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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..
Century - Group - Romans - People - Heads
During the fourth century, a group of Romans mysteriously decapitated already dead people and buried the heads between each owner's legs.
In this case, a team of mathematicians designed a machine-learning problem called "estimating the maximum" or "EMX."
EMX - Ads - Website - Viewers - Ads
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?
Problems - Mathematicians - Learning - Problem - Case
In other machine-learning problems, mathematicians can usually say if the learning problem can be solved in a given case based on the data set they have. Can the underlying method Google uses to recognize your face be applied to predicting stock market trends? I don't know, but someone might. The trouble is, math is sort of broken. It's been broken since 1931, when the logician Kurt Gödel published his famous incompleteness theorems. They showed that in any mathematical system, there are certain questions that cannot be answered. They're not really difficult — they're unknowable. Mathematicians learned that their ability to understand the universe was fundamentally limited. Gödel and another mathematician named Paul Cohen found an example: the continuum hypothesis.
The continuum hypothesis goes...
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