"Nature's great book is written in mathematical symbols." (Galileo Galilei, “The Assayer”, 1623)
"Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth." (Galileo Galilei, “The Assayer”, 1623)
"The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics." (Galileo Galilei, “The Assayer”, 1623)
"[…] nature does not multiply things unnecessarily; that she makes use of the easiest and simplest means for producing her effects; that she does nothing in vain, and the like" (Galileo Galilei, "Dialogue Concerning the Two Chief World Systems", 1632)
"Well, since paradoxes are at hand, let us see how it might be demonstrated that in a finite continuous extension it is not impossible for infinitely many voids to be found." (Galileo Galilei, "Dialogue Concerning the Two Chief World Systems", 1632)
"[Paradoxes of the infinite arise] only when we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this […] is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.” (Galileo Galilei, "Two New Sciences", 1638)
“Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined. In spite of this men cannot refrain from discussing them.” (Galileo Galilei, "Two New Sciences", 1638)
“The length of strings is not the direct and immediate reason behind the forms [ratios] of musical intervals, nor is their tension, nor their thickness, but rather, the ratios of the numbers of vibrations and impacts of air waves that go to strike our eardrum.” (Galileo Galilei, "Two New Sciences", 1638)
”[…] it is astonishing and incredible to us, but not to Nature; for she performs with utmost ease and simplicity things which are even infinitely puzzling to our minds, and what is very difficult for us to comprehend is quite easy for her to perform.” (Galileo Galilei)
“All truths are easy to understand once they are discovered; the point is to discover them.” (Galileo Galilei)
“By denying scientific principles, one may maintain any paradox.” (Galileo Galilei)
“Mathematics is the key and door to the sciences.” (Galileo Galilei)
“The laws of Nature are written in the language of mathematics […]” (Galileo Galilei)
“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)
"We cannot teach people anything; we can only help them discover it within themselves." (Galileo Galilei)
"[Paradoxes of the infinite arise] only when we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this […] is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.” (Galileo Galilei, "Two New Sciences", 1638)
“Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined. In spite of this men cannot refrain from discussing them.” (Galileo Galilei, "Two New Sciences", 1638)
“The length of strings is not the direct and immediate reason behind the forms [ratios] of musical intervals, nor is their tension, nor their thickness, but rather, the ratios of the numbers of vibrations and impacts of air waves that go to strike our eardrum.” (Galileo Galilei, "Two New Sciences", 1638)
”[…] it is astonishing and incredible to us, but not to Nature; for she performs with utmost ease and simplicity things which are even infinitely puzzling to our minds, and what is very difficult for us to comprehend is quite easy for her to perform.” (Galileo Galilei)
“All truths are easy to understand once they are discovered; the point is to discover them.” (Galileo Galilei)
“By denying scientific principles, one may maintain any paradox.” (Galileo Galilei)
“Mathematics is the key and door to the sciences.” (Galileo Galilei)
“The laws of Nature are written in the language of mathematics […]” (Galileo Galilei)
“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)
"We cannot teach people anything; we can only help them discover it within themselves." (Galileo Galilei)
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