Strawberries go well with chocolate. Chocolate goes great with peanut butter. Strawberries and peanut butter make a good PB&J sandwich. So the three must taste pretty good together, right? Sure they do; Little Debbie made a snack cake with all three once. There are plenty of food triads like this, that we've used to concoct new recipes. But mathematicians have been seeking a different outcome, called the incompatible food triad.
That conundrum goes like this: Can you think of three foods where any two of those foods taste good together, but all three combined taste disgusting?
Like so many long-lasting mathematical mysteries, this one is more difficult than it sounds. Thus far, it has stymied at least four generations of academics, who have not been able to come up with a group of foods that definitively fit the bill, nor a way to prove that it can’t be done. George Hart, an engineering professor and mathematical sculptor, has been chewing on the Incompatible Food Triad for 36 years. “Is there a theorem that says if a and b are good, and b and c are good, and a and c are good, then a and b and c must be good? That’s something that, on the face of it, seems reasonable,” he says. “But then when you look for an argument, a truth, you don’t find one.”
It's not that people haven't tried. Read the history and progress of the search for the incompatible food triad at Atlas Obscura.