Jonathan Michael Borwein (20 May 1951 - 2 Aug 2016) had many talents, among which were his abilities to make discoveries in mathematics, to seek tenaciously for proofs of these, and to do both of those things in collegial concert with other workers. In this colloquium I shall give three examples of situation in which I had the pleasure of seeing those talents in action. They concern multiple zeta values, walks on lattices, and modular forms. In each case I shall give a notable identity, comment on its proof, and indicate further work that was provoked by the discovery. The identities in question are chosen to be comprehensible to anyone with an undergraduate education in mathematics and also to people, like myself, who lack that particular qualification.