Transcendental number theory (specifically the context of concurrency)

Transcendental number theory studies numbers that are not roots of any algebraic equation with rational coefficients, meaning they cannot be expressed as solutions to polynomial equations with simple fractions. In the context of concurrency, it involves understanding how certain mathematical constants (like π or e) are fundamentally non-algebraic, which influences fields like geometry and cryptography. This area helps mathematicians discern the nature of special numbers, proving, for example, that π and e are transcendental, and explains why certain equations or constructions in mathematics cannot be simplified or solved using algebraic methods alone.