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Was the Bunkbed Conjecture Disproven?
How Three Students Push the Boundary of Proof
Mathematicians are constantly redefining what it means to prove something. Back in Euclid’s day, proofs were often accepted with simple visual demonstrations. Yet, many errors have been found in his classic textbook Elements when he relied too heavily on intuition rather than sound logic.
It wasn’t until the 18th century that math began to move beyond Euclid and think hard about what exactly a proof could be. Several important works were created about the logical steps that were considered acceptable for a proof to be valid. This is the concept of proof that we rely on today, although it has faced some tests. One large controversy concerns the proof of the four-color theorem. This simple theorem states that every map divided into sections can be colored in such that no section is touching a section with the same color as itself.
Proving this theorem was a significant challenge. There were several supposed proofs published that were later shown to be false. Eventually, mathematicians boiled it down into 1,834 smaller cases. If they could check that each of these component maps could be…