[fdej]

I think the name "ball arithmetic" is Joris's idea. I don't have a good reference at hand, but I believe the idea of using a centered form of intervals is as old as interval arithmetic itself. Ball arithmetic has been used quite a bit for complex interval arithmetic, where it sometimes offer better enclosures than rectangular intervals, and another nice point of ball arithmetic is that it generalizes to more general normed spaces. However, before Joris's and my own work, I think very few people realized how useful ball arithmetic is specifically for arbitrary-precision arithmetic.

[eternalban]

Thank you.

So that sent me chasing interval arithmetic's history -- https://en.wikipedia.org/wiki/Interval_arithmetic -- and that page is also silent as to where did it come from. But academic.ru has the (surprising to me) answer that none other than Archimedes (not a surprise) used it:

"Interval arithmetic is not a completely new phenomenon in mathematics; it has appeared several times under different names in the course of history.

For example Archimedes calculated lower and upper bounds 223/71 < π < 22/7 in the 3rd century BC. Actual calculations with intervals has neither been as popular as other numerical techniques, nor been completely forgotten."

https://en.academic.ru/dic.nsf/enwiki/1037936