What Is Verification?
Proof writing in Mathematics is the closest thing I can think of to formal verification of a claim. The logical machinery written symbolically in a series of steps to arrive at a conclusions is, to me, the purest verification of a claim.
Of course, with it comes a specialized understanding of the symbology and language of mathematics, the precursor claims the proof depends on, and the actual communication of the proof. It's a fairly complicated process, one which is tough to learn, tough to use, and tough to actually review!
However, because it's a formal procedure, we can write software that can mechanically verify a proof! This is 1) fascinating 2) unbelievably powerful.
Because software itself is a form of proof (a declaration of steps to accomplish a goal), we can build and maintain formal verification of these operations. Strictly speaking, this is what a compiler does! Clearly, a compiler doesn't go far enough in verifying behavior, because otherwise we wouldn't have UB or bugs in modern software, but it guarantees compiled code will do what it says it will do.
Beyond compilation, testing can bring us closer by isolating behaviors and guaranteeing behavior when provided with a given criteria for operation. However, this can only guarantee what you think to test! In many ways complex testing requires the full attention of the developer, and even still runs into missed behaviors!
And none of this actually tells you if what you wrote is what is actually being requested! Did you understand the requirements? Did the requester understand their own request? How do you arrive at "finished and correct" when the standards for such are often quite loose?
In my eyes this is the field we as developers need to study and apply our knowledge to. There's always been this form of "last mile" problem plaguing software projects, and it's only getting worse. Unfortunately, this is as far as I've really gotten on the problem, there is a ton of work to do towards solving this.
And I think we may be close!