(number theory) A theorem stating that, given a fixed base b, the set of numbers that are the sum of a prime and a positive integer power of b has a positive lower asymptotic density.

A theorem stating that, for a thermodynamic system exchanging heat with external reservoirs and undergoing a thermodynamic cycle, ∮(𝛿Q)/(T_surr)≤0,, where 𝛿Q is the infinitesimal amount of heat absorbed by the system from the reservoir, and T_surr is the temperature of the external reservoir (surroundings) at a particular instant in time.

(geometry) A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides.

(calculus) A generalization of the fundamental theorem of calculus to the two-dimensional plane, which states that given two scalar fields P and Q and a simply connected region R, the area integral of derivatives of the fields equals the line integral of the fields, or

The theorem that the prime counting function is of the same order of magnitude as x / ln x, i.e., for the prime counting function π, there are positive constants c and C such that:

(physics) A theorem in mechanics showing the relationship between the kinetic energy of a system to the virial of Clausius.

(mathematics) A formula giving the expansion of a binomial such as (a+b) raised to any positive integer power, i.e. (a+b)ⁿ. It's possible to expand the power into a sum of terms of the form axᵇyᶜ where the coefficient of each term is a positive integer. For example:

(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.

(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.

(physics) A no-go theorem stating that no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.