Checking available definitions of mathematical proof and then looking at my mathematical argument, I found I still didn't have enough to be sure! And long ago got tired of thinking I had something which was correct, only to discover later I was wrong! And under that pressure found myself switching to what I decided to call a functional definition. Through the years have refined it. And now have something I think is quite formal:
mathematical proof (noun): a mathematical argument that begins with a truth and proceeds by logical steps to a conclusion which then must be true.
So yeah, I made that up. The original form was good enough for me to look over my mathematical argument and determine, yes, it was a proof! Which was a huge relief. I call that a functional definition as unlike typical what I call descriptive definitions, you can use it to see for certain with certain kinds of abstractions like mathematical proof, if you have the thing. Rather than talk a lot on that subject will give one of my latest:
entertainment (noun): any socially accepted activity chosen in order to alter mood in a desired way which is unlikely to bring harm in any way.
Where I was considering theory on social media, and concluded that I could explain certain social media metrics relating to what I see now as audience levels, by considering entertainment value others must see in public presentations. But what was entertainment? So I sat down and came up with a functional definition, which notice covers everything from a roller coaster ride, to a sad movie or play, to dinner with friends. While it also excludes dangerous things like taking illegal drugs.
Functional definitions are remarkable to me in contrast to descriptive definitions and my most powerful one is not needed to be given for this discussion, but will note I have it as an intriguing point on which to end.
Faced with various issues I concluded I needed a functional definition for science.
And it is by far my most prized.