gus_massa

Main discussion: https://news.ycombinator.com/item?id=48998362 Probably you shoud read the fist few paragraphs of that post, but it escalates quickly.

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.

clicki http://google.com/maps?q=obelisco+buenos+aires&gs_lcrp=EgZja...

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.

Feature request?: Bridges like in Risk?

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.

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.

Are you quoting an email or something?

I like the UI. But, it's lie reverse minesweeper?

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".

Do you have an official translation? English is the shared language here and pos in other languages never get traction.

In the online version, I can play only against the best AI?

I got the country codes (BR, MX, ...) instead of the flags. (Chrome, Win 10)

Initially I didn't notice that it was possible to enable the automatic voice. Perhaps instead of a checkbox it's better to have two buttons in the first screen: "Start" and "Start with voice".

(Anyway, the checkbox is better if the kid is going to play it multiple times.)

What is the minimal difference that it ignores? 3 kilometers and 2 miles are probably good answers to the same question.

I don't understand your question. Do you want to learn Python?

Probably this is the wrong site to ask that question, but if you write a longer explanation you may be lucky and someone may help to link to the correct site.

Side note: From Wikipedia:

The surfaces of nonconvex polyhedra can have various Euler characteristics:

It's strange because the examples use weird faces, but in most (all?) of them it is possible to split the weird faces into a few poligonal faces and get V-E+F=2. For example https://en.wikipedia.org/wiki/Small_stellated_dodecahedron use faces that are stars that intersect other faces and the intersection is not an edge. Replacing each star with 5 triangles the Euler characteristic is 2.

It's too hard. I know enough geography to play only in a few parts of the map.

How good is the AI? We made a few mathematical games a few years ago and our problem was that the computer used perfect strategy. We had to add an easy mode. Perhaps your AI can have an easy model that does a shallow search to avoid stupid errors.

Your time control method is usual on some chess games, but traditional go is very different. In case you get too many angry request https://en.wikipedia.org/wiki/Time_control

If you don't have an AI, you can try to be available to play when you post. For example the servers sends you a SMS to alert you when a player is waiting. [Remember to disable it during work, sleep and family time.] Perhaps repost during next weekend. Do you have a friend that can help to be a AI replacement?

Nice game. I draw like 10 "horses". The first didn't move the legs because I didn't understand the idea, then I started to add moving things, and then weird things like the space invader. Anyway, mines were not as good as other examples I saw.

I don't see any selection neither.

It may be nice to start in the same continent of the player. I know better the countries near here [Argentina]. North America is quite linear, so it may be boring to plat there.

Which programming language do you like? I can try to find one post about it.

URL?

I expected the countries to be a painted when they are selected.

Yep, it has been happening since a long time.

Mathematician here. AI is very good. Better than me now. My guess is that most of the times it's easy to show that a counterexample is a counterexample, instead a long proof can be misclassified as slop.

They still remember https://es.wikipedia.org/wiki/Holodomor

Nice and fun, but I'd like that the fame enforces a minimal turning radius.

There's no reason to think that it won't provided if asked for, but it hardly seems relevant.

My guess is that the chat will look similar to a full transcription of a (multi month?) discussion between a few mathematicians. Full of dead ends and stupid errors (bit by the human and Claude) that would be embarrassing. We all know how bad it is, and we prefer to keep it behind the curtain.

I got to the biggest/smallest section. It's weird that the instructions appear at the bottom and the numbers at the top. I had to switch my vision to read it.

Are you planing to add localization? [Hi from Argentina!]