The Infinite and Mathematics

“The progress of mathematics can be viewed as progress from the infinite to the finite.” (Gian-Carlo Rota)

“The whole universe is one mathematical and harmonic expression, made up of finite representations of the infinite.” (Fritz L Kunz)

"Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite." (Cassius J. Keyser, “The Human Worth of Rigorous Thinking, 1925)

"Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is, finite means.” (Hermann Weyl, “Mind and Nature”, 1934)

“Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory.” (Hermann Weyl, “Axiomatic versus constructive procedures in mathematics”, The Mathematical Intelligencer, 1985)

"Mathematics as we know it and as it has come to shape modern science could never have come into being without some disregard for the dangers of the infinite." (David Bressoud, “A radical approach to real analysis”, MAA, 2007) 

“Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.” (Marston Morse)

"Mathematics is the only infinite human activity. It is conceivable that humanity could eventually learn everything in physics or biology. But humanity certainly won't ever be able to find out everything in mathematics, because the subject is infinite. Numbers themselves are infinite."  (Paul Erdos)

“The infinite more than anything else is what characterizes mathematics and defines its essence. […] To grapple with infinity is one of the bravest and extraordinary endeavors that human beings have ever undertaken.” (William Byers, “How Mathematicians Think”, 2007)

"Mathematics, in one view, is the science of infinity." (Phillip J Davis & Reuben Hersh, “The Mathematical Experience”, 1999)