That’s the beauty of math

In $2019$, mathematicians finally solved one of the hardest math problems—one 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. 

Πηγή: popularmechanics