Nice quote about mathematics, science, and engineering.

“The first paradigm,
theory, is rooted in mathematics and consists of four
steps followed in the development of a coherent, valid
theory:
(1) characterize objects of study (definition);
(2) hypothesize possible relationships among them
(theorem);
(3) determine whether the relationships are true
(proof);
(4) interpret results.
A mathematician expects to iterate these steps (e.g.,
when errors or inconsistencies are discovered.
The second paradigm, abstraction (modeling), is rooted
in the experimental scientific method and consists of
four stages that are followed in the investigation of a
phenomenon:
(1) form a hypothesis;
(2) construct a model and make a prediction;
(3) design an experiment and collect data;
(4) analyze results.
A scientist expects to iterate these steps (e.g., when a
model’s predictions disagree with experimental evidence).
Even though “modeling” and “experimentation”
might be appropriate substitutes, we have chosen the
word “abstraction” for this paradigm because this usage
is common in the discipline.
The third paradigm, design, is rooted in engineering
and consists of four steps followed in the construction
of a system (or device) to solve a given problem:
(1) state requirements;
(2) state specifications;
(3) design and implement the system;
(4) test the system.
An engineer expects to iterate these steps (e.g., when
tests reveal that the latest version of the system does
not satisfactorily meet the requirements).”