It is not easy to define a new result in, say, mathematics. I cannot do this.
I think that a new result must contain new ideas or techniques, ...?
Can we speak of a new result in the following situations:
(a) Author X extends Theorem A, case p=1, to case p= 2, using the same idea
and a slight and easy modification of the proof of Theorem A. (If Theorem A was proved
by author Y and author X does not say anything of Y's proof, this is a plagiarism?)
(b) Author X extends Theorem B about functions of a complex variables, to the case
of several variables using the same idea and an easy modification of the techniques
used in the proof of B.
Etc.
Very good question!
It is very difficult to know whether a result (theorem and proof) is new or not. It is often the case that a theorem that pops up, which appears to be a new result that is, in fact, a variation of or an extension of what was found by someone else. Sometimes this will happen because of a lack of access to publications that are not accessible to an author.
In that case, a "new" result turns out to be a novel expression of a result found earlier or simultaneously by someone else.
A famous case of simultaneous discovery occurred during the 17th century, when Newton and Leibniz independently (one believes) discovered the calculus (differentials and integrals). This is an example where Newton had the edge in terms of theory and Leibniz had the edge in terms of notation.
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