Analytic number theory | Unsolved problems in number theory | Additive number theory | Conjectures about prime numbers
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold for all integers less than 4 × 1018, but remains unproven despite considerable effort. (Wikipedia).
Harald Helfgott: Towards ternary Goldbach's conjecture
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory
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
Primes, Complexity and Computation: How Big Number theory resolves the Goldbach Conjecture
This lecture, which begins at 2:45, shows how Big Number theory, together with an understanding of prime numbers and their distribution resolves the Goldbach Conjecture, which states that every even number greater than two is the sum of two primes. Notions of complexity and computation,
From playlist MathSeminars
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
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
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Quadratic Goldreich-Levin Theorems - Madhur Tulsiani
Madhur Tulsiani Member, School of Mathematics April 26, 2011 Decompositions in theorems in classical Fourier analysis which decompose a function into large Fourier coefficients and a part that is pseudorandom with respect to (has small correlation with) linear functions. The Goldreich-Levi
From playlist Mathematics
Milton Jara : The weak KPZ universality conjecture - 1
Abstract: The aim of this series of lectures is to explain what the weak KPZ universality conjecture is, and to present a proof of it in the stationary case. Lecture 1: The KPZ equation, the KPZ universality class and the weak and strong KPZ universality conjectures. Lecture 2: The marting
From playlist Mathematical Physics
Goldbach Conjecture - Numberphile
Professor David Eisenbud on the famed Goldbach Conjecture. More links & stuff in full description below ↓↓↓ Catch David on the Numberphile podcast: https://youtu.be/9y1BGvnTyQA Extra footage from this interview: https://youtu.be/7D-YKPMWULA Prime Playlist: http://bit.ly/primevids Prime
From playlist David Eisenbud on Numberphile
Are Prime Numbers Made Up? | Infinite Series | PBS Digital Studios
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Is math real or simply something made up by mathematicians? You can’t physically touch a number yet using numbers we’re able to build skyscrapers and launch rockets int
From playlist An Infinite Playlist
Inference: A Logical-Philosophical Perspective with Alexander Paseau
In this talk, Professor Alexander Paseau, Faculty of Philosophy, University of Oxford, will describe some of his work on inference within mathematics and more generally. Inferences can be usefully divided into deductive or non-deductive. Formal logic studies deductive inference, the obviou
From playlist Franke Program in Science and the Humanities
Goldbach Conjecture (extra footage) - Numberphile
Main video: https://youtu.be/MxiTG96QOxw Extra footage from interview with David Eisenbud at MSRI. Ribet on Fermat: https://youtu.be/nUN4NDVIfVI Maynard on Twin Prime: https://youtu.be/QKHKD8bRAro Prime Playlist: http://bit.ly/primevids NUMBERPHILE Website: http://www.numberphile.com/ N
From playlist David Eisenbud on Numberphile
[BOURBAKI 2019] Homology of Hurwitz spaces and the Cohen–Lenstra (...)- Randal-Williams - 15/06/19
Oscar RANDAL-WILLIAMS Homology of Hurwitz spaces and the Cohen–Lenstra heuristic for function fields, after Ellenberg, Venkatesh, and Westerland Ellenberg, Venkatesh, and Westerland have established a weak form of the function field analogue of the Cohen–Lenstra heuristic, on the distrib
From playlist BOURBAKI - 2019
Lec 1 | MIT 6.042J Mathematics for Computer Science, Fall 2010
Lecture 1: Introduction and Proofs Instructor: Tom Leighton View the complete course: http://ocw.mit.edu/6-042JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Fall 2010
Prime Numbers - What is Known and Unknown, by Keith Conrad
This talk by Keith Conrad (UConn) was part of UConn's Number Theory Day 2017.
From playlist Number Theory Day
Interview at Cirm: Terence TAO
Terence Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing
From playlist English interviews - Interviews en anglais
Gödel's Incompleteness Theorem - Numberphile
Marcus du Sautoy discusses Gödel's Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: https://youtu.be/mccoBBf0VDM Extra Footage Part Two: https://youtu.be/7DtzChPqUAw Professor du Sautoy is Simonyi Professor for the Public Understanding of Sc
From playlist Animations by Pete McPartlan
Mertens Conjecture Disproof and the Riemann Hypothesis | MegaFavNumbers
#MegaFavNumbers The Mertens conjecture is a conjecture is a conjecture about the distribution of the prime numbers. It can be seen as a stronger version of the Riemann hypothesis. It says that the Mertens function is bounded by sqrt(n). The Riemann hypothesis on the other hand only require
From playlist MegaFavNumbers