Hacker News new | past | comments | ask | show | jobs | submit login

The issue is that the computer-generated proofs operate at a very low level, step by step, like writing a program in assembly language without the use of coherent structure.

The human proof style instead chunks the parts of a solution into human-meaningful "lemmas" (helper theorems) and builds bodies of theory into well-defined and widely used abstractions like complex numbers or derivatives, with a corpus of accepted results.

Some human proofs of theorems also have a bit of this flavor of inscrutable lists of highly technical steps, especially the first time something is proven. Over time, the most important theorems are often recast in terms of a more suitable grounding theory, in which they can be proven with a few obvious statements or sometimes a clever trick or two.




Consider applying for YC's Spring batch! Applications are open till Feb 11.

Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: