In $2019$, mathematicians finally solved a hard math puzzle that had stumped them for decades. It’s called a Diophantine Equation, and it’s sometimes known as the “summing of three cubes”:
Find $x, y$, and $z$ such that $x³+y³+z³=k$, for each k from one to $100$.
On the surface, it seems easy. Can you think of the integers for $x, y$, and $z$ so that $x³+y³+z³=8$? Sure. One answer is $x = 1, y = -1$, and $z = 2$. But what about the integers for $x, y$, and $z$ so that $x³+y³+z³=42$?
That turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (For the record: x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Obviously.)
That’s the beauty of math: There’s always an answer for everything, even if takes years, decades, or even centuries to find it. So here are nine more brutally difficult math problems that once seemed impossible, until mathematicians found a breakthrough.
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