How the world’s hardest math problem affects your business
Lessons from the OpenAI Millennium Problem Controversy
It’s not easy to make a million dollars, but there is one fairly straightforward method: just answer a single math question. But the Millennium Problems have a six-figure prize because they are the hardest and most important unsolved questions in mathematics.
Last week, OpenAI – the company behind ChatGPT – claimed that its AI solved one of these problems [1]. That in itself is groundbreaking news. But controversy soon erupted – other mathematicians claimed that OpenAI’s AI agents may have had access to their work, and they wondered if the AI “copied their homework” and used it to come up with the solution [2].
But I believe there are a number of consequences here that should be examined – and they have nothing to do with advanced mathematics.
1: OpenAI made a smart decision about which Millennium Problem to attempt.
When you throw a ball in the air, its movement is governed by the equations of gravity. If you throw it up, it eventually stops and comes back down. These equations are relatively simple, and no matter how hard you throw the ball, you can predict that it always returns to earth.
Fluids, on the other hand, are governed by the generally unsolvable Navier-Stokes equations. The Millennium Problem, however, doesn’t ask for every solution of the Navier-Stokes equations; the Millennium Problem simply asks to find a single solution with a particular property (in this case, that the solution equals infinity). All that is needed to win fame and money is to find a single example that proves this property true.
This makes it a great candidate to solve using AI. AI is great at problems that can be solved in parallel. You can spin up several thousand models, have each come up with a different example, and then check if each example goes infinite. If you’ve got access to lots of computers – which OpenAI certainly does – each model can all work at the same time, taking only as long a single model to find a thousand solutions. And because LLMs are designed to be "creative” - that is, the same input doesn’t always produce the same output – you don’t have to worry about the models repeating each other’s work. This is how OpenAI solved this particular mathematical question [1].
Of course, AI models make mistakes. In this case, however, it doesn’t matter if AI produces thousands of wrong answers – as long as the AI comes up with one correct solution, it has solved the Millennium Problem. It will certainly take longer if the AI makes mistakes, but since each example is generated independently, mistakes don’t compound. While humans do need to validate the answer, they only need to validate the few answers that reach infinity.
So what can you take away from this strategy? First, AI's advantage is not always that it is smart – often, the main advantage is that it can do a complicated task many times in parallel, reducing the overall time it tasks to accomplish a goal. Second, you can use AI that makes mistakes if it’s easy to identify when the AI might be right. Sometimes it is more expensive to come up with only correct answers than it is to quickly generate many answers and keep only the best ones. You don't always need to choose the most powerful AI model if you can work more efficiently with smaller models.
2: The appearance of trust is important to AI adoption.
Most companies do not worry when their data is stored with the same service as a competitor. If Honda uploads the plans for the 2027 Accord to Microsoft Azure, they can be confident that it is not going to somehow end up in the hands of Toyota. Traditional data storage providers have a strong incentive to keep your data entirely separate, since their business model is to provide this security.
AI companies, on the other hand, have several incentives that would support potential cross-contamination. These companies want to get their hands on as much training data as possible, and user-submitted data is ideal for training a model: the user has put it in a format that the AI can understand, and the user might even provide corrections or commentary on the AI’s responses. Secondly, current laws are unclear on whether a model “steals” the data used to train it. In the arms race to produce the most powerful model, AI companies might find it more profitable to hire lawyers and lobbyists than to reduce the amount of available training data.
While many AI companies offer plans that shield user data from exposure, these same companies are starting from a position of consumer mistrust. They’ve benefited from legal gray areas on copyright law, threaten the livelihoods of creative industries, and participate in other legal but uncomfortable activities (e.g., destroying thousands of rare books [3]) in the quest for ever more training data.
The main takeaway from this situation is this: people view AI from a fundamentally different position than they do other software products. The mathematicians that accused OpenAI of using their work were not anti-AI, but active contributors to AI research – and even they considered data misuse to be a clear possibility. So, before you add AI to your offerings, consider the optics. An advanced capability may counterintuitively drive users away if they think their data may be sent to an unscrupulous AI provider. On the other hand, advertising a less powerful model may be a benefit if you can host it entirely on your own servers. It’s not enough anymore to just choose the best performing model.
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