Goldbach's Conjecture

Challenging problems in mathematics often involve expressing all of the elements of one number set in terms of those of another set. Perhaps the best known of these building block techniques is that of the Fundamental Theorem of Arithmetic. It concerns expressing any integer greater than 1 as a product of primes. In such a setting, a prime is its own representation.

The representation is unique and rests in its validity on the historic methods of mathematical induction (a method of proof dating from the early modern era). Though Euclid includes this fundamental result in Book 9 of the Elements, it is offered without proof. Proof omission calls attention to a general lack of demonstrative methods in arithmetic in this early time frame.