(mathematics) A theorem stating that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.

Goddard-Thorn theorem

(calculus) The theorem that any real-valued differentiable function that attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. In mathematical terms, if f:ℝ→ℝ is differentiable on (a,b) and f(a)=f(b) then ∃c∈(a,b):f'(c)=0.

(mathematics) The result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform.

(physics) Any theorem stating that a particular situation is not physically possible.

(mathematics) A theorem used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed.

A theorem stating that the interaction picture does not exist in an interacting, relativistic quantum field theory.

(physics) A no-go theorem stating that, during measurement of an entangled quantum state, it is not possible for one observer, making a measurement of a subsystem of the total state, to communicate information to another observer.

(mathematics) A theorem about discrete dynamical systems. One of its implications is that if a discrete dynamical system on the real line has a periodic point of period 3, then it must have periodic points of every other period.

A mathematical theorem, important for quantum logic, proving that the Born rule for the probability of obtaining specific results for a given measurement follows naturally from the structure formed by the lattice of events in a real or complex Hilbert space.