Constructivist Ideas
From the other direction there has been considerable clarification of what constructive mathematics is; without the emergence of a 'master theory'. For example according to Errett Bishop's definitions, the continuity of a function (such as sin x) should be proved as a constructive bound on the modulus of continuity, meaning that the existential content of the assertion of continuity is a promise that can always be kept. One could get another explanation from type theory, in which a proof of an existential statement can come only from a term (which we can see as the computational content).
Read more about this topic: Existence Theorem
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“To the men of this world, to the animal strength and spirits, to the men of practical power, whilst immersed in it, the man of ideas appears out of his reason. They alone gave reason.”
—Ralph Waldo Emerson (1803–1882)