Since this is taking much longer than I anticipated (I really hope it's not because I'm giving the wrong answers) as a sort of first hint here's a roundup of what you do know.
Begins with P
Given value of science
Noun
It was invented
Audience gave loud applause to Theory
It exists
It works in both theory and practice
Studied in a mainstream environment
Also, it seems the audience have changed their mind and decided to give some rather late *loud applause* for 'Process'.

Can we change the audience?

Sorry if it's been mentioned. I'm ever so wrung out.

[Rosie] Incompetence rising? NO *audience laugh... then quickly fall silent*
[INJ] Businesslike? YES (but in the same way as Theory and Practice)
[Software] Filling the time available? NO
[Projoy] Intarwebs? NO
[Dujon] 3.14? NO-*is deafened by audience applause*

[INJ] Sliced diagram? NO
[Projoy] Numerical? YES *more applause from the audience*
[Software] What's the chance? NO

INJ's got it.

Please, miss, can I have another go?

No, not a theory. How about Fermat's Conjecture?

[INJ] Itself and one? NO
[Rosie1] Triangular numbers? NO
[Rosie2] Quantum mechanics? NO
[Projoy1] Square of the Hypotenuse? N- *audience explodes into applause* NO
[Projoy2] Pythagoras no greater than two? N- *audience applauds even louder, if that's even possible* NO

If this is right, the winner should really be Dujon.

[Dujon, Rosie] Shiny yellow maths? NO *audience shout "Colder!"*