| I got busy, so I wanna say thanks to everyone who tagged in for me. So many great answers. I'll link a few that speak the most to my own feelings. Why do I like it? I am, as klodolph notes [1], a dyed-in-the-wool algebraist. It's where I find the most beauty and joy in mathematics. [1] https://news.ycombinator.com/item?id=22202606 This invention/discovery is a fundamental development in abstract algebra, not a terminal one. Quaternions are just a jumping-off point, and I've always found the Caley-Dickenson construction that pauldraper explains[2] absolutely beautiful. [2] https://news.ycombinator.com/item?id=22202513 Why would I want it specifically as a tattoo? jfengel points out the special history of that specific equation[3]: it was (allegedly) carved into a bridge in Dublin when Hamilton stumbled onto it, but the carving is gone. Kinda fitting to give it new permanence. [3] https://news.ycombinator.com/item?id=22202513 So, putting it all together: it's a fundamental development in abstract algebra, which is my jam. It's could have been permanently inscribed in a bridge, but that's been lost to time, so giving it new permanency seems fitting. Also, it's practical. My first thought was actually the Cayley table for the Klein four-group[4], but that would be a lot harder to get tattooed in a nice visible way. How I went from there to Hamilton's quaternion equation is left as an exercise to the reader. (If you're new to Cayley tables, they're just fancy times tables. Replace "e" with 1.) [4] https://en.wikipedia.org/wiki/Klein_four-group#Presentations |