An OpenAI model solved the Erdos unit distance problem. Erdos roughly said, “The number of edges of the same distance between N points can’t compound faster than close to 0%.” The model found a method of placing points so that it compounds at about 1.4%. This visualization is a crude way of visualizing how that works.
What is the most frequently occurring sentence in Wikipedia? ANS: A 213-word paragraph about how minor planets are named, which appears in 418 Wikipedia articles, word-for-word! There are ~380,000 asteroids. Wikipedia has 418 pages for these - including one for each thousand-range of asteroids. Every single one of these pages includes the phrase: As minor planet discoveries are confirmed, they are given a permanent number by the IAU’s Minor Planet Center (MPC), and the discoverers can then submit names for them, following the IAU’s naming conventions. The list below concerns those minor planets in the specified number-range that have received names, and explains the meanings of those names. ...