isaacfrond

I'd say it's totally immaterial how it was written

> Surely researchers like this have the processing power to run them at home,

Nobody has that power. Certainly not mathematicians.

The paper does not resolve P versus NP, but it does make an important advance in a closely related area. To prove that P ≠ NP, it would be enough to show that every algorithm for an NP-complete problem requires superpolynomial time. We cannot prove anything remotely that strong. For explicit NP-complete problems in unrestricted computational models, we cannot even prove superlinear lower bounds. There is therefore an enormous gap between the lower bounds we can prove and the superpolynomial bounds we would need.

VP and VNP are closely related algebraic analogues of P and NP. Here the paper proves new lower bounds for computing the permanent, a VNP-complete polynomial, in particular models of arithmetic computation: roughly (n^2\log\log n) arithmetic gates for unrestricted division-free circuits, and (n^4/\log n) size for the more restrictive formula model. These are still polynomial bounds, so they do not separate VP from VNP. But lower bounds on the resources needed to compute explicit functions are exactly what would ultimately be required for such a separation, and meaningful lower bounds of this kind are exceptionally rare.

You are confusing who is the party that is injured--as many in this thread are. We are not talking about the consumer who buys a non-fairtrade t-shirt, when he would rather had a fairtrade one. It's about the t-shirt producers who is legitimately fairtrade but whose business is now in the shitter because of a lying AI.

This is not such a decision though; it's a first instance decision at a lower court.

But probably long after most of the network is gone

The proof is here: https://www.overleaf.com/project/69dd1d8437eba662fda82929

In the article just before that code:

The loop is of paticular interest to us. Abridged:

I wouldn't either. The difference for female and males reeks of the law of small numbers.

What's your recommendation for 'some basic business books'?

If you'd read the wikipedia article, you'd know that actual research shows that Betteridge's law is not true. The majority of articles with a yes/no question in the heading, answer the question with yes in the body.

Only accepting bugs with a fix is not a solution. Because who is going to vet the patches? Are you going to accept a Chinese patch for some obscure security issue? This is how real security problems are introduced.

I don't believe you.

You prompted chatgpt to create movie based titles and then passed it off as regular output.

With the prompt "suggest 10 titles for this article" + the article text, I get the following _normal_ titles.

1. When the Brain Misreads the World: How Uncertainty Shapes Thought and Behavior

2. CogLinks: A Virtual Brain That Teaches Us How the Mind Adapts

3. The Neural Balancing Act: How the Brain Decides Under Uncertainty

4. Modeling Mental Flexibility: Simulating How the Brain Learns and Adapts

5. Inside the Decision Machine: How New Models Reveal the Brain’s Hidden Algorithms

6. Uncertainty, Meaning, and Misfires: Understanding the Neural Roots of Psychiatric Disorders

7. When Circuits Go Off Course: What a Virtual Brain Teaches Us About Mental Illness

8. The Thalamic Switchboard: Linking Flexibility and Habit in the Human Mind

9. From Neurons to Algorithms: Building a Bridge Between Brain Biology and Psychiatry

10. Toward Algorithmic Psychiatry: Simulating Brain Circuits to Decode Mental Disorders

I tried it. In 70% of questions I preferred gpt-5.

It's a pity that the responses are all very short.

Please see the dropbox comment: https://news.ycombinator.com/item?id=9224

50000 * 3s, with s in seconds is very much linear.

Actually gym classes are a dumb leftover from the turn of the century (no not that turn, the 1900 turn). It serves no purpose anymore. Modern students get no meaningful skills, no lasting health benefits. It's mandatory exertion for a grade.

Learning to drive a car at school would do a whole lot more good!

Why not?

A hacker news favorite:

https://news.ycombinator.com/item?id=35081277

https://news.ycombinator.com/item?id=29621646

The article is a bit misleading. The kind of wearable he means are glucose level measuring devices. This link is a bit better:

https://www.reuters.com/business/healthcare-pharmaceuticals/...

Granted with such a device you still have to do something with the data for it to make you better, but I think this makes a lot more sense. Many people are diabetes 2, or close to it, and they have no idea. A continuous glucose measuring device could very quickly be a real eye-opener, in a way a fitness tracker does not. --> I don't need no Fitbit to tell me, I skipped my 5k again, but I do need a sensor to tell me that my blood glucose is too high.

The article nowhere mentions individual compensation to descendants by Harvard. I suspect the bankruptcy comment is an institutional fear of financial liability tied to large-scale identification of descendants.

Mathematics isn't monolithic—it depends heavily on the axioms you choose. Change the axioms, and the theorems change. ZFC, ZF¬C, intuitionistic logic, non-Euclidean geometry—each yields a different “math,” all internally consistent. So it’s not right to say math “just is” in some absolute sense. We’re not just discovering math; we’re exploring the consequences of chosen assumptions.

For instance:

Under Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC), every set can be well-ordered, but we do get the Hahn–Banach paradoxes.

Under ZF without Choice, analysis as we know it no longer holds.

In constructive mathematics, which avoids the law of the excluded middle, many classical theorems lose their usual formulations or proofs.

Non-Euclidean geometries arise from altering the parallel postulate. Within their own axioms, they are as internally consistent and "natural" as Euclidean geometry. Do non-intersecting lines exist in this universe? I've no idea.

The M functions are the MacMahon’s partition functions (see the paper [1]). They were not known to relate to the sum of divisors. The M_a function counts partitions in a parts but weighing multiplicities in the partion.

[1]: https://arxiv.org/abs/2405.06451

That’s assuming the administration will allow you to administer the exams onsite which is increasingly not the case. Online students bring in more money.

> The claim of inevitability is crucial to technology hype cycles, from the railroad to television to AI.

Well. You know. We still have plenty of railroad, and television has had a pretty good run too. So if that are the models to compare AI to, then I have bad news for how 'hype cycle' AI is going to be.

The article itself lists as successful, even breakthrough, applications of AI: protein folding, weather forecasting, and drug discovery.

That is some cool jazz

No kidding. First AIs were passing the bar exam—now they’re writing it.

I don't really see the scandal though. I pretty much _only_ use AI for tasks that I could do myself.

Some of the Gemini stuff is almost at airport level. I'm surprised. Everything is going so fast.

The odd thing, is that with technical stuff, I'm continually rewriting the LLM's to be clearer and less verbose. While the fiction is almost the opposite--not literary enough.

I wonder how well humans would do in this chart.