David Perkins - Collected Quotes

"A function acts like a set of rules for turning some numbers into others, a machine with parts that we can manipulate to accomplish anything we can imagine." (David Perkins, "Calculus and Its Origins", 2012)

"Despite its deductive nature, mathematics yields its truths much like any other intellectual pursuit: someone asks a question or poses a challenge, others react or propose solutions, and gradually the edges of the debate are framed and a vocabulary is built." (David Perkins, "Calculus and Its Origins", 2012)

"If we wish the word ‘continuous’ to prohibit jumps in a function, its definition must somehow control the vertical change of the function at a sort of microscopic level. That is, at any point on a ‘continuous’ function, the nearby points ought to be as ‘close’ as possible." (David Perkins, "Calculus and Its Origins", 2012)

"Mathematicians approach problems the way rock climbers do cliffs: the more difficult the pitch, the more exhilarating the ascent. After a climb has been solved, others look for new routes, or try equipment that no one else has used, simply for the joy of pioneering." (David Perkins, "Calculus and Its Origins", 2012)

"One trick to seeing beauty in mathematics is to nurture this sense of 'odd as it may seem' while at the same time understanding the subject well enough to know that oddities arise despite our attempts to set the subject on a simple, straightforward footing." (David Perkins, "Calculus and Its Origins", 2012)

"Ever since the discovery of irrational numbers fractured the Greek belief that all numbers were proportions, mathematicians have sorted numbers into categories and hunted for numbers that defied existing categories." (David Perkins, "φ, π, e & i", 2017)

"Imagine that each proof in this book is like a painting that one sees upon entering a gallery full of artwork, in which each work presents an artist’s unique vision of the same theme." (David Perkins, "φ, π, e & i", 2017) 

"Mathematicians linger on cherished topics, illuminating them from a variety of viewpoints, much like artists and poets try over and over to capture truths about the human condition. Re-proving something important in a new way brings joy to both the discoverer and the audience." (David Perkins, "φ, π, e & i", 2017)

"Much of the final resistance to complex numbers faded as it became clear that their behavior posed no threat to the rules and operations of algebra. On the contrary, quite often the complex realm opened paths that made already existing results easier to prove." (David Perkins, "φ, π, e & i", 2017)