GSV Without Loss of Generality is a user on mathstodon.xyz. You can follow them or interact with them if you have an account anywhere in the fediverse.

An emotionally satisfying metaphor for learning new maths is taming a wilderness: going from an excess of confusing and disconnected terms, to seeing the thing whole, knowing what to use where.

But, for (formal) students, that's wildly inaccurate, since we're in general treading smooth paths initially hacked out of the wild a century ago or more, trod by thousands before us. Even if we can't see it yet, we know there's well-definedness underneath. Real mathematical wilds are often untameable.

GSV Without Loss of Generality @gleech

"Remember! Most strings are incompressible, most reals uncomputable, most theorems unprovable, most programs undecidable."

― Gwern

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@gleech Statistically ... All of them ?