origins (1116903) writes "On the STOC 2007,thesis about faster integer multiplication was submitted.
According to the thesis,multiplication can be calculated faster than ever.
Schönhage&Strassen algorithm was known as fastest(O(n log n log log n)) but now Martin Fürer algorithm was((n log n 2^O(log* n)).
improvement of multiplication algorithm after decades is quite interesting.
Martin Fürer's homepage