Math

How many lambda calculus programs exist with exactly $N$ terms? This exploration dives into deep questions about computational complexity, from counting programs like (λx. x x) (λx. x x) to analyzing the non-computable BB(N) busy beaver function that grows faster than any computable sequence. We examine Chaitin’s constant $Ω$ and why determining program convergence connects to unsolved problems like the Collatz conjecture collatz(3n + 1).

We explore a solution to finding Pythagorean triples with a product constraint, achieving O(√n) time complexity by reducing the problem to the well-known 3SUM problem.

Exploring methods to extract human-readable step-by-step solutions from Mathematica’s symbolic computation, addressing the black-box problem in automated mathematical derivation.