An article describes a new and more efficient method of (manual) multiplication. Here, efficiency is defined as fewer operations and simpler operations. Addition is considered easier than multiplication, e.g. multiplying two large numbers is usually done by adding their logarithms. I admit I did not read the scientific paper, but I did test out the Karatsuba method mentioned in the article. By chopping up larger numbers, calculating two products, two sums and two crossterms, and then adding/subtraction these components gives the answer. Fewer operations, even if you chop possible subterms (after chopping) once more and repeat the procedure.
However, since the idea is it make it easier to do the calcuation manually, I’m not sure I agree it’s simpler. THe simplest method is serial calculation of each digit with each other, is replaced with fewer mathimatical operations, but more bookkeeping operations. Something you absolutely need pen and paper for. And if you have to partition multiple times, you’re going to be plugging in numbers all over, which seems error prone to me. I guess if you frequently must multiple large number it pays off to train yourself in this method, but after a first try I think it replaces operations with bookkeeping.
Since computers are excellent at bookkeeping, I can see how a math library in compute-heavy operations might benefit from such methods.