Comment by svat

Come on. Prof David Harvey is the leading expert on this exact topic (integer multiplication algorithms), and here he has spent a lot of effort and time to digest the main new idea(s), and write 30+ pages explaining exactly what he's understood and why he believes the result is plausible. About the main “gadget”, he writes “I have worked through all the steps pretty carefully, and I think it checks out.” All this is useful information, and is the best we have so far from a reliable human source. I think it deserves more than a flippant response to the first line.