The Infinite and Its Difficulties I

"The infinite is imperfect, unfinished and therefore, unthinkable; it is formless and confused." (Aristotle) 

“These are among the marvels that surpass the bounds of our imagination, and that must warn us how gravely one errs in trying to reason about infinites by using the same attributes that we apply to finites.” (Galileo Galilei)

"The eternal silence of these infinite spaces terrifies me." (Blaise Pascal)

“[…] the notion of the infinite […] forces itself upon our mind and yet is incomprehensible. When this notion takes possession of the understanding we have only to bow before it.” (Louis Pasteur)

“The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.” (David Hilbert)

“The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have; but also the infinite, more than any other notion, is in need of clarification.” (David Hilbert)

"Our minds are finite, and yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of that infinitude." (Alfred N Whitehead)