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Just knowing something is true without knowing why is a lot less helpful in figuring out what else is true.
by kd0amg 6y ago
Just knowing something is true without knowing why is a lot less helpful in figuring out what else is true.
- wisnesky 6y agoYou are right that computer generated proofs are often tough to understand, and that understanding is often the intended goal of writing a proof. But proofs can be useful for reasons besides human understanding, especially so in engineering. For example, when a browser establishes a secure session with an encryption protocol, the reason it is secure has to do with the difficulty of finding a proof that eg certain numbers factor, but no human cares about this proof. As another example, a compiler can use a proof that a program is type correct to optimize it, but humans would not find such proofs interesting at all.
- sukilot 6y agoThat's great, but not relevant to mathematicians doing their jobs.
- whatshisface 6y agoKnowing which conjectures were true would probably help mathematicians work more efficiently. At the very least nobody would spend time searching for counterexamples to true conjectures.
- zxcmx 6y agoExistence proofs remain popular however, as do establishing upper or lower bounds.