> If the Jacobian is a nonzero constant everywhere this means that nowhere does the the function flatten out. [...] What was conjectured is that this local invertibility property everywhere would mean global invertibility.
> it doesn't overturn much. [...] the resolution of this is a "surprise" in that it is a very long open with many failed proof attempts. But the direction it resolved was not surprising.
> From a comment by j2kun https://news.ycombinator.com/item?id=49000833 , someone asked Fable and there was an almost counterexample in 2d but it uses division too. [Instead of f=x^2+7xy they have something like f=x^2+7x/y so it's not a polynomial.] It looks like the new trick was to use a third variable to avoid the division.
I expect Centaur Field Medals to be awarded. It's not clear how much steering Levent Alpöge did to get the result. In math it's very common to hide the search pattern and show only a simplified path to reach the final result.
> Even a baguette, surprisingly enough, can provide enough electricity to light up an LED.
This make no sense. Did they rediscover the Galvanic battery? In that case, the energy comes from the wires made of different materials, not from the baguette.
Does someone have a more technical explanation because the press article is horrible.
From a comment by j2kun https://news.ycombinator.com/item?id=49000833 , someone asked Fable and there was an almost counterexample in 2d but it uses division too. [Instead of f=x^2+7xy they have something like f=x^2+7x/y so it's not a polynomial.] As far as I know, nobody know what trick to make to avoid that division. It looks like the new trick was to use a third variable to avoid the division. Note that the implementation of the trick is not straightforward. The almost counterexample was sitting around for almost 30 years, and nobody knew how to fix it.
From another old comment, someone else was trying to find a counterexample with 16 variables using a computer to make thousands of attempts and failed. So it's far from obvious that the trick to add a variable solves the problems.
I think it was published on purpose. After the match, a lot of people went to the street. I'd describe the feeling as sad but supportive. There was a strong rumor that Monday would be a national holiday. The x/tweet says that it will be delayed for another day.
I can't find a good source with hard numbers, but here are some photos: https://www.ambito.com/deportes/pese-la-derrota-miles-hincha... I read estimations from 7000 to 300000. The number 300000 is clearly false, because it's the number of people after the previous match that was defectively bigger. 7000 is to small, probably counting a small part just after the match.
The photo is near google.com/maps?q=obelisco+buenos+aires&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCDQ5MzZqMGo3qAIAsAIA&um=1&ie=UTF-8&ved=1t:200715&ictx=111 So it's like a 100m x 100m full of people. Not very overcrowed, so I guess like 2/m^2. But usually it extends like 3 blocks to the South and 3 t the North (100x600) and like 4 to the East and 2 to the West, but the street in not so wide (50x600). The density is not constant, so add 1/m^2 persons or perhaps .5/m^2. This rough approximation gives like 100000 persons.
You must also include side streets, and substract trees. It's more complicated. [After the previous gane, we went there but only like 3 blocks away to avoid overcrowded areas, and went to eat pizza nearby, like 5 blocks away.] Also there were smaller concentration in other parts of the city and in other cities.
Back to your question...
With a few thousands of people in the streets, there was a strong rumor that Monday would be a national holiday, when the players would arrive. I'm not sure why, but the decision in the x/tweet was to wait until the players organize some reception. Later Messi decided to wait another day in USA and the reception lost strength.
In my opinion, most people want to say thank you, but nobody was happy enough to organize a big party.
I still can't understand all the details, but it's very interesting to read that chat. Anyway, instead of close to lore laundering, for me it's "standing on the shoulder of giants".
IIUC the idea is that of most "discoveries" by AI were actually a better bibliography search. I agree with that.
In this case, in the link you posted, it looks like the AI or the human pick an almost solution and made the AI tweak it until it got a real solution. I'm not sure if the tweak is an usual one or brute-forced or something in between. I should ask one of my friends that work in Algebra.
Tao's post is more about understanding the new result than guessing how it was found. The chat with Clause is more iluminating.
I'm mostly replying to your "standing on the shoulders of giants" part, when in some cases, the giant is the work you did in the past and forgot about :)
I'll cherry pick a few comment I like. I think they are worth reading but I'll quote a highlight of each one.
From kingstnap https://news.ycombinator.com/item?id=49000867
> If the Jacobian is a nonzero constant everywhere this means that nowhere does the the function flatten out. [...] What was conjectured is that this local invertibility property everywhere would mean global invertibility.
From mswphd https://news.ycombinator.com/item?id=48999959
> it doesn't overturn much. [...] the resolution of this is a "surprise" in that it is a very long open with many failed proof attempts. But the direction it resolved was not surprising.
Can I quote myself? https://news.ycombinator.com/item?id=49007165
> From a comment by j2kun https://news.ycombinator.com/item?id=49000833 , someone asked Fable and there was an almost counterexample in 2d but it uses division too. [Instead of f=x^2+7xy they have something like f=x^2+7x/y so it's not a polynomial.] It looks like the new trick was to use a third variable to avoid the division.
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