"The classification theorems of mathematics are among the ultimate triumphs of human intellectual achievement. A classification theorem provides a complete list of all objects in a given category as well as a scheme for matching an unknown object from the category with exactly one of the canonical examples."
"Equations are the mathematician's way of working out the value of some unknown quantity from circumstantial evidence. ‘Here are some known facts about an unknown number: deduce the number.’ An equation, then, is a kind of puzzle, centered upon a number. We are not told what this number is, but we are told something useful about it. Our task is to solve the puzzle by finding the unknown number." (Ian Stewart, "Why Beauty Is Truth", 2007)
"[…] statistics is the key discipline for predicting the future or for making inferences about the unknown, or for producing convenient summaries of data." (David J Hand, "Statistics: A Very Short Introduction", 2008)
"What could mathematics and poetry share, except that the mention of either one is sometimes enough to bring an uneasy chill into a conversation? [...] Both fields use analogies - comparisons of all sorts - to explain things, to express unknown or unknowable concepts, and to teach." (Marcia Birken & Anne C Coon, "Discovering Patterns in Mathematics and Poetry", 2008)
"The presentation of mathematics where you start with definitions, for example, is simply wrong. Definitions aren't the places where things start. Mathematics starts with ideas and general concepts, and then definitions are isolated from concepts. Definitions occur somewhere in the middle of a progression or the development of a mathematical concept. The same thing applies to theorems and other icons of mathematical progress. They occur in the middle of a progression of how we explore the unknown." (Michael P Starbird, [interview] 2009)
"To the average layperson, mathematics is a mass of abstruse formulae and bizarre technical terms (e.g., perverse sheaves, the monster group, barreled spaces, inaccessible cardinals), usually discussed by academics in white coats in front of a blackboard covered with peculiar symbols. The distinction between mathematics and physics is blurred and that between pure and applied mathematics is unknown. But to the professional, these are three different worlds, different sets of colleagues, with different goals, different standards, and different customs."
"Mathematics does not merely describe the problem in an abstract way, it allows us to find a previously unknown 'solution' from the abstract description. It is surprising that the unknown can be transformed into the well known when we succeed in describing the problem mathematically." (Waro Iwane, "Mathematics in Our Company: What Does It Describe?", [in "What Mathematics Can Do for You"] 2013)
"Symbols transcend the medium of communication. They are ubiquitous in our language, and play a sizable role (though perhaps not a central one) in mathematical imagery linking the conscious and subconscious, the familiar and unknown, to give us cultural/emotional predispositions to meaning, all to enhance the creative process."(Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)
"Unlike symbols in poetry, mathematical symbols begin as deliberate designs created by mathematicians. That does not stop symbols from performing the same function that a poem would: to make connections between experience and the unknown and to transfer metaphorical thoughts capable of conveying meaning. As in poetry, there are archetypes in mathematics. If there are such things as self-evident truths, then there probably are things we know about the world that come with the human package at birth." (Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)
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