Further down there is a discussion between number theorist about if the Quasi-Riemann Hypothesis is the biggest deal in 200 years or only 100. The consensus is that if a human had done it then it would deserve the Fields medal:
https://news.ycombinator.com/item?id=49986803The sub n log n result is astonishing: https://github.com/openai/math/blob/main/preprints/Integer-m...
Here's a great article 2019 on the quest to achieve the n log n boundary:
> Schönhage and Strassen’s ungainly n × log n × log(log n) method held on for 36 years. In 2007 Fürer beat it and the floodgates opened. Over the past decade, mathematicians have found successively faster multiplication algorithms, each of which has inched closer to n × log n, without quite reaching it. Then last month, Harvey and van der Hoeven got there.
and
> 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 (opens a new tab) that if another unproven conjecture is also true, this is indeed the fastest way multiplication can be done.
As far as I'm aware no one seriously believed sub n log n multiplication was possible. It just seemed such a logically sensible boundary it was taken as true-but-unproven.
https://www.quantamagazine.org/mathematicians-discover-the-p...
The sub n log n result is astonishing: https://github.com/openai/math/blob/main/preprints/Integer-m...
Here's a great article 2019 on the quest to achieve the n log n boundary:
> Schönhage and Strassen’s ungainly n × log n × log(log n) method held on for 36 years. In 2007 Fürer beat it and the floodgates opened. Over the past decade, mathematicians have found successively faster multiplication algorithms, each of which has inched closer to n × log n, without quite reaching it. Then last month, Harvey and van der Hoeven got there.
and
> 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 (opens a new tab) that if another unproven conjecture is also true, this is indeed the fastest way multiplication can be done.
As far as I'm aware no one seriously believed sub n log n multiplication was possible. It just seemed such a logically sensible boundary it was taken as true-but-unproven.
https://www.quantamagazine.org/mathematicians-discover-the-p...