What is the role of mathematics in progress of science and technology?

Mathematics has played and continues to play a critical
role in expanding fields of science and technology because of the basic requirement that
research needs to be able to quantify and accurately evaluate the results of
changes/advances in a field of endeavor.

As research is
done to develop new treatments for medical conditions, knowing the amount of medication
administered is critical when evaluating the effect of the treatment, just as knowing
exactly how much of what chemicals went into creating the medication. As amounts are
adjusted and outcomes assessed, the mathematical data created may be used to extrapolate
further possible treatment procedures or doses.

As new
methods of building or manufacturing goods are developed, mathematical formulas and
models may be applied to test the structural and functional soundness of the design
before it is mass produced, thus saving millions of dollars and untold time.
Computer-aided design is becoming increasingly important in this type of use - and it is
all based on application of mathematics.