Turneyboy

Well openai and anthropic are sitting on absolute treasure troves of private data that is their users' interaction with their models.

The labs have their users as the perfect training data source now. Much better than mechanial turk.

Most likely this is decompiled and not the way it was originally written.

That's not what happened. The claims of this for Navier-Stokes were already exagerated. It was dramatic but there was AI involved on both sides to make progress and the final proof did not use the same approach.

Finally, the list of hundreds of solved problems after that completely defeated any argument in that direction.

That's a bit of a stretch of the term engineer

The claim is that competition is what's preventing them from unilateral disarmament.

It's not illegitimate to model the solar system from the perspective of earth. It just makes the model more complicated than if you do it from the sun's perspective.

That's all true but there is a reason why these problems have remained unsolved for decades and are now all falling at the same time. The reason is not mathematicians being more incentivized.

Many of these are lean formalized. Arguably a much higher bar than whatever peer review provides in terms of verification.

They grow over time if you consider a lineage of models as the same model.

Incredible stuff.

An ex colleague of mine who is a world class mathematician recently got an ERC with ambitious goals to advance his field.

Literally every optimistic goal proposed to be worked on during this multi-year window has been solved in this one post. His and his entire group's work has just been done for him! They are all depressed as hell right now.

Except it runs into an excess problem. As an example, Berlin - just one city - has 7 professional orchestras. They are supported by the government financially to the tune of 200 million EUR per year. There is a very real opportunity cost here and quite a bit of a wealth transfer to old people at the same time (since the audiences for classical music tend to be on the older side).

You could pump a large part of those resources into supporting other kinds of music and arguably the outcome would be more interesting.

Maybe you shouldn't give much credence to your intuitions if you don't really know much about the subject. Obviously experts have those simple intuitions too except they also know the details of the theories underlying it all so they can form informed opinions.

Why would the implementation of this not simply be a fee that the mail carriers have to impose?

Isn't that by far the simplest solution that removes any and all bureaucracy for almost everyone and still catches 99% of the cases?

Not to forget mathematicians from other fields. They might be equally unfamiliar with most of our research topics.

Yes we do have plenty of practice adjusting our explanations to the audience.

You are also discounting your time which is not fair

How about the doesn't need to be paid in cash? The government claims a percentage of the company over time...as always only above some level of valuation

Well for one with a gigantic derivatives market compared to the underlying one it becomes relatively cheap to manipulate the underlying market.

If you can make a gigantic bet on the price going up and then buy a large amount of Bitcoin that moves the price up you can win from that. See the Jane street India derivatives market issue.

In particular that means that if you fill the border up to a depth of 2 on one board with pieces, it becomes a theoretically inpenetrable fortress.

For an overdone example see 2024,4219.

I absolutely agree. Not re-running the computation for the first 4*10^18 and claiming a new record is absolutely disingenuous. I could verify just a single example that hasn't been covered before and claim a new record with this logic.

That is not to say that this is not a cool project. The distributed nature and running so seamlessly directly in the browser is definitely cool and allows people to contribute compute easily.

It may be that grandiose claims of new records are needed to make people donate their computational resources but I am not a fan of deceptive claims like this.

You are assuming that the underreporting will be uniform. In reality people may be underrporting things they are embarrassed about and maybe even overreporting the opposite.

This is a flaw in the data that is much harder to account for.

Well if you consider 1/z as a function of a complex coordinate it definitely makes a lot of sense to set it to infty. That identifies +infty and -infty if you restrict yourself to the real numbers.

Yeah but width-first immediately gives you the solution for any finite alphabet. So in that sense it is trivial.

The nice thing about formal verification is exactly that. You have a separate tool that's very much like a compiler that can check those 1200 pages and tell you that it's true.

The source of truth here is the code we wrote for the formal verification system.

AI allowed him to avoid detection for a long time. It allowed him to create thousands of songs so that the each one would only get moderate amounts of streams thus not raising suspicion.

Had he created songs by hand they would rack up millions/billions of botted streams but them not being international hits anyone had ever heard before would have made it obvious botting behaviour.

I agree. It's a volume of water bounded by a sphere. I'm just being pedantic about the common use of the word in this thread.

I'm also somewhat surprised no one else was being pedantic about this. I expect better from HN :)

I'm not sure if you are kidding but just in case you are not this is very misleading and in fact misguided.

Refering to polynomials as exponential just results in confusion essentially removing any meaning from the word. Any function can be written as something involving exponents, so that statement becomes meaningless.

Ok I don't mean to be pedanntic but a sphere is just the boundary of a ball. If we are trying to capture volume we should be talking about balls of water.

We know how to do this and have observed this tons of times at this point. This would not be novel in any way. This is about exciting the nucleus which is completely different.

It's essentially just the boundary of the Mandelbrot set which makes sense as that's where the calculation is the most unstable.