It may be that we have evolved to see the world as beautiful -- it may be the origin of our aesthetic sense, the underlying definition of beauty. So scientific theories, models of the world, are necessarily beautiful because they describe the, by definition, beautiful world.
Thus mathematics is effective by natural selection. We study only the beautiful subset of mathematics, having used our aesthetic of the beautiful real world to identify that subset in the first place. We are studying "the same kind of beauty", and so this beautiful mathematics naturally maps to the beautiful world: it is effective.
If the world could have evolved differently, it would have different laws, but they would be beautiful to creatures in that world, if they had evolved an analogous sense of "beauty is the way the world is". Would those other-world laws be beautiful to us, too? They might be ("any highly evolved form is beautiful"), but with a "strange, alien beauty" if the world is very different. But then again, it might be that "any highly evolved form is beautiful to a creature that evolved under the same laws". We might have to work to see the meta-beauty.
So if our aesthetic sense has evolved with the world, to describe things that fit in the world, then beauty should guide our engineering, too. We can use the same aesthetic sense to make beautiful artefacts that fit with the world.