Verify vs Prove

Question

Can the terms "Verify" and "Prove" typically be taken as synonymous when reading math texts or in discussion with mathematicians?

If not equivalent, then what are the definitions of "Verify" and "Prove"?

Answer 1

Verify means "check", used when you need to check some details or whether an argument is true (in for example an already given proof).

Prove means that you need to show something is true by finding the argument yourself.

Answer 2

Here, while Maths proving a solution and verifying a solution may be synonyms but are literally different. Verifying means to check as commonly done. Proving means putting down your own opinion in using any other formulae in your way. Now hope you all must have understood. Understood ???

Answer 3

"Verify" is weaker than "prove", and a verification usually involves checking a finite number of cases or carrying out some routine calculations.

"Verify Goldbachs' conjecture for all even integers less than 1 million" - tedious but straightforward

"Prove Goldbach's conjecture" - much more difficult !

Answer 4

I believe there is a difference in common use between ''prove" and ''verify". To highlight this, I'd like to give an example.

Example

Prove that if $5x-7$ is odd, then $9x-2$ is even for $x \in \mathbb{Z}$.

Proof

Assume that $5x-7$ is odd. Then $5x-7 = 2n + 1$ for some integer $n$. One may verify \begin{equation*} 9x + 2 = (5x-7) + (4x+9) = 2(n + 2x + 5) \end{equation*}

Because $n + 2x + 5$ is an integer, $9x + 2$ is even.

$\Box$

In this sense, "verifying" $9x+2 = 2(n + 2x + 5)$ is functionally the same as "proving" the result, but it is a matter of algebra. In other words, I would ask a reader to verify something that is well-known but perhaps tedious, whereas a proof typically requires insights at the level of the course or paper.

Note: This slightly edited example was taken from the excellent textbook Mathematical Proofs: A Transition to Advanced Mathematics by Gary Chartrand, Albert D. Polimeni, and Ping Zhang. The comments on 'verify' versus 'prove' are my own.