Soon AI mathematics will be 10x or 100x or 1000x more productive than humans in the proofing theorems business. Mathematics of old style is dead, they should develop ideas how to deal with that as a math community.

If a human doesn't understand the proof, it might be useful for certain kinds of engineering, but not really that useful for mathematics except as an existence test.

I don't known, can't we just also indirectly observe the wide platonic landscape of mathematics through observing AI results which humanity could not produce in a 1,000,000 years.

I imagine this will become one kind of branch of mathematics.

> But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal.

This is true. There can still be some funding for recreational aesthetic mathematics, like you can get some funding for various art projects or philisophy, literature, poetry, general humanities and community-building projects or sports funding or things like that. But currently many mathematicians are funded by the public purse with the understanding that this contributes to science and engineering and technological development at some point. I'm not saying that intellectual pursuits for the sake of human mental satisfaction is not worth funding in a society. The question is the amount of people needed. Tax payers pay for it. You have to tell them why, and why so many people need to be funded to do that. Many people have various hobbies they enjoy. But generally they don't get government money for doing it as the general rule. Maybe in a post-scarcity world.

Given what a know about the 2008 financial crisis, wouldn't an AI analysis in the years before that crisis of the real state funds helped to understand the risk of them better and avoid the big exposure.

Probably not. On the contrary, it would probably just amplify the mood.

The problem wasn't the analysis, given it was found out before it happened. The problem was politics, and as usual pushing the system to its limits and beyond.

I'd say it was more to do with how incentives lined up among different actors.

There's always risk somewhere in a financial system.

if people use it to make money, does this not mean that they providing some sort of service which is valued and hence it improves lifes?!

In an ideal world, that would be true, but the actual world is very far from that. As an extreme example, AI is very useful to automate scamming people.

No, money and value have been decorrelated for a long time. At least 5 years and arguably since Reagan.

Like it was so correlated back in 1600? Under the Romans? But perhaps you just mean that the increased financialization of the US economy means that the percentage of economic wealth devoted to actions without value is increasing? Sort of a modern trajectory to 1789 with the foppish nobles not realizing how much everyone else can get along without them?

There are a multitude of methods of obtaining money that do not benefit society.

Proofing open math conjectures

What about recent models providing correct proofs to open math problems?

I haven't tried it, but I saw Leanstral, an LLM specialized in writing Lean proofs, posted on HN recently and it claims to outperform some larger general purpose models. It didn't beat Claude Opus, but it seems to do decently at one tenth the cost. It's plausible that further research could yield other models that are smaller and more effective at limited tasks, reversing the trend of ever growing models.

What about it?

The timeline lists "Sled tracks seen to broken bond ice, EMS called" at 16:44. He was pulled from the water at 18:57. The article text further clarifies:

Parents discovered sled tracks from home onto broken pond ice through which he fell.

He left the house at 16:00, which is why they give the range of 147 to 177 minutes.

Yes but ultimatively it could been 16:43 to 18:57 which is 134 Minutes.

The first two reported timestamps are 16:00 and 16:30 which both fall conveniently on the half hour. This leads me to conclude that these are guesses, and could be either early or late. It seems most likely that the mother was not exactly aware of the time the child left the house. There is an incentive to minimise (to avoid it looking like a failure of supervision).

What we are certain of is the 16:44 call to the EMS, so you're right, 134 minutes is the lower bound. However, it's not unreasonable to assume that the parents did not immediately call on noticing the child missing, so the gap between 'noticing missing' and 'calling EMS' is real and non-zero.

The gap between 'leaving the house' and 'noticing missing' is something I'm less clear on: how did the parents 'notice' the child was missing when he was knowingly allowed to leave the house earlier? There's still a non-zero gap between 'last sighting' and 'realisation that he's missing' (i.e. he definitely wasn't missing at ~16:00, when the mother saw him leaving the house... what changed so that the parents believed he was missing at ~16:30? Was he supposed to check in with Dad and missed the check-in, etc?)

Either way, a difference of ±10% doesn't really make that much impact in interpreting the results.

I matters for scientific rigor just because the kid was missing does not mean he drowned.

Yes it's still more than 2 hours.

two hours underwater! that's insanity.

It seems below about ~80F you lose consciousness. This kid was nearly half that. Moreover, there have been other similar cases: https://pubmed.ncbi.nlm.nih.gov/32482520/

> It seems below about ~80F you lose consciousness.

Interestingly, the case report notes that "classic cardiac electrical activity" started once the patient reached 82°F.

FWIW, I got the 80F figure from the table at https://en.wikipedia.org/wiki/Hypothermia#Classification

Ice-cold water won't let you have enough strength to cling to ice for two hours. Ten to fifteen minutes at most.

Survivors of Titanic would say that the shouts of people clinging to something in the water died off pretty fast.

Well problem is that humans are so noisy through lifestyle, enviroment and genes that any proof for either is really hard.

Another problem is that there haven't been natural experiments in low dose exposures the way there unfortunately have been for high dose exposures.

LNT does also damage, as people refusing necessary CT scans or countries switching of nuclear power because of fear.