The Googology Wiki (a collection of notations and numbers which must have valid sources + more approximations)
What is googology? Genspark (AI) collected and summarized information on googology. Recommended for beginners to get some background information.
Sbiis Saibian's excellent large number site: One to Infinity: A Guide to the Finite (a guided tour about number systems. There, he made a system, named Extensible-E, recommended for beginners)
Large Numbers at MROB by Robert Munafo. Recommended for beginners.
Polytope sites by Jonathan Bowers (check out the Big Number Central for his googology works, including illion numbers, BEAF and infinity scrapers!)
Large Numbers Gradually Increasing by Douglas Shamlin Jr. It goes from zero to numbers described using Bird's array notation. Recommended for beginners. (a video series/playlist about numbers increasing, but only shown in Bird's array notation)
Numbers -Infinity to Infinity by NO! (a playlist about numbers increasing, since it's fun to watch, as well as it provides tips, hence it's recommended for beginners. However, this does not include all of the parts.)
1 to Absolute Infinity in One Video by NO! (a journey of numbers from 1 to Absolute Infinity. NOTE: the video is 14 hours long, combined from Large Numbers Gradually Increasing. Therefore, please watch it when you're free.)
Ultimate List of Large Numbers videos (originally by Douglas Shamlin Jr., but reuploaded by Dr2xmillion 2023 because the original videos were removed)
2024 version (by Douglas Shamlin Jr. himself, includes the largest computable numbers ever)
Hexation and Graham's Number by Prime Newtons (discussing hyperoperation and Graham's number)
XRQ CORPORATION's googology sites:
DeepLineMadom's googology sites:
SeveralLegend9998's googology sites: SeveralLegend9998's Googology Series and SeveralLegend9998's New Googology Series
NO!'s standard / fictional googology site: NO!'s Official Website
Jesse Kohn's standard / fictional googology site: Jesse's Official Site
JoshuaDR.0809's fictional googology site: JoshuaDR.0809's Website
kien6886's fictional googology site: kien6886's Official Site
Who Can Name the Bigger Number? by Scott Aaronson
The Busy Beaver Challenge: [July 2nd 2024] We have proved “BB(5) = 47,176,870”
Shtetl-Optimized: BusyBeaver(5) is now known to be 47,176,870
Quanta Magazine: With Fifth Busy Beaver, Researchers Approach Computation’s Limits
The Busy Beaver Challenge: The Story of Proving BB(5) = 47,176,870
Note that the BB(5) in the above articles is actually FF(5).
An interactive diagram for ordinals up to ε(ε0)
大数入门 for those who know Chinese. Beware though, the article contains tons of mistakes.
Large Number in pixiv dictionary for those who know Japanese.
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Googology Wiki page - HaydenTheGoogologist2009