Full Idea
A proof does not only serve to convince us of the truth of what is proved: it also serves to reveal logical relations between truths. Hence we find in Euclid proofs of truths that appear to stand in no need of proof because they are obvious without one.
Gist of Idea
Logic not only proves things, but also reveals logical relations between them
Source
Gottlob Frege (Logic in Mathematics [1914], p.204)
Book Reference
Frege,Gottlob: 'Posthumous Writings', ed/tr. Hermes/Long/White etc [Blackwell 1979], p.204
A Reaction
This is a key idea in Frege's philosophy, and a reason why he is the founder of modern analytic philosophy, with logic placed at the centre of the subject. I take the value of proofs to be raising questions, more than giving answers.