Alright, young explorers, fasten your seatbelts as we dive into the world of proofs and the mathematical universe!

Our pal, Thomas Tymoczko, came up with this fancy term 'non-surveyable proof.' Imagine a proof so massive and complicated that humans have a tough time verifying it - a bit like trying to read a giant book, but the pages keep multiplying. Like the 1979 computer-assisted proof of the four-color theorem by Appel and Haken - it's a biggie! Picture you're given only four colors and asked to color a map in such a way that no two adjacent areas have the same color. A computer cracked this riddle in 1979!

Tymoczko suggests a proof must meet three criteria, like a pie split into three slices.

• Convincingness: The proof should be persuasive, like a good salesman selling its conclusion.
• Surveyability: The proof should be manageable for humans to verify, like being able to read and understand a book.
• Formalizability: The proof should only use logical relationships between concepts, like building a LEGO model using only the given instructions.

Some folks criticized these computer whizzes, calling their proofs non-surveyable. Imagine trying to follow a robot's instruction manual, but the instructions are too many to handle. Tymoczko reckoned these computerized proofs were changing the game, replacing the good old logical deduction with trust in computational processes. This is like accepting a delicious cake baked by a robot without knowing the recipe.