As a geometry student quondam et futurus, I might as well say that Boost's argument has a bit of a flaw of its own.
Namely: If you skip over the intervening stages of a mathematical proof, you can end up in entirely the wrong place.
Still, even a broken sword can be reforged, as George knew. And Sigurd used his father's formerly broken sword to slay Fafnir the dragon... who used to be a dwarf.
The path of metamorphosis is not always clear to the naked eye. That's where imagination must come in. But of course doing your background research helps tremendously.