Breaking news in the algorithmic/arithmetic world!
Integer multiplication in time O(n · log n). 
It means you can multiply two n-bits integer using roughly n log n operations. It's a *very* important problem because a lot of mathematical software rely on efficient integer multiplication.
It breaks the last best known algorithm  (Schönhage–Strassen), that was in O(n · log n · log log n)
And, if seriously, one question right away: what about hardware, can it be translated into the number of gates?
@erou Seems like it can:
"The main results of this paper also hold in the Boolean circuit model [40, Sec. 9.3], with essentially the same proofs." 👍
Yep that's still an open question. In the paper they explicitly say that they were interested in the theoretical complexity!
Go on and make the comparisons 😎!
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