"A model is a good model if it: 1. Is elegant 2. Contains few arbitrary or adjustable elements 3. Agrees with and explains all existing observations4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out." (Stephen Hawking & Leonard Mlodinow,"The Grand Design", 2010)
"A proof is simply a story. The characters are the elements of the problem, and the plot is up to you. The goal, as in any literary fiction, is to write a story that is compelling as a narrative. In the case of mathematics, this means that the plot not only has to make logical sense but also be simple and elegant. No one likes a meandering, complicated quagmire of a proof. We want to follow along rationally to be sure, but we also want to be charmed and swept off our feet aesthetically. A proof should be lovely as well as logical." (Paul Lockhart, "Measurement", 2012)
"Nothing illustrates the extraordinary power of complex function theory better than the ease and elegance with which it yields results which challenged and often baffled the very greatest mathematicians of an earlier age." (Peter D Lax & Lawrence Zalcman, "Complex proofs of real theorems", 2012)
"The ultimate arbiter of truth is experiment, not the comfort one derives from one's a priori beliefs, nor the beauty or elegance one ascribes to one's theoretical models." (Lawrence M Krauss, "A Universe from Nothing: Why There Is Something Rather than Nothing", 2012)
"The correlation coefficient has two fabulously attractive characteristics. First, for math reasons that have been relegated to the appendix, it is a single number ranging from –1 to 1. A correlation of 1, often described as perfect correlation, means that every change in one variable is associated with an equivalent change in the other variable in the same direction. A correlation of –1, or perfect negative correlation, means that every change in one variable is associated with an equivalent change in the other variable in the opposite direction. The closer the correlation is to 1 or –1, the stronger the association. […] The second attractive feature of the correlation coefficient is that it has no units attached to it. […] The correlation coefficient does a seemingly miraculous thing: It collapses a complex mess of data measured in different units (like our scatter plots of height and weight) into a single, elegant descriptive statistic." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)
"This is what it means to do mathematics. To make a discovery (by whatever means, including playing around with physical models like paper, string, and rubber bands), and then to explain it in the simplest and most elegant way possible. This is the art of it, and this is why it is so challenging and fun." (Paul Lockhart, "Measurement", 2012)
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