Source: https://youtu.be/cCKOl5li6YM

If you ever worked on a low level CPU design, an FPGA or built your own ALU, then you might have come across the problem of multiplication. A naive approach has a complexity of O(N²). There seems to be no way around it.

That is also what the russian mathematician Kolmogorov believed. Until … one of his students came up with a different method and actually a reduced complexity. His name was Karatsuba. (Does it ring?) Why is this so interesting? Because it makes multiplication faster. In software and in hardware.

A Gentleman going by the name Nemean looks at the problem in very much detail as well as very high quality.

Take a look at the video, it is quite interesting.