MATHQUOTES
 

Topic: infinity

Certainly he who can digest a second or third fluxion need not, methinks, be squeamish about any point in divinity.

TOPICS: philosophy, fluxions, infinity, religion

And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities?

TOPICS: infinity, fluxions, philosophy

Even as the finite encloses an infinite series, / And in the unlimited limits appear, / So the soul of immensity dwells in minuta / And in the narrowest limits, no limits inhere. / What joy to discern the minute in infinity! / The vast to perceive in the small, what Divinity!

TOPICS: infinity, series

I  am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author.

TOPICS: infinity, nature, God

SOURCE: Nouveaux Essais de l’Entendement humain

No one will expel us from the paradise that Cantor has created for us.

TOPICS: infinity, Cantor

The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

TOPICS: Cantor, genius, infinity, set theory

Hilbert was referring specifically to Cantor’s set theory, which for the first time allowed a mathematically rigorous definition of infinity.

 

I  love mathematics…principally because it is beautiful, because man has breathed his spirit of play into it, and because it has given him his greatest game—the encompassing of the infinite.

TOPICS: beauty, infinity

The study of infinity is much more than a dry academic game. The intellectual pursuit of the absolute infinity is, as Georg Cantor realized, a form of the soul’s quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment.

TOPICS: infinity, God

Zeno was concerned with three problems… These are the problem of the infinitesimal, the infinite, and continuity…From his to our own day, the finest intellects of each generation in turn attacked these problems, but achieved broadly speaking nothing…Weierstrass, Dedekind, and Cantor,…have completely solved them. Their…solutions are so clear as to leave no longer the slightest doubt or difficulty. This achievement is probably the greatest of which our age can boast.

TOPICS: Cantor, infinity

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