What Is Scientific Research?

                What Is Scientific Research?
 

Written by A. Yavuz Oruc in Handbook of Scientific Proposal Writing. New York: CRC Press. 2012. pp18-181.

The term scientific research is used broadly to refer to an investigation of open problems in a scientific field. The synergy between the two words that constitute the term codifies its meaning. We will explore these two
words and the synergy between them to give as complete a description of the term scientific research as possible. We begin with the second word first.

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The Merriam-Webster online dictionary* defines research as “careful or diligent search,” “studious inquiry; especially investigation or experimentation aimed at the discovery or interpretation of facts, revision of
accepted theories in the light of new facts or practical application of such new or revised theories or laws,” or “collecting of information about a particular subject.”

Others define it more succinctly as “human activity based on intellectual application in the investigation of matter.” We will adopt the following more generic definition to focus on the essence of research:

Research is a process of understanding a problem, and discovering facts to help solve it. Researching a problem can thus be viewed as solving or completing a puzzle. However, in this puzzle analogy, obtaining the missing pieces may involve steps that may go far beyond searching for them. The pieces may exist in some other form and may have to be modified before they can be used, or they may not even exist and may have to be created. Exactly how the pieces are obtained and the puzzle is solved depends on the model of
research process used.

One such model is that of a mathematical investigation in which Mathematical results are customarily established using five basic entities:
(1) axioms (postulates), 
Axioms are generally the ground rules of a mathematical investigation. All statements must agree with the axioms of the mathematical domain within which the research activity is carried out.
 
(2) definitions and propositions, 
Definitions and propositions form the front end of such an activity. They are introduced to formalize the problems to be solved.

(3) lemmas
Lemmas serve as auxiliary puzzle pieces

(4) theorems
Theorems correspond to blocks of puzzles, and corollaries extend the solutions of puzzles to the solutions of other similar puzzles. In this setting, stating and proving lemmas should constitute a research activity if they have not been stated or proved before. They are like creating new pieces to solve a puzzle. Stating and proving theorems is similar to putting smaller pieces together to make bigger pieces of a puzzle. This would also be a research activity if the theorems in question have not been stated and proved elsewhere.

(5) corollaries.
On the other hand, corollaries are more like consequences of theorems and lemmas. Stating and proving corollaries, in and of themselves, should therefore be viewed more as a process of extending known results. However, in some cases, coming up with corollaries and proving them may involve considerable creativity and effort and thus constitute a legitimate research activity.