I have been very lucky to work in so many new ballets, but that is what a dancer's work is.
To put it simply, we first explain what we are talking about, and then explain why what we are saying is true (pace Bertrand Russell).
Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.
The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.
What binds us to space-time is our rest mass, which prevents us from flying at the speed of light, when time stops and space loses meaning. In a world of light there are neither points nor moments of time; beings woven from light would live "nowhere" and "nowhen"; only poetry and mathematics are capable of speaking meaningfully about such things.
A good proof is one that makes us wiser.
A proof only becomes a proof after the social act of "accepting it as a proof".
This is my friend that we use a lot. Say hello to the trampoline.
Seeing God without seeing the Self, one sees only mental image. Only he who has seen Himself has seen God, since he has lost individuality, and now sees nothing but God.
The process of socialization is nowhere near complete at age five or six, when modern children start spending up to half their waking hours taking their cues from other people's children. Because they accompany their parents' daily routine, homeschooled kids spend plenty of time interacting with people of all ages, which I think most people would agree is a far more natural, organic way to socialize.
This above all: be true, be true, be true.