So ... what kind of a person drops $37,500 on a pair of crazy "Back to the Future" shoes??? A 22-year-old British rapper named Tinie Tempah ... that's who.

TMZ spoke with Tinie's rep ... who told us the London native is a serious shoe collector ... and he simply fell in love with the Marty McFly sneakers at the charity auction in L.A. last night.

We're told Tinie -- whose new song "Written In the Stars" has become a worldwide hit -- is on his way to South Africa at the moment.

No word if he's actually wearing the shoes on the plane ... but he should be.