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...
Nobody serious would deny this is incredible progress, but GP is making an unmotivated leap to RSI, so I respond to that framing. It’s an interesting argument to be had but I suspect few of us have standing to say one way or the other.
(Gesturing at the number of problems solved, or the number of years the problem was open for, isn’t an argument.)
In fact, every one of the results is basically just novelty crap as far as the world goes.
Let me know when AI discovers the cure to cancer or aging etc.
I for one think understanding more about how the world operates is just about the highest calling possible.
> when AI discovers the cure to cancer or aging etc.
A guy I knew did this. It successfully shrunk cancer tumours in his dog: https://www.the-scientist.com/chatgpt-and-alphafold-help-des...
Graph theory (which the OpenAI math results had many proofs in) is directly applicable to cancer modelling and drug design.
But sure. Novelty crap.
But sure, let me know when they do. I'll be waiting.
I'm not sure how you define "knowing how the world works", but knowing that a very very niche algorithm upper bounds that we thought was x^100 and now we now it's x^99, isn't that interesting. It doesn't really tell us much more about the world and it doesn't have any applications for our day to day lives.