Goldbach's Conjecture

Prove Goldbach's conjecture by showing that every even integer greater than 2 can be expressed as the sum of two prime numbers, thereby establishing the strong (binary) form of the conjecture.

Background

In the Recommendations section, the author argues that mathematicians should embrace AI to advance core mathematical goals. As an illustrative example of high-impact objectives, the essay explicitly mentions proving Goldbach's conjecture alongside realizing the Langlands program and resolving the P ≠ NP problem.

Goldbach's conjecture is a longstanding open problem in number theory asserting that every even integer greater than 2 is the sum of two primes. The essay invokes this conjecture to exemplify the kind of major theorem-proving milestones that would underscore AI's positive role in mathematical discovery.