Why Proofs?
We spend a lot of time in Honors Geometry doing proofs. But why are proofs important in mathematics?
Students may complain that if we already know it's true, why do we need to prove it? But making sure that something is always true is only one reason for doing a proof. By the time a mathematician proves anything important in mathematics, everyone is usually quite confident that it's true.
The real reason for doing proofs in mathematics is not to be sure that a theorem is really true. We do a proof to understand why that theorem is true.
As we do proofs in geometry, we will sometimes run into unexpected connections. The interior angles of a triangle always add to 180 degrees because of the parallel line postulate. There are many proofs of the Pythagorean Theorem, and that places it at a busy intersection of important ideas in mathematics.
This article expands on this idea in reflecting on the recent proof of the P-NP problem in computer science. Even if you have no idea what the P-NP problem is, the article may prove interesting.
Students may complain that if we already know it's true, why do we need to prove it? But making sure that something is always true is only one reason for doing a proof. By the time a mathematician proves anything important in mathematics, everyone is usually quite confident that it's true.
The real reason for doing proofs in mathematics is not to be sure that a theorem is really true. We do a proof to understand why that theorem is true.
As we do proofs in geometry, we will sometimes run into unexpected connections. The interior angles of a triangle always add to 180 degrees because of the parallel line postulate. There are many proofs of the Pythagorean Theorem, and that places it at a busy intersection of important ideas in mathematics.
This article expands on this idea in reflecting on the recent proof of the P-NP problem in computer science. Even if you have no idea what the P-NP problem is, the article may prove interesting.
