The Moessner Miracle. Why wasn't this discovered for over 2000 years?

Video Description

Today's video is about a mathematical gem that was discovered 70 years ago. Although it's been around for quite a while and it's super cool and it's super accessible, hardly anybody knows about it. 00:00​ Intro 04:58 Chapter 1: Making our own proof 09:55​ Chapter 2: Some more amazing facts 13:11​ Chapter 3: Post's proof 23:36​ Supporters If after watching this video you'd like to find out more about Moessner's result, the following PhD thesis features a very comprehensive bibliography: https://ebooks.au.dk/aul/catalog/book/213 The proof by Karel Post that I matholologerise in the second half of this video is contained in this paper: Karel A. Post. Moessnerian theorems. How to prove them by simple graph theoretical inspection. Elemente der Mathematik, (2):46–51, 1990. Post also proves a couple of generalisations of Moessner's theorem. Another good write-up of the same proof can be found in Ross Honsberger"s 1991 book More Mathematical Morsels. Honsberger says about Moessner that "he was internationally known in the field of recreational mathematics for many spectacular results in arithmetic". Have to have a closer look at some point at what else exactly he did :) Post's article can be accessed here: https://www.e-periodica.ch (search for "Moessnerian theorems"). Sadly most other articles about Moessner's theorem are located behind paywalls. Here is another very pretty proof of the basic cubes result by Anthony Harradine and Anita Ponsaing using actual 3d cubical shells https://www.qedcat.com/misc/StrikeMeOut.pdf It's well worth exploring further than what I get around to reporting in this video. If you do, you'll discover interesting connections with super-factorials, higher-dimensional counterparts of Pascal's triangle, and so on. Challenge for the programmers among you: write a program that turns a sequence of highlighted integers into the corresponding Moessner sequence. Today's music is "Just Jump" by Ian Post. If you are interested in the t-shirt google "math whisperer t-shirt". If you don't understand the math whisperer bit, you did not watch the video to the end :) Enjoy! Burkard 14. Sep. 2021: I just added Russian subtitles prepared by Michael Didenko. Thank you very much Michael.