1836.152673426(32)
So, it differs about 0.153 from its nearest integer. Over 30% of all reals are that close or closer to their nearest integer, so I wouldn’t call that extraordinary at all. 1/137.035999177
Closer, but still not extraordinary. The math is different but I think it’s about a 1:15 chance that a random real will be relatively that close to the reciprocal of an integer.
https://en.wikipedia.org/wiki/Linear_algebra#History: “Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy”
That’s an application of linear algebra in the 19th century.