All conventional aircraft have tailplanes that produce downwards lift in normal flight.
Deflection of the elevators will change this dynamic for a short time, while the input is maintained.
If the tailplane produced upwards lift in normal, straight and level flight, any deviation would cause loss of control of the aircraft. A nose down pitch would be made worse by the lift of a tailplane producing upward lift. It would cause the aircraft to pitch even further forward. As this is not the case, then the assumption that the tail produces positve lift is false.
Get a wind tunnel and an Airfix model of a Jet Provost and see for yourself.
Anyone who thinks differently is reading the wrong book.
The design of aircraft and tailplanes/foreplanes is over 100 years old and hasn't changed since then.
Once again, FBW fighter may well be very different in that they are designed to be inherently unstable, but for conventional airliners, this is not the case.
Maths do not enter into it. Physics does.
It's a good thing pilots don't need to have a clue what makes their aircraft fly. If they did, pilots wouldn't last very long...
I think the practical reason why tailplanes usually produce negative lift, is the need for sufficient decalage in
all parts of the envelope. To achieve sufficient decalage for the most rearward CofG, you end up having negative lift for a more forward CofG.
If possible, you'd probably prefer zero lift from the tailplane, when not maneuvering. Positive lift would mean you are generating induced drag, and the wing probably has a better lift to drag ratio than the tailplane. I.e., you want the lift to be generated by the wing, not by the tailplane.