Lefschetz hyperplane theorem
Have you ever played connect-the-dots? You know, where you have a bunch of dots on a page and you draw a line from one to the next until you have a picture? That's sort of what math people do too. But instead of dots, they have something called "algebraic varieties" which are like shapes made out of equations.
One really smart math person named Solomon Lefschetz figured out a way to connect all the dots in certain types of shapes called "projective varieties". But he didn't just connect them with a regular line - he used something called "homology" which is kind of like a fancy way of counting the ways the dots are connected.
And when he did this for a certain type of projective variety called a "hypersurface", he found something really amazing! He found that the number of ways the dots were connected had to be the same as the number of times a straight line touched the shape in a certain way. This is called the "Lefschetz Hyperplane Theorem".
So now when math people study these kinds of shapes, they can use the Lefschetz Theorem to help them count the number of lines that touch the shape in a certain way. Pretty cool, huh?
One really smart math person named Solomon Lefschetz figured out a way to connect all the dots in certain types of shapes called "projective varieties". But he didn't just connect them with a regular line - he used something called "homology" which is kind of like a fancy way of counting the ways the dots are connected.
And when he did this for a certain type of projective variety called a "hypersurface", he found something really amazing! He found that the number of ways the dots were connected had to be the same as the number of times a straight line touched the shape in a certain way. This is called the "Lefschetz Hyperplane Theorem".
So now when math people study these kinds of shapes, they can use the Lefschetz Theorem to help them count the number of lines that touch the shape in a certain way. Pretty cool, huh?