michael_nielsen

A few addenda: (1) as lots of people have pointed out, it'd have been more accurate to name them Hindu-Arabic numerals; (2) the ancient Greeks seem to have known much of this (which I didn't know);

(3) the ancient Babylonians ditto (which I did know - it was meant as a thought experiment about discovery and lines of insight, not history); (4) @DavidDeutschOxf has a lovely discussion of number systems in chapter 6 of "The Beginning of Infinity".

(5) Via @CXGonzalez_, a paper arguing that for educated romans, the computational difficulty of working with roman numerals was comparable to us working with Hindu-Arabic: http://csjarchive.cogsci.rpi.edu/Proceedings/2008/pdfs/p2097.pdf …

(6) I haven't published anything specifically on improving Hindu-Arabic numerals. But here's some related work inspired in part by that problem: on "Magic Paper" (new interfaces for mathematics) http://cognitivemedium.com/magic_paper/index.html …

"Toward an Exploratory Medium for Mathematics" (on developing a logic of heuristic discovery, to underly creative exploration) http://cognitivemedium.com/emm/emm.html 

And "Thought as a Technology" (about the idea that we internalize the interfaces we use as part of our thinking; interface designers actually help us think new thoughts): http://cognitivemedium.com/tat/index.html 

1/ One issue here, speaking of the cognitive aspects of this, is the cognitive LOAD involved in learning both systems. If you are not using numbers much above 100, then, arguably the Roman numeral system is easier