Devil's advocate: OpenAI not being able to use compute is highly correlated to many other AI companies not being able to find a meaningful use of this compute.
Failure to take into consideration those kind of correlations ("If my biggest client isn't able to buy it, I would be able to find someone else who will") is one of the principle causes why many risk models turned out to be garbage during the Great Financial Crisis.
But I also doubt Nvidia is on the hook if OpenAI just no longer wants the compute. I bet they are only on the hook if OpenAI cannot pay for it (is insolvent in some way).
I also have to bring up that OpenAI has already spat out an inference chip that beats Nvidia on flops per watt. So they could potentially not need the compute while other ai companies do.
This war started as a regime change operation in Iran, one of the shakiest regimes in the world pre-war, but ironically the war might end up with most of the nations who supported the war (either vocally or quietly) "regime changed" (loosely defined), including Israel, US, some European countries and now possibly some Gulf nations, awhile the Iranian regime seem to have tightened its grip more than ever.
Yet MAGA supporters were saying early in the war that they are "plan trusters" as prior US admins sucked at regime change because it is a "skills issue" and none of the prior admins had the triple digits IQ of Hegseth, Trump and Bessent.
If they were going to try this it needed to be done months earlier when the protests were raging. Instead the brain trust fumbled the initiative and let the Iranian leadership kill and scourge their local allies into compliance. Then fumbling the decapitation strike coupled with the decades of preparation for a decapitation strike (via redundancy of command) the genius brigade seemed to be unaware of because they fired all the experts, and the total repression of the protesting populace, led to an unusually strong system in Iran. They also almost certainly let racism play a big role in underestimating the Iranians, who are a very technically sophisticated society and have been preparing for this scenario since day one of the revolution.
Everything that’s happened was predictable and predicted, which is why other administrations who were more than happy to topple foreign governments when it suited them to not do so in Iran. MAGA feels like the junior dev that blames the compiler for their own syntax errors.
Not sure where you get the shaky regime idea, but Iran was not on the verge of collapse from protests prior to the war. It may have been on the verge of more aggressive clamping down from the IRGC, but collapse wasn’t around the corner.
>This war started as a regime change operation in Iran
I believe this war started with a tomahawk missle murdering a school full of children and then the US denying involvement. I very clearly remember it. US attacks Iran unprovoked. First act, murder their children in school. If you wanted to solidify opposition to the US in Iran, I don't think they could have done a more effective job.
They haven't denied it yet, it's still under investigation. They may be able to workout they were the only country in this war with Tomahawks responsible for the triple-tap missile strike, after the mid terms. Or they may just move on from it and never talk about it again, like the Epstein files.
All the Kingdoms in middle east are very fragile. Gulf coast countries economies are crashing due to the blockade. Bahrain, UAE, Kuwait, Qatar, Saudi Arabia. One Arab spring away from a new government and this could be the spark.
The goal wasn't regime change. They didn't even propose a replacement, unlike Venezuela where there was someone to step in. Trump admitted it was Israel's demand, plus there are signs of market manipulation.
Some Iranian-Americans are very pro-Shah, particularly the many kicked out during the revolution. They were celebrating the war like it'd bring back the Shah, but frustrated that the US govt and even Western media as a whole ignored the exiled royal family... because that's not the point of the war.
Do you even realize that one of the only reason anybody still supports this war is precisely because of comments like yours? By dividing people into teams, and antagonizing them, you result in people never willing to stomach giving an inch and doubling down on stupid.
Obviously this war has been the US' latest great failure, and at the beckoning of a foreign power which makes it especially catastrophic. If people could focus on this, rather than trying to divide things into teams and then sling mud, they'd have vastly better outcomes come November (and on) than just using it for divisive mudslinging which does nothing but ensure that all elections, regardless of how bad the decisions of a incumbent, or how awful a challenger, will remain these sort of 50/50 coinflips.
I am saying that adding your tribal bit to your post is just completely self defeating. And yes, the goal is indeed to avoid hurting people's feelings. I don't know why you'd mock that. People are not machines, and when you make somebody angry at you, or otherwise make him feel insulted - he'll happily argue that 2+2=5 just to avoid giving an inch to you.
Bridge building hasnt worked. Hillary's biggest campaign failure was drawing back from her deplorables comment, she should have leaned into it - thats what Trump did, go harder into division, and he's president now. Instead of being milquetoast corporate stooge full of fake politics talk, she might have seemed to actually stand for something. You're bringing 1990s politics into the 2020s and its proven multiple times it doesnt work any more. A small group of fanatics is actually more powerful than a large cohort of half-committed these days.
It's not about bridge building, but rather not bridge burning. When people are antagonistic to 'the other side', it means the last thing in the world they'd ever think of doing is aligning with you. 2028, after Iran, should be a landslide. But watch - it's going to be another coin flip. And people themselves are creating that scenario by acting like half-witted tribal kids on a playground, instead of actual thinking/empathetic adults.
It's universal. Politics in the US has become so completely broken. Last presidency was Weekend at Bernie's, now we have one where El Presidente is trying to LARP as General Jack D. Ripper.
The reason people accept, and even defend, all of this is solely because they find "the other side" detestable, and people like our GP here play exactly into this by making themselves completely detestable to anybody that's already not as far out, and in the same direction, on the partisan horseshoe of stupidity as they are.
Do you realise that the only reason the average US taxpayer keeps getting wrecked into one pointless forever war after the other no matter who is in power is because the elites are never held accountable for their mad self-enriching adventures?
Holding people like Hegseth (who literally insider traded defense equities right before the start of the war) and Trump accountable (who practically made a gazillion insider trading each mad meme he posted while the world burnt) is not "dividing people into teams"
Is it possible that they claim they used a "new internal model" to provide an excuse for "training" on new user data, knowing full well this new user data will include Buckmaster's chat?
So the entire "new internal model" is 'parallel construction' in criminology speak to justify spying on Buckmaster's work in a legal way.
It doesn’t seem this is a question of ToS though. I would hope it is abundantly clear to anyone and everyone:
THEY’RE USING YOUR DATA
As they involve themselves directly, explicitly in the process of scientific research and discovery, it becomes a question of scientific and professional ethics.
Determinants are easy to use but very hardly to grasp intuitively, this is not a minority point of view. See countless of StackOverflow questions begging for a conceptual exposition of determinants.
The easiest conceptual handle is geometric: volume expansion, but seeing how this is related to the combinatorial sum over all permutations, or how those two point of views are related to the algebraic one (that a set of equations having a solution or not), is not easy to see even in the 2D case.
I won't be surprised if math professors don't have this issue like you said (especially if someone is comfortable with wedge products), but the vast majority of newcomers who are interested in understanding why something works rather than just how to use it struggle all the time with determinants.
It seems to me more like determinants are often badly motivated. The way I remember it from Apostol's Calculus was like "a volume multiplier would be very useful; it needs to be a signed volume for linearity, which implies antisymmetry. Here are axioms collecting these requirements. They're uniquely satisfied by the determinant. Proof: ..."
Agreed that it should help if you got to learn wedge products first (I didn't).
Yes, but that doesn't prove that the determinant is actually the real signed volume multiplier.
I think this is what led me to feel unhappy about determinants when I was a first-year university student. You need to actually prove that the determinant is the volume of the N-dimensional parallelepiped, and the axiomatic proof doesn't do that.
So you need basically two extra lines after proving those things so that people can say "okay, the determinant eats ignores all input vector non-orthogonality so that it gives volume".
I found that “properties of the determinant uniquely determine this formula that I guessed” approach to determinants to be extremely unconvincing when I was learning linear algebra.
This might come down to details of how you explain it: iirc Apostol took those basic moves (axioms) and calculated what the formula would have to be, rather than starting with a formula and checking that it has the properties of a signed volume.
But I don't know, it's been a very long time for me. It's good to have a variety of approaches to the subject.
This is indeed a good concise description of how to connect the two, but even making peace with this, there is something still magical in how the permutations in the sum cancel neatly (in an inclusion-exclusion kind of a way) to get the volume.
I think the volume explanation is one of the most intuitive pieces of math in existence, personally! Uninvertibility of a tranformation corresponds to a volume of zero because the transformation must squish two dimensions together, leaving them impossible to differentiate, det(AB) = det(A)det(B) because applying two transformations applies their scaling successively, det(A^-1) = 1/det(A) because you have to undo the scaling to invert a transformation etc. I don't think the permutation definition is even strictly necessary; if I recall correctly Linear Algebra Done Wrong defines the determinant in terms of its geometric definition and develops its formula from the properties it must have. I think that the concept is well worth the investment of initial confusion. Axler disagrees, however.
But if you see the geometric view then the permutation sum, for certain obsessive learners they want to see why they are equivalent and thats the hard part.
We do a 2 step anonymisation:
1. Mask all symbols, timestamps etc. So the agents cannot infer the assets/time periods.
2. Mathematically transform numerical values and returns. E.g. the market return targets are not the raw market returns, but neutralised and manipulated. So even the agents have certain bullish/bearish biases, it cannot make use of it, as we use the transformed values.
ah i thought so, interesting. I think the challenge is to do 2 while still keeping it realistic, which actually gets very close to synthetic data generation.
we do affine transformations of the data, so all return/ pnl measures are still the same as with untransformed data. The transformation doesn’t change the conditional distribution of the data, which is what alphas ultimately measure
This is not new, most famous conjectures are believed to be true mainly because an already enormous brute force search was conducted finding no counter-example.
Hmm this sounds like an incumbent missing a paradigm shift because they didn't want it to disrupt their core (usually enterprise) business, although riding the shift would have ultimately delivered an order magnitude larger business.
Classical example is Microsoft actively undermining mobile because it threatened selling Windows or enterprise licenses.
Or Yahoo fighting Google's model because the latter model's didn't depend on taking enterprise deals to rank results.
ten years is a very long time in technology, RISC-V ecosystem could be so vibrant and advanced that it might prove more cost effective for Apple just to feed off it (assuming Apple is still relevant by then).
It's almost like trying to predict if the smartphone leaders in 2006 (Nokia / RIM) would want to adopt this new mobile operating system that hardly anyone uses (android) in 2016.
The thing is Apple designs its own ARM cores. They don't use the vibrant ecosystem of ARM for all the important parts of the CPU; they compete with it on their own and manage to win. They only pay a small amount per device for an architecture licence that's very generous for Apple, in large part because Apple was an initial seed investor and first customer of ARM.
If all the current investments in ARM don't suffice to beat Apple's own efforts, I don't see how they could ever need to use RiscV's community to achieve their goals.
As long as ARM keeps the architecture up-to-date and the fees minimal, Apple's staying.
10 years is relatively short time in hardware, that is only at best 4 cycles. In today's world it is only 3 cycles. The amount of time, energy and resources required to switch from ARM to RISC-V only to save $100M a year makes very little sense. That is assuming you can get the same performance switching over in the first place. Which right now isn't the case in the next 5 years.
And I wouldn't be surprised ARM gives Apple some other patents protection as well as discount on other IPs.
Well you can see from the original poster's timeline, that 10 years from now will be effectively 16 years into Apple's ARM journey, so you can add two more cycles.
And also from the timeline you can see that the average Apple hardware transition period is 2.75 cycles, so I wouldn't bet too much that their ARM journey will last more than 6 cycles.
Unlike the unit distance problem, the impressive thing here is that it is a proof rather than a counter-example.
However, it seems the proof is extremely concise so it seems that it is exploiting a clever trick that somehow all the experts missed.
So not to dunk on this amazing result (or move the goal post), but it seems now the only achievement that AI hasn't managed in mathematics is presenting an autonomous "theory-building" proof of an open conjecture. That is a proof that requires creating a substantial new theory (developed say in at least 30+ pages) to crack an open problem.
It is very concise, and reads precisely as you suggest: to exploit properties already discovered and therefore combined in a novel way.
I'm just delighted by the prose. It reads like an old paper. The ones that were just straightforward theorems with proofs that do exactly what they say.
In my (very) limited use of GPT-5.6, I have noticed it is quite concise in general, and significantly better at abstract thinking. Doing a PR review of a large change it was interesting to see Fable and 5.6 mention a few similar points with Fable much more long-winded and less readable, while 5.6 caught more "second-level" concerns and Fable more "in the code" concerns, so they both are quite useful in concert.
In general, I would not be surprised if 5.6 was a much better tool for high mathematics than Fable based on the abstract thinking. For my dev workflow, I have flipped my approach from planning with Opus 4.8 high and implementation with GPT 5.5 to planning with 5.6 high and implementation with Fable medium (and I might even drop to Fable low). This is only on the company dime, of course.
This has since been the case with recent models from OpenAI vs Anthropic, seems it's a matter of their philosophies embedded into the model, much like Conway's Law.
Hmmm... seems to me that if you can find a solution without creating the desired explanation - then that's a problem with the original question - not the solution itself.
And discovering a bad question leads to the correct question. No?
> then that's a problem with the original question - not the solution itself
I think there's a good counterexample to this:
Atiyah/MacDonald proove the Nullstellensatz ultimately by using some trick involving determinants.
They give a very nice theoretical treatment of the content and context of the theorem. But the proof at one crucial point uses techniques that live conceptually outside of this context: While its possible to see that the argument is sound, it does not give a good explanation of _why_ it's true within the context of the theorem.
(You could of course argue that they did not give enough context
... but that's exactly my point: the trick makes the proof work but hides the explanation)
I was baffled enough by this comment to take my copy and look. The Nullstellensatz is an exercise late in the book long after Noetherian rings are introduced and they don't even do the Rabinowitz trick in the hints as they have enough theory to hit it the hard way. Determinants are nowhere to be found.
The determinant trick I'm referring to is used in prop 2.4 (in the Version I found via Google).
They use the determinant of the adjugate matrix if I remember correctly... But they just hit the reader with this without any motivation or even naming it.
For Nakayama lemma (but they give a cleaner proof later). Note that the book was from the 1960's and from lectures at Oxford: matrix manipulations like that were a lot more commonplace.
>(You could of course argue that they did not give enough context ... but that's exactly my point: the trick makes the proof work but hides the explanation)
Can't one see it in another way: that the trick illuminates a deeper explanation, connection the theorem's context and the stuff that's conceptually outside of that context. And that the problem is we don't know why the two domains (the context and the conceptually outside of it one) are related and cooperating in this way.
But a proof isn’t an explanation it’s a proof. Proof by assuming the opposite is true and demonstrating a contradiction is very indirect and not at all directly explanatory yet it’s a proof non the less. The goal of proofs is to demonstrate something to be provably true, not expository knowledge gathering.
In fact most mathematicians (myself included!) think the more clever the trick the better the proof! The trick itself being clever is interesting because it often yields a new way of tackling or thinking about your own proofs. A bland explanatory proof that elicits some conceptually “why” is only preferable if it has a reason for doing so - does understanding why yield a new avenue of research? Often then the “why” is quite a clever trick too.
I think it’s a bit the opposite of programming. There you want your solutions to demonstrably not be clever and the code be its own documentation. It’s a different discipline.
Thank you for the validation. I only dabble in mathematics - so it's reassuring to hear what I remember - a clever proof is still considered a positive thing.
I do (of course) understand the issue that non-constructive proofs can be frustrating - and a constructive proof of the same theorem is valuable tool in seeing exactly why a truth is true.
But I guess I've never seen a non-constructive proof (in a space where no constructive proof is available) considered a failure.
clever tricks has value for sure. But the main way progress is done in mathematics is by building new theory, the proof of Fermat's Last Theorem is much more important because of the math it created to solve the problem, rather than actually solving the problem.
Right. I think I understand - this question was expected to produce a new theory and the clever solution avoided that.
Like I said below, I think this is a fantastic result. It discovered that this question really wasn't asking the right question. That's a determination that has eluded the humans examining the problem - and a real step forward - albeit not the hoped-for step.
Grant Sanderson recently distinguished mathematicians that create syntax (he might use the word ontologies in some circles) from those who manipulate it on the Dwarkesh podcast. I liked this delineation a lot. We seem to be at ‘manipulating syntax’.
Creating useful ontologies still seems a ways off here. Not to complain about this awesome result, just to think about where some future goalposts might be laid (and of course complained about / discussed at length when reached)
For comedy’s sake, I asked ChatGPT 5.5 about the significance of the problem and the chance that 5.6 would solve it with a three page solution. It said close to zero.
I invited it to search the internet and it remains extremely sceptical.
- double check the proof (provided it with the prompt and proof artifacts)
- double check some of the claims made in this comment section (no math involved newer than 30 yo, no human contribution or review, no mathematician affirmations, proof assistants not being developed enough in this area to support machine checking a proof like this)
- check for any mathematician feedbacks
It stalled out (bad first impression much? lol). I then retried with 5.5, expressing the same request and my personal skepticism, and it returned to me with cautious optimism and no obvious issues found.
I think the fact that I provided it with the actual artifacts in question vs. you simply asking it to speculate about them is a really interesting UX difference. Like certainly, a coveted 50 year old math problem having a few pager proof is not going to be very likely. But then skim reading the proof by a frontier model is not going to yield any obvious issues either. Both responses are perfectly defensible given the context (I don't necessarily think these qualify as sycophancy), but we'd walk away with entirely different impressions if we didn't know about each other's requests.
And I'm not even trying to suggest you were wrong to not approach it in the ways I did. It's a perfectly reasonable and human way to prompt it the way you describe. It's just not the way I'd do it, but I have a hard time articulating why. And it's clear that the model was never going to help with this difference either.
Half a century of computing, and we're still trying to make the machine think on the users' behalf :)
I considered it, but I figured that whatever I did there would be inconclusive. Instead I tried to figure out the blast radius of this being proven, and I didn’t get very far with that either.
> Verdict: I checked every step and found no error. The argument appears to be a correct proof of the Cycle Double Cover conjecture, modulo two standard cited results (the reduction to loopless cubic graphs and the Jaeger–Kilpatrick 8-flow theorem, both real and well-established).
> Two caveats: this would settle a ~50-year-old open problem in three pages, so it deserves independent expert scrutiny regardless of my check; and I couldn't reach the web from here to confirm the paper's provenance or any community response, so I can't tell you its status beyond the mathematics itself.
the unit distance problem's paper was human-summarised and condensed significantly from the initial LLM output, so it seems the model did do some theory-building there (possibly providing motivation for the clever trick as a natural deduction, at least in its eyes) before humans cut off all the chaff; I imagine the development was similar here.
A clever trick is way better than a stupid trick yeah. I don't get complaining about a concise elegant solution either unless a specific problem with the actual proof was brought up.
Open any technical textbook in an area slightly outside your domain and you will quickly disabuse yourself of the notion that majority of words are obscure. Most complex words are just technical/jargon not archaic or forgotten.
Failure to take into consideration those kind of correlations ("If my biggest client isn't able to buy it, I would be able to find someone else who will") is one of the principle causes why many risk models turned out to be garbage during the Great Financial Crisis.
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