William Thurston's quote? 
Mathematics is not about numbers, equations, computations, or
  algorithms: it is about understanding.

Is this from Thurston? If yes, where and when it has been said. I've checked "ON PROOF AND PROGRESS IN MATHEMATICS" and it is not there. 
 A: I'll post this as an answer since it's too long for a comment. Even though it does not directly answer the question, I would like to mention that a related quote appears in a very interesting dialogue between Rota and Sharp in 1985 (https://fas.org/sgp/othergov/doe/lanl/pubs/00326965.pdf):

ROTA: Mathematics is the study of analogies between analogies. All
  science is. Scientists always want to show that things that don’t look
  alike are really the same. That’s one of their innermost Freudian
  motivations. In fact, that’s what we mean by understanding.
SHARP: You often hear that the purpose of a scientific theory is to
  predict, That’s not correct. The purpose is understanding. Prediction
  is one way to test whether our understanding is correct. Simplicity,
  scope, and beauty are as important as prediction in judging whether a
  theory leads to understanding.

A: This quote is from the book "Mathematicians: An Outer View of the Inner World" (Mariana Cook and Robert Clifford Gunning, Princeton University Press, 2009).
https://www.jstor.org/stable/j.ctt2jc8h2
"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding. I’ve loved mathematics all my life, although I often doubted that mathematics would turn out to be my life’s..."
