woopsn

My interpretation is they don't care about scooping mathematicians they were just trying to scoop a competitor. They had a short window in which to complicate Anthropic's priority, when Anthropic announced be able to say "ok nice but we did that too". Upon realizing they'd misunderstood, incredibly they said to this academic (who did not resolve NS) okay well just go ahead and claim the prize, so long as you're not Anthropic let's make this a good story.

If you spend $20M working out a Millennium Prize problem, in what universe would you offer that an unrelated effort should take credit? This is a branding game rather over whether software engineers are going to use codex or claude. In that light $20M (or whatever it was) might be worth it to squash even the rumor that claude code is more capable. Engineers look up to mathematics, while at the same time business and probably most engineers think the problem was to solve the problem. GPTs solved one the hardest known problems so they can solve my company's problem.

Some go further looking at these people, very on-the-nosely likened by one commenter here to ants, talking about education and responsibility and "core values" etc and just don't care. There was a major problem at the beginning of the week that is not a problem now and that is uncomplicated progress.

It's not wrong for OpenAI/Anthropic to do math for product development or even just branding but seemingly at no cost now they could work in an arena real mathematicians aren't interested in, versus just mowing the field. Everyone involved on their side should admit the purpose of these demonstrations is not to engage mathematical ideas it's about Claude/Codex. there's no shame in that. Which is better at solving random hard Diophantine systems? That would seem to tell me as much as I need to know insofar as a model's value is represented by raw mathematical power - then, take my money just as well!

Assuming the worst accusations are not true I think there are ways forward going to be acceptable for all. The labs themselves do not represent Terrance Tao as some kind of gate-keeping dinosaur in this. They're not interested, not the kind of entity that can care about theoretical mathematics. These dudes are paid 7-8 figure salaries ultimately for the product, they solve a Millennium Prize problem then pretty quickly seem to move past it.

I guess by their own account they were doing competitive analysis on the product and incidentally solved NS. Probably the two companies should agree to benchmark on random diophantine systems, which are harder and more applicable anyway. It wasn't "brute force" but they did spend $10-20M over the course of a few days based on a rumor, which is ... something. The fact they're not actually taking credit, and published no insights other than "it's a vortex" shows the company really has no business in mathematics. They're not interested (the guy said as much) and it obviously won't pay the bill - rather, they were able to pre-empt an announcement they thought Anthropic may have been preparing to make.

Big leaps in insight I don't think are received as elegant, generally. Fourier's contemporaries actually thought he was wrong (which he was), about both the series and heat equations, and even with the whole thing worked out it's not really straightforward. It fits into integral transforms/linear operators but in a way more complicated than can explained in those terms alone. Plus truncation error is commonly unbounded! Complex numbers and "fluxions" were also objectionable on their face although now one can frame them more or less elegantly.

> I could never imagine an LLM in its current form inventing something as elegant as the Fourier transform.

This is the crux imo. It doesn't really matter what absolute capability AI has at the moment, but whether we are on track with respect to architecture and training approaches. In my mind the only test for AGI is, if the thing trained up to the cut-off of Fourier's time (or Descartes, Newton etc), it should arrive at or exceed their insight.

^ As a measure of intelligence. But it's probably the case either way that LLM is more valuable in terms of the coordinated grunt work we'll put it to, than leaps of insight.

A proof may be impossible to fully grok, since about Leibniz - but problems will be solved now without even understanding the problem statement.

I don't disagree yet it's also clear "hard science fiction" is meaningless if it's just, the people in this universe wear clothing, make campfires etc.

I have great respect for her but this isn't the only essay she's jarringly defensive (imo) in response to a critic. Ok sure, a sock is "technology"...

CoT evidently helps but a bias towards both correctness and innovation has to come from somewhere. The article implies OpenAI's proofs may be supported by Lean but regardless, who knows how many people are trying to disprove the next conjecture each day throwing away nonanswers. Fundamentally these systems are more powerful with better training and sampling methods, or better prompting. Tokens matter but you can rewrite many prompts to get a much better, faster answer using fewer tokens vs allowing "thinking" to go on and on.

Hey cool project! I built a solar system visualizer some years ago but just using the ephemerides data, no physics. This is ambitious. Noting your age I would say, invest some time in the basics - Euler, Improved Euler, finite differences, explicit vs implicit, multi-step methods etc.

Eg I see you've got a powerful adaptive Runge-Kutta method implemented in integrator.js. While that will do really well, for the sake of study you might make the solver implementation swappable and experiment with basic techniques. Some are very slow. Some maybe unstable and blow up the solar system. Why? Numeric methods are not one size fits all - see what the different tradeoffs are and how they respond to fiddling parameters. Understand the fundamentals.

A key thing about the undecidability problem wrt physics is preparation of the initial state. In math and computer science it is relatively straightforward to prepare such problems now (though this represented an enormous leap conceptually), but the "undecidability" of all physical problems relies on construction of materials that are clearly unconstructable - systems of infinite negentropy (eg Turing machines), infinite mass (the lattice), bespoke local interactions etc. Problems standing in the way of physics decidability are typically chaos, far from equilibrium mechanics, elementary SNR considerations and so forth, not problems of logic.

The infinite lattice doesn't represent a "real" physical processes, it's just mathematical technique for closing a (fundamentally) quantized combinatorial sum over millions of interacting elements. The gap problem exists in the limit. For real systems the spectrum can be measured (in principle) by probing the ground state. The computational paradigm is incredibly general but only within what's apparently a pretty atypical thermodynamic regime (the ordered universe).

I hate ads but they're intrinsic to media culture, fact you need 10 minutes of video media to wake up, go to the bathroom, at work, to decide dinner with your spouse, and then immediately when you get home etc. I'm not judging but you are not really going to great lengths to avoid ads.

Interesting quotes from the discovery emails. - https://www.lesswrong.com/posts/5jjk4CDnj9tA7ugxr/openai-ema...

"At some point we’d get someone to run the team, but he/she probably shouldn’t be on the governance board"

"generally, safety should be a first-class requirement"

"Probably better to have a standard C corp with a parallel nonprofit"

"Because we don't have any financial obligations, we can focus on the maximal positive human impact"

"The underlying philosophy of our company [OpenAI] is to disseminate AI technology as broadly as possible as an extension of all individual human wills, ensuring, in the spirit of liberty, that the power of digital intelligence is not overly concentrated and evolves toward the future desired by the sum of humanity"

"The outcome of this venture is uncertain and the pay is low compared to what others will offer, but we believe the goal and the structure are right"

"do you have any objection to me proactively increasing everyone's comp by 100-200k per year?"

"The output of any company is the vector sum of the people within it."

"it's totally OK to not share the science (even though sharing everything is definitely the right strategy in the short and possibly medium term for recruitment purposes)"

"Frankly, what surprises me is that the AI community is taking this long to figure out concepts. It doesn't sound super hard."

"Powerful ideas are produced by top people. Massive clusters help, and are very worth getting, but they play a less important role."

"Deepmind is causing me extreme mental stress."

"At any given time, we will take the action that is likely to most strongly benefit the world."

"Would be worth way more than $50M not to seem like Microsoft's marketing bitch."

"Ok. Let's figure out the least expensive way to ensure compute power is not a constraint..."

"Within the next three years, robotics should be completely solved . . . In as little as four years, each overnight experiment will feasibly use so much compute capacity that there’s an actual chance of waking up to AGI"

"We think the path must be: AI research non-profit (through end of 2017), AI research + hardware for-profit (starting 2018), Government project (when: ??)"

"Satisfying this means a situation where, regardless of what happens to the three of them, it's guaranteed that power over the company is distributed after the 2-3 year initial period"

"As mentioned, my experience with boards (assuming they consist of good, smart people) is that they are rational and reasonable. There is basically never a real hardcore battle. . ."

"The current structure provides you with a path where you end up with unilateral absolute control over the AGI. You stated that you don't want to control the final AGI, but during this negotiation, you've shown to us that absolute control is extremely important to you. As an example, you said that you needed to be CEO of the new company so that everyone will know that you are the one who is in charge. . ."

"Specifically, the concern is that Tesla has a duty to shareholders to maximize shareholder return, which is not aligned with OpenAI's mission"

"During this negotiation, we realized that we have allowed the idea of financial return 2-3 years down the line to drive our decisions . . . this attitude is wrong"

"i remain enthusiastic about the non-profit structure!"

". . .apparently in the last day almost everyone has been told that the for-profit structure is not happening and he [Sam] is happy about this"

"Our goal and mission are fundamentally correct"

"We also have identified a small but finite number of limitations in today's deep learning which are barriers to learning from human levels of experience. And we believe we uniquely are on trajectory to solving safety (at least in broad strokes) in the next three years."

"Our biggest tool is the moral high ground. To retain this, we must: Try our best to remain a non-profit. AI is going to shake up the fabric of society, and our fiduciary duty should be to humanity. Put increasing effort into the safety/control problem, rather than the fig leaf you've noted in other institutions. It doesn't matter who wins if everyone dies. Related to this, we need to communicate a "better red than dead" outlook — we're trying to build safe AGI, and we're not willing to destroy the world in a down-to-the-wire race to do so."

"The sharp rise in Dota bot performance is apparently causing people internally to worry that the timeline to AGI is sooner than they’d thought before."

"This needs billions per year immediately or forget it."

"all investors are clear that they should never expect a profit"

"We saw no alternative to a structure change given the amount of capital we needed and still to preserve a way to 'give the AGI to humanity' other than the capped profit thing, which also lets the board cancel all equity if needed for safety. Fwiw I personally have no equity and never have."

It's a kind of superposition representation a la Kolmogorov-Arnold, a learnable functional basis for elementary functions g(x,y)=f(x) - f^{-1}(y) in this sense with f=exp.

It's largely out of Meta's hands now anyway. The risk here not so much to privacy (it's Apple) but they'll walled garden the model space somehow for sure.

Relatively grandiose post sweeps in all kinds of claims about the universe to merely warn a big corporation can copy your idea easily.

As of now the site is in-fact a C&C/botnet. Cloudflare naturally fixates on such risks, not speech (generally). The basic purpose of 1.1.1.2 is to not wind up part of botnet.

In the technophile's future people aren't just getting dumber, not wanting to think or forgetting how - they aren't allowed to think. Maybe about anything. It's too big liability, costs too much to support, moreover detracts from the product. Like Sam A telling those Indian students they aren't worth the energy and water. That's what we're dealing with.

There's a paragraph on discovery that multinomial distributions are normal in the limit. The turn from there to CLT is not great, but that's a standard way to introduce normal distributions and explains a myriad of statistics.

A provocative aside in bad faith, anyway a completely minor point within the overall post, which some of the people he's telling to fuck off might have read

Good post. I guess the transistor has been in play for not even one century, and in any case singularities are everywhere, so who cares? The topic is grandiose and fun to speculate about, but many of the real issues relate to banal media culture and demographic health.

Why anything except universal algebra? I mean, granted, I myself dove right into topos theory...

Will or should? It's plausible, this same argument was made in an article the other day, but basic type/static analysis tools are cheap with enormous payoff and even those methods aren't ubiquitous.

It's a little arbitrary. Look at the graph on page 6, there's no steep gap in the spectrum there. 16 just about the balance point

Well that's stupid. I submit though, connecting stochastic process directly to shell you do give permission for everything that results. It's a stupid game. Gemini mixes up LEFT and RIGHT (!). You have to check it.

I would submit once you obtain a certain level of experience it becomes IDEAL to begin with implementation, in case a mathematical analysis may be either trivial or impossibly non-trivial... Of course if you're dealing in exchange rates and risk management, understand the math!

They ask a yes/no question and inject data into the state. It goes yes (20%). The prompt does not reveal the concept as of yet, of course. The injected activations, in addition to the prompt, steer the rest of the response. SOMETIMES it SOUNDED LIKE introspection. Other times it sounded like physical sensory experience, which is only more clearly errant since the thing has no senses.

I think this technique is going to be valuable for controlling the output distribution, but I don't find their "introspection" framing helpful to understanding.

The output distribution is altered - it starts responding "yes" 20% of the time - and then, conditional on that is more or less steered by the "concept" vector?

Either life really is extremely rare (most likely), or intelligent life is, or it isn't actually trivial/correct to destroy alien planets. If the galaxy were actually like that we would have been toast a long time ago. In reality dark forest is a generate thesis since it implies we're alone, so no aliens anyway.

It's worth reading Doron Zeilberger's many opinions about proof/rigor and other things.

https://sites.math.rutgers.edu/~zeilberg/OPINIONS.html