Yes, people did. Well at least I did. We knew we can use QCD to compute loops and to some degree masses in the lattice. But there were serious doubts the underlying mathematical theory was sound.
For many it didn't even matter. It would just mean that at those energies the theory is not even valid.
I am not certain on the extend of this proof but QED is probably not sound on it's own and we have been using that even longer. lambda phi^4 behind symmetry breaking and the higgs is strongly believed to be unsound on its own.
Yes, but it has also been known for 50+ years that QED has a Landau pole and might be UV trivial or inconsistent, whereas QCD has asymptotic freedom and is thus controlled at UV.
More to the point, QCD has been experimentally tested both at UV (deep inelastic scattering) and at IR, while the physical meaning of testing QED at UV Landau pole regime is unclear.
Woah, they got QCD! I didn't think they could do that. Three things jump to my mind:
1. Is it really true? Did they get the basic conditions right?
2. Would I ever be able to understand the proof
3. But the most important one. Can we compute hadronic masses now?
This is an incredible scientific achievement. One of our most fundamental theories is mathematically sound. Without the use of AI is very likely I would have never seen this in my lifetime
I'm still shelled shocked, but my initial reaction is caution. Wait what did they claim to have proof exactly?
I can't see their pdf in natural language either.
> However, the paper itself and the formalization that it claims for support are not
in a form that is readily usable to anyone who wants to understand or check it. This is
not just because of the needless length or complexity of the argument (which is indeed
overwhelming as presented), or because the formal repository is not in normal form, or
because much of the text is misleading or poorly organized, but mainly because there
is so much irrelevant puff to push through.
Oh wow, I'm fairly impressed. I wouldn't have expected AI to solve a problem this hard just now.
There have been claims of complex structures on s6 (or absence of them) quite a few times over the last 15 years. Some by acclaimed mathematicians.
There was some discussions on HN a few days ago:
Hehe, I really like them. And I always recommend those. It's not always that you have some nice books on deep concepts in mathematics for the "general" public
As per usual for the last two years I'm working on an open source spreadsheet engine called IronCalc. It is super exciting. We have a proof of concept at
In the last couple of months my partner and myself quit our jobs to work on that. I am pretty sure that in a year from now the world is going to have a fairly competent spreadsheet alternative.
My capacity is fairly limited but I am trying to build a community around it. Join us!
I find in software the more constraints I can find the better the innovation ends up being, and business model is an excellent constraint - even just knowing what a responsible amount of effort is versus the value you anticipate.
Admittedly, I originally misunderstood your product as being more like google sheets - where it becomes a cloud drive of sorts with spreadsheets on top. At which point the risk of losing access to the tool would make adoption very unlikely.
I am not certain on the extend of this proof but QED is probably not sound on it's own and we have been using that even longer. lambda phi^4 behind symmetry breaking and the higgs is strongly believed to be unsound on its own.
reply