Comment by thereitgoes456
1 day ago
> this is not reliant on just extrapolating existing theories but actually shows novel/surprising approaches
"Surprising" is a, well, surprisingly high bar to clear, and requires thorough understanding of not only the paper, but existing work in the area. ("Novel" is tautological.)
How did you determine this in 1 hour? Are you a researcher in multiple of these areas?
Can you give an example, or explain more how you came to this conclusion?
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: > 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.thereitgoes456
17 hours ago
famouswaffles
9 hours ago
saberience
11 hours ago
nl
10 hours ago
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.
I am asking about approaches, not results.
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.)
Those Theorists are arguing whether the QR Hypothesis result is the biggest Number Theory Advance in 1 or 2 centuries because there was zero progress on it whatsoever and many believed that would remain the case in our lifetime. Any approach there would be surprising as no-one had the faintest clue how to begin this at all. There are like at least a dozen of these results that would have catapulted a human to instant fame and the highest accolades in the field. If you think about it, it would be impossible for there to be no surprising approaches.
It's interesting to theoretical mathematicians only, for anyone else it's just noise which doesn't affect our practical day to day reality at all.
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.
> novelty crap
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.
2 replies →
One surprising result is the sub n log n multiplication. Galactic, as one might expect, but if you polled human researchers 24 hours ago, most would say something like it was very unlikely.