Are we living in a Platonic world?  The great Austrian mathematician Kurt Gödel may have thought so.  If you're not familiar with Plato's thought, he suggested that outside of this world lies another world, a world of eternal ideas from which all ideas in this world derive.  Everything we come to know in this world we come to know on the basis of these eternal ideas (or forms).  What is true in this world is therefore determined by what is "Truth" beyond it.  So did Gödel say, in roughly like manner, that mathematical concepts and ideas "form an objective reality of their own, which we cannot create or change, but only perceive and describe."
     Mathematicians like to say that their truths are timeless, that they are truths that everyone, regardless of nationality or origin, comes to perceive and accept.  They are universal statements about reality.  Ironically, we cannot really prove these truths.  Although we all for instance understand and accept that two plus two equals four, we cannot independently prove it.  We can only use the mathematical to prove the mathematical.  So it becomes circular.
     On the other hand, if mathematics' truths are indeed objective and universal, we have a very good argument for the necessity of universals in our lives.  We need universals, within or outside of this world, to make sense of ourselves and our lives.  We cannot build a life meaning on particulars.  We need universals to decide what is really true.
     The issue for most us, then, is not so much whether universals necessarily exist but more of how we access them.  How do we access Truth?  How do we access what innately is, but what we do not physically see?
     Ah, the challenge of finitude, the challenge of God:  understanding what it means to be finite in an infinite (but bound and ordered) universe.