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we developed our mathematics constructively,
we formalized our mathematics in Martin-Löf type theory, in Agda notation,
we pressed a button, and
after a few seconds we saw the integer we expected in front of us.
Well, it was a few seconds for the computer in steps (3)-(4), but three years for us in steps (1)-(2).
Why formalize?
Most people formalize mathematics (in Automath, NuPrl, Coq, Agda, Lean, .) to get confidence in the correctness of mathematics - or so they claim. The reality is that formalizing mathematics is intellectually fun.
Entertaining considerations aside, my initial motivation for computer formalization, about 10 years ago, was to write algorithms derived from work on game theory with Paulo Oliva. In particular, this had applications to proof theory, such as getting programs from classical proofs. Our first version of a (manually) extracted program from a classical proof was written in Haskell, in a train journey coming back from a visit to our collaborators