OpenAI recently claimed to solve an important open problem in math concerning the behaviour of fluids. And OpenAI did answer an important open math problem as described in the official problem statement . But morally OpenAI just found a bug in the problem statement. This is at least part of the reason OpenAI is not claiming the prize. In our view the Clay Institute should correct the problem specification and list this one as co-sponsored by OpenAI. As OpenAI can, technically, claim the money they would be in effect funding a replacement prize offered going forwards so co-sponsoring is fair.
There are clear cultural similarities between web3 and AI. There is also a lot of overlap in investors, founders, developers, users and pretty much everything else. And we think there is an important lesson in this AI incident for web3 compliance because too often in web3 some claimed innovation is simply straightforward non-compliance.
To see this connection first we need to describe, in non-technical terms, what OpenAI did and we need to work through the "bug" in the problem spec. At that point it is easy to see how a human would be unlikely to follow this route. And why, maybe, a human that did follow this route would have published a claimed bug in the specification rather than a purported solution.
After covering all of those details we will analogize to web3. Once what OpenAI did is explained the web3 parallels are easy to see.
The Hard Problem
The Navier-Stokes equations are the standard tool used by scientists and engineers to model fluid flow. If you have ever seen a computer simulation of air over a car or plane wing: that is Navier-Stokes simulation software. We worked on software in this space decades ago .
The real problem here, the thing the Millenium Prize is morally about, is understanding how and why smooth fluids develop messy looking flows and turbulence and all the vagaries of fluids in the real world. Is this because of subtle, random variations in density and velocity and such in real environments? Or would this still happen even under ideal conditions? Turbulence, and apparent randomness, are obviously properties of fluids in the real world. You can see this moving your hands while swimming as a child. But is this part of fluids? Or the randomness and non-smoothness of the real world? Does this well-loved model capture all the essentials of real fluids or is something more needed? That is clearly an important scientific question and it motivates the inclusion of this thing on the Prize list.
On a technical level, the hard and important problem OpenAI took on was determining whether the standard Navier-Stokes tool can generate certain types of anomalies in finite time starting from smooth and calm conditions. If an ideal fluid modeled by simple smooth equations breaks down then those messy features are a thing about fluids and not about environmental imperfections.
That is the basic problem. But of course we need some restrictions. If you can apply infinite force then you can probably cause all kinds of blow-ups. Similarly if you can jolt things in physically impossible ways – say you switch instantaneously from pushing the fluid to pulling it – maybe that can cause a problem. It is not possible in the real world to generate infinite force or change velocity instantly. So the official statement of the Navier-Stokes problem is that all the forces involved must be "smooth."
Smooth is a technical math word. It means something specific about functions. Another, adjacent, math word that matters here is "analytic." Smooth is a weaker condition than analytic. All analytic things are smooth, but not all smooth things are analytic. For any mathematically-fluent readers: smooth functions are infinitely differentiable everywhere while analytic functions are the limit of their power series everywhere. If you half understand that and vaguely remember Taylor Series from school: Taylor Series work for analytic functions everywhere but not for smooth ones. Maybe they only fail at one point. But if there is at least 1 point where the Taylor series does not converge to the function then it is smooth but non-analytic. Anyway, analytic functions are smoother than smooth-but-not-analytic functions.
Determinism & Physics
Classical physics is deterministic. If you do something exactly the same two times in a row the exact same thing happens. A thrown ball goes the same distance every time. A swung pendulum has the same period and path. Applying the same amount of heat to a pot of water boils it in the same time every time.
Of course real experiments are subject to the vagaries of the world. But the equations, the ideal modelling from physics class, give a single unique and identical answer each time you solve them.
But this is not true when you apply non-analytic forces. In general when things are non-analytic physics stops being simple and smooth and, for lack of a better word, Newtonian in the sense Newton meant when he said I can calculate the motion of heavenly bodies, but not the madness of people .. This is, mathematically, linked to the famous three-body problem .
If we are a little bit sloppy with our math we can say this is sort of the same thing as Chaos Theory . When you apply non-analytic forces the math might give you more than one solution for what the future looks like. How exactly nature decides which we get, and if that is chaotic, is a bit of a deeper and partially philosophical question. But the core point is: once you start allowing non-analytic things we already know how to get randomness from classical, smooth, physics. The ball flies along a different path each time you throw it.
Of course all of this is idealized. We cannot apply precisely the same force for exactly 1 second in any kind of lab. None of this is about the engineering challenges of real life. The point is that even under ideal conditions introducing mathematically pure and perfect non-analytic stuff can give us the vagaries of the real world.
OpenAI's solution relies on this feature. If the problem statement required an analytic force the approach would not have worked. In fact proof that OpenAI's method cannot be generalized to handle more types of forces was quick to appear. If the problem is restated to require an analytic force the vast majority of the recent work does not apply at all. There is of course some value in knowing an approach cannot work. But truthfully that is about it.
Our intuition for the OpenAI result is that certain types of sharp corners which are physically impossible but mathematically straightforward can generate pathological behaviour even in viscous fluids. If a corner is sharp enough in the right (non-physical) ways, and you jam in back and forth enough times, you can create blow-ups even in ideal fluids. Maybe somehow that turns out to connect to something useful in the real world. But consider what the intuition for OpenAI's result would be if it applied to analytic forces: there are strange corner shapes we can construct and shake back and forth in laboratories to reliably create pathological behaviour in even very thick fluids under ideal conditions. The counterfactual intuition clearly leads immediately to all kinds of fascinating further work. People would be in the lab already working on this.
The key element is that OpenAI's approach depends very carefully on the use of their special smooth but not analytic force. When we use models we expect them to only approximate reality and that is fine so long as the model does not blow up if there is a tiny deviation from the idealized state. We can use gravity to reliably model how the Moon goes around the Earth without getting into the exact details of the shape of the Earth or the Moon. But if a gravity model gave wildly different results for a perfectly spherical Earth and an Earth with the real shape we would not consider that a good or useful model because the exact shape of the Earth is changing all the time. OpenAI's solution depends carefully on this kind of fragile configuration. If we soften some edges on the force ever so slightly the proof breaks. Nobody can go into a lab and do anything interesting with this result. We learned nothing about the physical world.
It is in this sense that OpenAI only sort of solved the problem. Yes it solved the problem as stated on the website. But OpenAI "explained" random, turbulent, blow-up behaviours emerging from smooth physics using a tool that we already know can do that in other contexts . So the theorem is true but there is little physical insight. There is not zero insight of course. And they did solve the problem as stated. But when you read the result it yields a mixture of "yeah, fine, sure, that makes sense" and a mild letdown feeling rather than some deep insight. Scientific American asked if they had solved the " wrong " problem.
Now math can be done for math's sake as abstract truth. This is why Hardy referred to the patterns in math as being more permanent than those of other areas. But physics is about understanding our physical world. There is little insight into the physics of fluids to be gleaned from the observation that non-analytic forces can induce singularities in formerly-smooth fluids. Some people might see an analogy with some "decentralized" stablecoin yield structure that relies on bonds in a securities account in the name of some labs entity. This just reuses a tool we already know can get there. There is no yield innovation in the design. And therein lies the web3 connection: claiming a breakthrough when you are really just reusing a standard tool but refuse to admit it.
Loopholes
OpenAI's computers took the problem statement literally. That is what computers do. And then those computers went off and found a way to resolve the open problem in line with the rules as written but without regard to the point of the problem. As this is math we can easily adjudicate right and wrong and correct and incorrect. Of course "the point of the problem" is not in the specification. It is not the LLMs fault it did what it did. There is no point asking your computer why it does what it does. OpenAI's tools understood the deeper goals here no better than your laptop understands your employer's strategic business issues which undergird the emails you send and receive.
Now for web3. Laws and regulations are not generally formulated with mathematical precision. Nor are they intended to be enforced with a narrow formulaic toolkit. If you are required to build an effective KYC/AML system you cannot fully discharge this responsibility by signing a contract with a three person startup with no compliance background that states they will provide an effective KYC/AML product. That is not how business works.
You can convince yourself that works. Maybe. You might be able to find a lawyer somewhere that tells you that effort could be used as part of a defense against charges your program is inadequate. Certainly you can find an LLM to tell you this is a clever idea. But it is clearly not true that is is a bulletproof strategy that can never backfire. If properly documented, again in an overly literalist fashion, it is probably guaranteed to backfire. If you run the business long enough something bad will happen.
What you have actually found is not even a loophole. It is just a way of convincing yourself you tried hard enough. In some absurd, naive and overly literal sense that probably appeals to people in the LessWrong and Effective Altruism communities as a "solution" – but it is not a solution. This is not the point of compliance processes.
This all feels very much linked to why those two communities keep popping up with ideas that only "work" when you strip away all the meaning and context behind the rules and words and requirements and instead plunge head first into a narrowly constructed statement of a business problem that we know by construction does not embed all the real requirements to legally do that thing.
We see something similar with systems that claim not to have custody but somehow, sometimes, clearly do . Or perpetual aspirations to remove clearly non-compliant behaviour from large systems run by listed companies. Or so many other now-obvious web3 patterns.
Are these really loopholes? Not really. Is a stablecoin that pays yield derived from bonds in a traditional account decentralized just because it has no freeze function? Not really.
To the extent the people designing the systems were ignorant of how they worked: obviously that cannot qualify as "effective." And if they did know and chose the route for some kind of minimal plausible defense strategy: that also cannot be effective by definition.
Financial rules are written such that ignorance and willful blindness do not work as defenses. Or at least are not supposed to work as defenses. Sometimes the rules do have loopholes. Sometimes enforcement is weak or crooked or just does not happen for a legitimate policy reason. There are lots of reasons a loophole might in practice work as a defense – and lots of reasons that defense might collapse.
In short, a lot of these folks look to be reading common law rules as though they are civil. "Oh the rules are simple and I found a loophole" may well work in a system where the rules are supposed to be prescriptive and rulings do not look to precedent from other cases (aka European civil law, where you are unlikely ot be granted a license for your novel thing in the first place). But your loophole is probably not real if it is a common law system and there are myriad cases ruling similar loopholes do not work. "But those are not exactly 100% the same as what I did so I am fine" you can hear. We have all had conversations with annoying people like that.
web3 Compliance
The simplest analogy of the OpenAI Navier-Stokes thing in web3 is a project that claims to be exempt from all manner of rules because it is decentralized while the entire thing is run off-chain by the team. This was common years ago. And it is still fairly common today. There is no actual innovation in such a project because building a non-compliant centralized product is not generally a challenge. You do not contribute to the discussion on financial service design by building a Liberty Reserve clone. And if your product is a few minor tweaks away from Liberty Reserve that may be enough to convince you – but it is almost certainly not going to be enough to convince a judge.
More generally in the web3 case a project claims to exploit a loophole like decentralization rendering it exempt from regulation while the actual system is just willfully non-compliant and contributes nothing to the discussion on system design. OpenAI's "solution" contributes nothing to the discussion on why fluids behave in the random and unpredictable ways they do in the real world because the "solution" employs tools we already know can create that sort behaviour. The question was supposed to be whether some new phenomenon exists within our existing framework to explain things we observe in the real world. Or if there is, provably, no such phenomenon in there and it is all about random variations. This is just as a high-throughput trading product that somehow uses a blockchain but is really just a centralized database contributes nothing to the discussion on how to build a high-throughput decentralized trading product.
Or maybe your product makes USD accounts available to users in jurisdictions where USD accounts are not generally available (or outright illegal). We wrote in May 2022 about how this product may look novel to the ignorant but is more commonly just known and illegal . "Our plan is to offer unrestricted currency trading services to residents of a country with exchange control laws" is not an innovative business plan. It may well be brazen. It will almost surely be profitable (for a while). But it adds nothing new to the discussion.
Connections
The common thread here is technical people without backgrounds in relevant areas leaning super-hard on literal readings of documents they do not really understand. We see this all the time in web3. A great examples is the many people who seem to believe fractional reserve banking means all the banks are always insolvent. If you do not accept such a belief is common then it is worth your revisiting Celsius just to see how many were taken in by transparently false claims. That is old and we are not going to look at current projects here. But the belief in fundamentally misunderstood things remains strong.
Mistakes and differences of opinion are of course part and parcel of life. But there is a huge difference between a difference of opinion and a product or idea that is incredibly leveraged to one narrow reading of a rule that was not meant to be taken that literally.
For math a literal reading of a document meant to be read literally is fine. If it turns out you are just exploiting an error in that document your work product may be of little value. But you still solved the problem as written.
Not so in financial services compliance. Just because you think your tool is effective, or your plan to eventually decentralize is sufficient, does not mean it is. You can look up math words and get tight, clear and unambiguous definitions and then go off and work from there. What do "intent" or "effective" or "sufficient" mean in so many different contexts? Reasonable people disagree on the outcomes of countless court cases around the world back throughout history. These are not theorems.
And this stuff is not math. The real risk is failing to understand the assumptions which underlie your strategy. Because a process that fixes assumptions like "xyz is sufficient to be effective" in stone and then cranks forward doing what management believes is just theorem proving will turn out to be incredibly highly leveraged to the belief the assumptions are correct precisely when they are most wrong . Prices are set at the margin. This works in markets and it also means a business built atop lawbreaking is likely to find the most growth in precisely the areas where it is most unlawful. Why? Because the margins will be the largest. If your neighborhood pharmacy stocked, without knowing, illegal drugs those would probably sell out first. And the shop would keep raising prices and collecting fat margins until the police showed up. The business would expand in the outlaw directions rather than focusing on widening the selection of soap and toothbrushes.
Theorem proving assembles absolutes of right and wrong. Compliance is about risk management. These worlds do not mix well.
There is a deep irony here that aspirationally decentralized financial architectures are likely far more brittle than traditional ones precisely because they depend so strongly on questionable assumptions. Knock one brick out and the whole thing collapses.
