I love blues. The music that is. I can listen to long programs playing this genre. Friends of mine love different kinds of art: Some like to visit the theater, others do sculpting. There are even those who go to the opera, god forbid.

There is one thing in common with all of the above. There is no problem in consuming more and more “items” of each. You liked a song? Nothing wrong with hearing another one, or hearing the same one again. Enjoyed play A in the theater? It’s fully legitimate to enjoy play B about the very same topic.

I also love math. Mathematical puzzles, funny historical stories about math, and of course famous proofs of known problems.

Unlike the worlds of music, sculpting and theater – math is an exact science. In other words: Things are either “right” or “wrong”. Even when dealing with statistic “estimations”, those are given with some well-defined significance or probability. This idea is especially emphasized when dealing with proving something. There is no “kind of a proof”… either you prove, or you don’t. After you did prove something, assuming you did it right, it’s now proved forever. For generations to come. No one can disprove it. The greatest scientists ever will not be able to disprove Pythagoras’ theorem, because it’s proven. In fact, since it is proven, they will have no incentive to try and refute it, as they know it’s a hopeless attempt. They will also have no incentive to try and re-prove it, as they already know it’s true.

Unlike music, sculpting and theater – consuming more and more mathematical “proofs” for the same claim is evidently problematic. A hundred mathematical proofs of the same theorem are exactly as good as a single proof, and equally make it “true”. You may compile a shorter proof, or a more beautiful one, but it will have nothing to do with the correctness of the proven thing.

“Moses received the Torah from Sinai and passed it on to Joshua,
and Joshua to the elders,
and the elders to the prophets,
and the prophets passed it one to the men of the Great Assembly.”

This is how many Jewish religious preachers open their “proof” for the Torah’s alleged godly origin. Some versions of this proof – titled “The Chain of Tradition” – contain several sub-claims, such as the Jewish tradition being the only one with a supreme being’s revelation in front of a whole nation (not true, but we’ll skip it for now), or the inability to invent certain parts of the story and convince many in their correctness (again, not true). The saga ends in “proving” the godly origin of the text, thus also proving many immediate conclusions, such as the need to follow the commandments etc.

And here we return to the essence of a correct mathematical proof. If you unambiguously proved that the text came from “God”… why do you need all those thousands of additional long-winded debates and indirect alleged proves? What’s with this stupid thing of ruminating animals, fish with scales, letter skips, the moon cycle, and many other gimmicks? You already proved!! Why do you need to prove again Pythagoras’ theorem, in quite bizarre ways?

Or perhaps somewhere deep inside you feel this was not really a convincing proof…?