It achieves a theoretical lower bound on the complexity. This is what the article says in like 1000 words because it's written for mathematical illiterates.
> Harvey and van der Hoeven’s algorithm proves that multiplication can be done in n × log n steps. However, it doesn’t prove that there’s no faster way to do it. Establishing that this is the best possible approach is much more difficult. At the end of February, a team of computer scientists at Aarhus University posted a paper arguing that if another unproven conjecture is also true, this is indeed the fastest way multiplication can be done.
Even if the conjecture is proven to be true, we may find a more efficient way to perform this operation than a boolean circuit.