The “anti-calculus proposition” is a little result by Paul Erdős that contrasts functions of a real variable and functions of a complex variable.
A standard calculus result says the derivative of a function is zero where the function takes on its maximum. The anti-calculus proposition says that for analytic functions, the derivative cannot be zero at the maximum.
To be more precise, a differentiable real-valued function on a closed interval takes on its maximum where the derivative is zero or at one of the ends. It’s possible that the maximum occurs at one of the ends of the interval and the derivative is zero there.
The anti-calculus proposition says that the analogous situation cannot occur for functions of a complex variable. Suppose a function f is analytic on a closed disk and suppose that f is not constant. Then |f| must take on its maximum somewhere on the boundary by the maximum modulus theorem. Erdős’ anti-calculus proposition adds that at the point on the boundary where |f| takes on its maximum, the derivative cannot be zero.