Unsolved problems in number theory | Diophantine equations | Conjectures

Lonely runner conjecture

In number theory, specifically the study of Diophantine approximation, the lonely runner conjecture is a conjecture about the long-term behavior of runners on a circular track. It states that runners on a track of unit length, with constant speeds all distinct from one another, will each be lonely at some time—at least units away from all others. The conjecture was first posed in 1967 by German mathematician Jörg M. Wills, in purely number-theoretic terms, and independently in 1974 by T. W. Cusick; its illustrative and now-popular formulation dates to 1998. The conjecture is known to be true for 7 runners or less, but the general case remains unsolved. Implications of the conjecture include solutions to view-obstruction problems and bounds on properties, related to chromatic numbers, of certain graphs. (Wikipedia).

Lonely runner conjecture
Video thumbnail

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

Video thumbnail

Can we tell if there's a wormhole in the Milky Way?

This is a brief comment on an article by Dennis Overbye that recently appeared in the New York Times https://www.nytimes.com/2019/11/13/science/wormholes-physics-astronomy-cosmos.html This article is about a paper which got recently published https://journals.aps.org/prd/abstract/10.110

From playlist Physics

Video thumbnail

The Infinite Monkey Theorem

Here's a re-enactment of the famous paradox known as the "infinite monkey theorem."

From playlist Cosmic Journeys

Video thumbnail

The Most Difficult Math Problem You've Never Heard Of - Birch and Swinnerton-Dyer Conjecture

The Birch and Swinnerton-Dyer Conjecture is a millennium prize problem, one of the famed seven placed by the Clay Mathematical Institute in the year 2000. As the only number-theoretic problem in the list apart from the Riemann Hypothesis, the BSD Conjecture has been haunting mathematicians

From playlist Math

Video thumbnail

Does Bigfoot Exist?

It's time we got to the bottom of this... Media: https://youtu.be/g3W4sMkwQ6k

From playlist Concerning Questions

Video thumbnail

Reverse Plane Partitions and Modules for the Preprojective Algebra - Anne Dranowski

Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Reverse Plane Partitions and Modules for the Preprojective Algebra Speaker: Anne Dranowski Affiliation: Member, School of Mathematics Date: November 19, 2020 For more video please visit http://video.ias.edu

From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory

Video thumbnail

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

Video thumbnail

Peter SCHOLZE (oct 2011) - 1/6 Perfectoid Spaces and the Weight-Monodromy Conjecture

We will introduce the notion of perfectoid spaces. The theory can be seen as a kind of rigid geometry of infinite type, and the most important feature is that the theories over (deeply ramified extensions of) Q_p and over F_p((t)) are equivalent, generalizing to the relative situation a th

From playlist Peter SCHOLZE (oct 2011) - Perfectoid Spaces and the Weight-Monodromy Conjecture

Video thumbnail

Strengthen Your Mind Like a Navy SEAL | David Goggins | Big Think

Strengthen Your Mind Like a Navy SEAL New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- What could almost destroy the bod

From playlist Best Videos | Big Think

Video thumbnail

Lone Star Ruby Conference 2011 Polyglot Paralellism: A Case Study in Using Erlang and Ruby at...

Title: Polyglot Paralellism: A Case Study in Using Erlang and Ruby at Rackspace Presented by: Phil Toland Two years ago Rackspace had a problem: how do we backup 20K network devices, in 8 datacenters, across 3 continents, with less than a 1% failure rate -- every single day? Many solution

From playlist Lone Star Ruby Conference 2011

Video thumbnail

What One Woman Learned Trying to Run Across California | National Geographic

Ali Butler Glenesk set a goal for herself to run across the entire state of California as she tests the limits of her body and her mind. She enlisted the help of friends to help reach her ultimate goal—be the fastest woman to run across California. ➡ Subscribe: http://bit.ly/NatGeoSubscrib

From playlist News | National Geographic

Video thumbnail

Interview: Andrew Skurka | National Geographic

Go behind the scenes and hear National Geographic grantee and adventurer Andrew Skurka talk about how he became a record-breaking, long-distance solo hiker. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for sci

From playlist National Geographic Live!: Season 1

Video thumbnail

Harmonic Measures and Poisson Boundaries for Random Walks on Groups (Lecture 1) by Giulio Tiozzo

PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, India), Anish Ghosh (TIFR, Mumbai, India), Subhajit Goswami (TIFR, Mumbai, India) and Mahan M J (TIFR, Mumbai, India) DATE & TIME: 27 February 2023 to 10 March 2023 VENUE: Madhava Lecture Hall

From playlist PROBABILISTIC METHODS IN NEGATIVE CURVATURE - 2023

Video thumbnail

Is there a black hole in every galaxy?

Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu

From playlist Science Unplugged: Black Holes

Video thumbnail

Oregon High (Full Episode) | Drugs, Inc: The Fix

Portland is the homeless Mecca of American youth. It attracts hundreds of people to its streets, who take advantage of the city’s generous social services. These are the customers that fund the deadliest drug market in America. ➡ Subscribe: http://bit.ly/NatGeoSubscribe ➡ Get more Nat Geo

From playlist Full Episodes | National Geographic

Video thumbnail

The Fyodorov-Hiary-Keating conjecture - Paul Bourgade

Probability Seminar Topic: The Fyodorov-Hiary-Keating conjecture Speaker: Paul Bourgade Affiliation: New York University Date: March 17, 2023 Through the random matrix analogy, Fyodorov, Hiary and Keating conjectured very precisely the typical values of the Riemann zeta function in short

From playlist Mathematics

Video thumbnail

The Pattern to Prime Numbers?

In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes. Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc The

From playlist Other Math Videos

Video thumbnail

What is infinity?

What’s the biggest number you can think of? Well, what about one more than that number? We can’t really comprehend the idea of infinity, but it’s still a useful concept in science. Brian Greene explains more. Subscribe to our YouTube Channel for all the latest from World Science U. Visit

From playlist Science Unplugged: Physics

Related pages

Big O notation | Journal of Number Theory | Graph theory | Chromatic number | Nowhere-zero flow | Diophantine approximation | Number theory | Modular arithmetic | Discrete Mathematics (journal) | Half-integer | Directed graph | Conjecture | Aequationes Mathematicae | Algebraic function field | Hypercube | Fractional part