Levels of Infinity Quotes

“Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.”
― Hermann Weyl, Levels of Infinity: Selected Writings on Mathematics and Philosophy

“With mathematics we stand precisely at that intersection of bondage and freedom that is the essence of the human itself.”
― Hermann Weyl, Levels of Infinity: Selected Writings on Mathematics and Philosophy

“The question of the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization.”
― Hermann Weyl, Levels of Infinity: Selected Writings on Mathematics and Philosophy

“While Brouwer has made clear to us to what extent the intuitively certain falls short of the mathematically provable, Gödel shows conversely to what extent the intuitively certain goes beyond what (in an arbitrary but fixed formalism) is capable of mathematical proof.”
― Hermann Weyl, Levels of Infinity: Selected Writings on Mathematics and Philosophy

“Mathematics is the science of the infinite. The great achievement of the Greeks was to have made the tension between the finite and the infinite fruitful for the knowledge of reality. The feeling of the calm and unquestioning acknowledgement of the infinite belongs to the Orient, but for the East it remained a mere abstract awareness that left the concrete manifold of existence lying indifferently to one side, unshaped and impervious. Coming out of the Orient, the religious feeling of the infinite, the apeiron, took possession of the Greek soul in the Dionysian-Orphic epoch that preceded the Persian Wars. Here the Persian Wars also mark the release of the Occident from the Orient. That tension and its overcoming became for the Greeks the driving motive of knowledge. But every synthesis, as soon as it was achieved, permitted the old antithesis to break out anew in deepened form. Thus, it determined the history of theoretical knowledge into our time. Indeed, today we are compelled everywhere in the foundations of mathematics to return directly to the Greeks.”
― Hermann Weyl, Levels of Infinity: Selected Writings on Mathematics and Philosophy

“Mathematics is the science of the infinite. The great achievement of the Greeks was to have made the tension between the finite and the infinite fruitful for the knowledge of reality. The feeling of the calm and unquestioning acknowledgement of the infinite belongs to the Orient, but for the East it remained a mere abstract awareness that left the concrete manifold of existence lying indifferently to one side, unshaped and impervious. Coming out of the Orient, the religious feeling of the infinite, the apeiron, took possession of the Greek soul in the DionysianOrphic epoch that preceded the Persian Wars. Here the Persian Wars also mark the release of the Occident from the Orient. That tension and its overcoming became for the Greeks the driving motive of knowledge. But every synthesis, as soon as it was achieved, permitted the old antithesis to break out anew in deepened form. Thus, it determined the history of theoretical knowledge into our time. Indeed, today we are compelled everywhere in the foundations of mathematics to return directly to the Greeks.”
― Hermann Weyl, Levels of Infinity: Selected Writings on Mathematics and Philosophy