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What if they are all wrong? (2020)
Conjectures are a staple of mathematics. They are everywhere, permeating every area, subarea and subsubarea. They are diverse enough to avoid a single general adjective. They come in al shapes and …
Some of them are famous, classical, general, important, inspirational, far-reaching, audacious, exiting or popular, while others are speculative, narrow, technical, imprecise, far-fetched, misleading or recreational. Thus, it’s much more noble and virtuous to say “ I dedicated my life to the study of the XYZ Conjecture ” (even if they never publish anything), than “ I am working hard writing so many papers to gain respect of my peers, get a promotion, and provide for my family “. I once had an idea of one (a nice cubic Cayley graph on “only” 3600 vertices), but Bill Cook quickly found a Hamiltonian cycle dashing my hopes (it was kind of him to look into this problem).
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