The Brilliant Mathematician Reads a Proof.

Please place yourself in the role of the brilliant mathematician. Now I shall teach you how to act when a rogue and unknown proof arrives at your door. (Or as my Modern Algebra professor says, “when someone hands you a problem in a dark alley…”)

Today I will hand you a proof that √2 is irrational. Which you may use as an example as you, the brilliant mathematician follow the steps below.

Step One:

Be wary of the proof. There are multiple ways to get a proof done, but thousands of ways to screw it up. Are you wary yet?

Step Two:

Begin reading the proof. First question the assumptions or underlying assumptions. Are those reasonable assumptions for this conjecture? (note to the mathematical audience: you can safely assume the basic assumptions of Modern Math hold; Euclidean Geometry, Algebra and the like are valid. Because you don’t have all year, you must finish reading this proof today)

Step Three:

You are ready to begin reading the proof. Consider the symbols they will use. For example, in my last proof I let: 0< q < n < m < π/2 It is a good use of your time to wonder why I chose q to be a companion of n and m. Maybe it’s important! (In my case it wasn’t- I didn’t like L yesterday…)

Step Four:

If the proof convinces you of something based on some assumptions and if the proof didn’t quite work out, you, the brilliant mathematician, may require yourself to re-read the pieces that have already been solidly checked. This is not a waste of time. I swear. Mathematicians do it all the time.

Step Five:

If you are convinced, then you may claim, “I find no fault in this proof” And I point out that “There are no errors” is completely different that what you have just claimed. Alternatively, you make exclaim a “Wow” or “Golly!” after reading the proof. But you should never immediately claim there are no errors.

Thus you have completed your first proof and you are beginning to understand how a mathematician is wary of the truth.