|There's more than one way to do things|
The only good way to ensure a program is correct is to run it on a computer.
and viceversa (s/program/proof/g):
The only good way to ensure a proof is correct is to run it on a computer.
If not, what was the reason for all Turing/Godel/Church efforts to fix David Hilbert's problem question on the completeness and consistency of mathematical systems? (Hilbert's program)
That's one of the meanings of Knuth's famous quote
"Beware of bugs in the above code; I have only proved it correct, not tried"
A constructive proof that uses only finite procedures (algorithms) and runs in a Turing-equivalent machine has more value than an ordinary mathematical demonstration.