Mathematicians have discovered a problem they cannot solve. It’s not that they’re not smart enough; there simply is no answer.

The problem has to do with machine learning — the type of artificial-intelligence models some computers use to “learn” how to do a specific task.

When Facebook or Google recognizes a photo of you and suggests that you tag yourself, it’s using machine learning. When a self-driving car navigates a busy intersection, that’s machine learning in action. Neuroscientists use machine learning to “read” someone’s thoughts. The thing about machine learning is that it’s based on math. And as a result, mathematicians can study it and understand it on a theoretical level. They can write proofs about how machine learning works that are absolute and apply them in every case.

(Mathematician Kurt Gode)

In this case, a team of mathematicians designed a machine-learning problem called “estimating the maximum” or “EMX.”

To understand how EMX works, imagine this: You want to place ads on a website and maximize how many viewers will be targeted by these ads. You have ads pitching to sports fans, cat lovers, car fanatics and exercise buffs, etc.. But you don’t know in advance who is going to visit the site. How do you pick a selection of ads that will maximize how many viewers you target? EMX has to figure out the answer with just a small amount of data on who visits the site.

The researchers then asked a question: When can EMX solve a problem?

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