jackson Pollock | The Art Assignment | PBS Digital Studios
You’ve heard of Jackson Pollock and know of his infamous “drip paintings,” but what is it that you’re supposed to do when you look at his work today? Why did it cause shockwaves in 1947, and what does it mean now? We explore the life, evolution, and legacy of Jackson Pollock. Thanks to o
From playlist The Case For
Richard Hain - 4/4 Universal mixed elliptic motives
Prof. Richard HAIN (Duke University, Durham, USA) Universal mixed elliptic motives are certain local systems over a modular curve that are endowed with additional structure, such as that of a variation of mixed Hodge structure. They form a tannakian category. The coordinate ring of its fu
From playlist Richard Hain - Universal mixed elliptic motives
How to paint like Jackson Pollock – One: Number 31, 1950 – with Corey D'Augustine | IN THE STUDIO
Learn how to paint like artist Jackson Pollock, one of the key figures of the postwar abstract expressionist art movement, with IN THE STUDIO instructor Corey D’Augustine. Explore the techniques of other New York School painters like de Kooning, Rothko, and Pollock in MoMA's new free, o
From playlist Expressionism to Pop Art | Art History | Khan Academy
Will Wormholes Allow Fast Interstellar Travel?
PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE ↓ More info below ↓ Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Check out the Space Time Merch Store https://pbsspacetim
From playlist Futurism and Space Exploration
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
Yanir Rubinstein - Ricci Flow and the Completion of the Space of Kahler Metrics [2011]
Name: Yanir Rubinstein Event: Workshop on Extremal Kahler Metrics Event URL: view webpage Title: Ricci Flow and the Completion of the Space of Kahler Metrics Date: 2011-03-24 @4:00 PM Location: 102 http://scgp.stonybrook.edu/video_portal/video.php?id=626
From playlist Mathematics