Numerical analysis is very much an experimental science.

I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.
george booleWhen I came back from Munich, it was September, and I was Professor of Mathematics at the Eindhoven University of Technology. Later I learned that I had been the Department's third choice, after two numerical analysts had turned the invitation down; the decision to invite me had not been an easy one, on the one hand because I had not really studied mathematics, and on the other hand because of my sandals, my beard and my "arrogance" (whatever that may be).
edsger w. dijkstraThe moment a mere numerical superiority by either states or voters in this country proceeds to ignore the needs and desires of the minority, and for their own selfish purpose or advancement, hamper or oppress that minority, or debar them in any way from equal privileges and equal rights—that moment will mark the failure of our constitutional system.
Our discombobulated lives need to sink some anchors in numerical stability. (I still have not recovered from the rise of a pound of hamburger at the supermarket to more than a buck.)
stephen jay gouldThe clerical work is par for the course. "Keep on file in numerical order" means throw in wastebasket. You'll soon learn the language. "Let it be a challenge to you" means you're stuck with it; "interpersonal relationships" is a fight between kids; "ancillary civic agencies for supportive discipline" means call the cops; "Language Arts Dept." is the English office; "literature based on child's reading level and experiential background" means that's all they've got in the Book Room; "nonacademicminded" is a delinquent; and "It has come to my attention" means you're in trouble.
bel kaufmanThe equations at which we arrive must be such that a person of any nation, by substituting the numerical values of the quantities as measured by his own national units, would obtain a true result.
james clerk maxwellAlthough I firmly believe that there is no such thing as a stupid question, there can indeed be stupid answers. 42 is an example. Not only is this a poor ripoff of Doug Adams' Hitchhiker's Guide, but it isn't even a prime number. Everyone surely knows that numerical answers to profound questions are always prime. (The correct answer is 37.)
donald normanYeah. And as Linus once said: most numerical problems today in pure CPU cycles are actually 3D games. … It's not "incorrect" to say that you want the result faster, even if that result doesn't match your theoretical models.
linus torvaldsA conceptual model is a mental image of a system, its components, its interactions. It lays the foundation for more elaborate models, such as physical or numerical models. A conceptual model provides a framework in which to think about the
The peculiar system of alphabetic numerals evolved by him with 33 consonants of the Sanskrit alphabet (Nagari script) denoted various numbers in conjunction with vowels which themselves did not represent any numerical value. For example khyughr (=khu+yu+ghr) is denoted by 2x100 +30x100^2+4x10^3 =4300,000 which is the number of revolutions of the Sun in a yuga (epoch)
Various relations being established in geometry between lines constituted under given conditions, as parts of geometrical figures, if we choose to adopt the idea of expressing these lines by numerical measures , we are then brought to the distinction of such lines being in some cases commensurable in their numerical values, in others not so. Their geometrical relations however are absolutely general, and do not refer to any such distinction.
Various relations being established in geometry between lines constituted under given conditions, as parts of geometrical figures, if we choose to adopt the idea of expressing these lines by numerical measures , we are then brought to the distinction of such lines being in some cases commensurable in their numerical values, in others not so. Their geometrical relations however are absolutely general, and do not refer to any such distinction.
The reason is not to glorify "bit chasing"; a more fundamental issue is at stake here: numerical subroutines should deliver results that satisfy simple, useful mathematical laws whenever possible . [...] Without any underlying symmetry properties, the job of proving interesting results becomes extremely unpleasant. The enjoyment of one's tools is an essential ingredient of successful work .
donald knuthIntermediate between mathematics , statistics , and economics , we find a new discipline which, for lack of a better name, may be called econometrics. Econometrics has as its aim to subject abstract laws of theoretical political economy or "pure" economics to experimental and numerical verification, and thus to turn pure economics, as far as possible, into a science in the strict sense of the word.