HotHotLava

When OpenAI and Anthropic simultaneously announced their disproofs of the Exponential Time Hypothesis, it sparked a lot of commentary about the significance of the result, and the implications for AI and the future of mathematics.

But there was not a whole lot written about the how, ie. what's the trick that allowed them to break the exponential time barrier for SAT? How does the proof actually work?

So this video started as an experiment, can a simple "Hey claude, make me a 10-minute explainer video of this recent result" prompt produce something that can explain a research-grade mathematical result to an interested layman like myself?

The answer turns out to be "no": While Opus 5.5 and Astra are able to comprehend and answer questions about the proof, both of them are no great judges of which steps might be hard for a human to follow, where to add motivation, and in what order to introduce results. (in that sense, they're similar to human maths professors)

So here I share the final stage of this experiment, after several more hours of polishing and fine-tuning the result, until I actually felt I understood the main ideas.

How does it open the door to that? That's literally the argument that was rejected by saying the fair use defense only counts for the legally-acquired media.

How can a software developer not do the one basic abstraction step to see them both as tools with some unknown, low probability of error?

The human developer+compiler+linker toolchain isn't free of bugs either, some percentage it will produce code that fails loudly and sometimes it will produce code that has silent bugs, be it due to wrong source code or due to compiler or linker bugs.

If the photocraft suite had been manually written in 2022, with the exact same source code as it has right now, they would be the poster open-source project that people would point to for the power of an open-source community over proprietary software and be praised for the high standards of the source code.

You want to, of course. There are several multi-billion dollar programs to subsidize fabs starting european offshoots. But so far not very successful, and it's not like one endeavour is blocking the other here.

> YouTube, Google, Google Maps

Just yesterday I tried out Gemini again after a while, and it was not able to open Google Maps in navigation mode to the destination i wanted.

For the purposes of writing this comment, i asked it to put on some Jazz in Youtube (i have youtube music with a premium account on the same device and same google account) and it started a Spotify Jazz playlist.

Google might still have the popular products from 20 years of history, but after years of them trying there's no indication whatsoever that they have the ability to shape it into a coherent product.

You get a dinner, but not even an all-inclusive travel package while you're there.

This is basically aimed at AI startups who are in SF anyways and need a platform for marketing. So no shortage of contestants.

Ford started mass producing cars in 1913, and yet there are plenty of car companies that started production 20+ years later and are still relevant.

Just open weights are not enough, I think as a nation state you'd at least want a whole sovereign training pipeline. Otherwise you are stuck when Kimi K4 stops releasing their weights.

But I don't see why this needs to be done on a state-by-state level, a sovereign EU model seems to be much more realistic in terms of funding.

Would that change anything about the conclusion? Having a "bug" that changes available model options for some small set of Pro users 3 months after launch certainly qualifies as a wtf-are-they-even-doing level of bug in my book.

"Risk" has nothing to with designing functional and elegant UIs, so I'm not sure why you would even make the comparison.

It means risk that the software stops working after an update. Which usually trades off iteration speed and best practices (i'm pretty sure the average startup has way better security practices by just delegating to google/aws than the average manufacturing software business) in exchange for a rigorous testing and rollout schedule.

So I'm also not sure that the article has a point at all, the human writing the code was never relevant to avoiding the "risk" in these industries in the first place.

"extremely severe" - aren't we laying it on a bit thick here? The whole impact seems to be that users who have telemetry turned off got this feature ~2 days later, when the bug was noticed.

Per the rules link that you yourself post, no, publication must not necessarily happen in a peer-reviewed journal.

Take a look at https://github.com/leanprover/comparator which was used to verify the result. It's of course not impossible that they're hitting some bug, but way harder than one would intuitively think. For starters, they'd have to hit two bugs in two independently written Lean kernels.

In what world is peer review a higher standard than formal verification in Lean?

Not in the world mathematicians have been living in for the past decades at least. Nearly all big theorems that have been formalized so far had been published beforehand, and it was usually regarded as a step up in rigor. Wrong results get published in peer reviewed journals all the time.

I feel like there's a pretty huge difference between using inputs and outputs as part of a general training corpus, and looking at a specific users workspace after hearing rumours and yoinking their ideas to beat them to the point.

Unless OpenAI finished a whole new training run on the latest data in the last few days, the possible allegation seems to be the latter.

The nice thing is, once all of these proofs are formalized in a machine-checkable language, it should be relatively straightforward to translate the corpus between different languages, if someone finds something with a nicer syntax.

What would be "noise" in this context? Random words, random sentences, random complete short stories?

How do you "easy" VPN into the US in 1995? The whole consumer VPN industry didn't exist back then.

I think you're vastly overestimating the average persons ability to use Blender if you can do that in an afternoon; just figuring out how to place a colored cube and the camera probably takes an afternoon if you pick up Blender for the first time.

Given that the pelican looks way better than the dragon, it almost seems like a certainty.

Usually I wouldn't expect anything to happen to a big company like this, but oof...this is so much worse than the title makes it sound. If they leave something like this in their store, then all user trust will be gone.

I'll bet there's also a good number of developers at Anthropic itself who are now surprised to learn that every api token etc. that may have appeared in a Claude Code bash command is now leaked to a third party. Whoever can gain access to this telemetry server is sure to find a lot of valuable stuff in there.

Well, yes, it is. That's why you're seeing them take proactive steps to address the problem, like this new policy.

It's an ironic situation; logically what should be the moat are the models, costing hundreds of millions of investment cost to train and operate so it would make sense if we see different provider focusing in different directions.

But right now we have 3-5 top contenders that are so evenly matched that the de-facto sticking point is mostly the harness, ie. the collection of proven plugins/commands/tools/agent features that are tuned to the users personal workflow.

Do you not know how ebay works? You put in the maximum price you're willing to pay, and if you win you're paying 2nd highest bid + 1. So you don't save any money by starting with a low bid.

Basically every AI agent released in the last 6 months can do this pretty well out of the box? What feature exactly are you missing from these?

It'd be equally hilarious if that VC money would be used to actually better society by crushing GEMA in court.

But realistically, all that will happen is that the "Pauschalabgabe" is extended to AI subscriptions, making stuff more expensive for everyone.

Please don't pretend to be dumb, "predictable" in this context means that you know the final price of the trip before you start the journey, instead of having an odometer.

And randomly hoping for a taxi to drive by maybe works as long as you exclusively travel between airports, train stations, and downtowns of major cities, but if you're even slightly more remote than that you'll have to call or use some random app to get the Taxi to pick you up.