Pre-computer lists of knots (from a mathematical point of view) go back to Listing, 1847, followed by the work of Tait, Kirkman, and Little (I don't have the exact dates, but late 19th century, I suppose). Also M G Haseman (early 20th century, I think).

Pre-computer lists of knots (from a mathematical point of view) go back to Listing, 1847, followed by the work of Tait, Kirkman, and Little (I don't have the exact dates, but late 19th century, I suppose). Also M G Haseman (early 20th century, I think).

EDIT: I found a few references: J.-B. Listing, Vorstudien zur topologie, Goettinger Studien 1 (1847) 811–875.

M. Haseman, On knots, with a census of the amphicheirals with twelve crossings, Trans. Roy. Soc. Edinburgh 52 (1918) 235–255.