Is Mathematics hard reality like science or creatively conceptual like poetry?

 Just watched a neat philosophy lecture on Pythagoras and it made me think of mathematics.  We all know science is physical reality.  It's tangible. something we can feel.  It has mass.  It has a cause and effect impact of us and your world.  Mathematics is intellectual and at least perceived as in the galaxy of scientific reality but is it really?  If a piece of wood is at a right angle, we know the wood is real but how are we to analyze its right angle?  Abstract thinkers (as they were back in the day) came up with a thought process that this piece of wood had a certain bend to it and that numbers, merely ways of counting physical objects, could be applied to this bend but was seeing a bend in the wood necessary at all?  Why would we need to conceptualize this angle in the first place?  It's a hunk of wood and has the laws of physical science behind it.  We MUST acknowledge it's a hunk of wood.  It can be in our way.  It can hit us over the head.  It has a potential impact outside ourselves we can't deny.  But must we acknowledge mathematics?  Nothing about the wood or ourselves changes if we don't see the wood is at a right angle.  Physical reality goes on whether we see it or not.  In that way, is mathematics a necessary application in the real world at all?  If we didn't conceptualize math, with all its intricate calculations, would we be the worse off for it?  

In that way, I see math as being a bit like poetry.  Like the poetry of beautiful things.  We experience beautiful things like flowers in the real world because they have mass like the block of wood.  We then think of ways we can creatively express what we're seeing in an aesthetic way.  We apply it to our emotions.  in contrast, we apply the idea of a right angle in a block of wood with pure intellect, largely free of the emotions.  We can get emotional over a right angle but it seems rather silly!  While it's virtually impossible to create good poetry about a flower without some sort of emotional aesthetic.  In that way, mathematics can be seen as emotionless poetry, intellectually creative yet devoid of any need for an emotional connection.  Mathematics is often very important for creating a sense of order in our lives which helps makes our existence bearable in a technical fashion.  It's a facilitator of problem solving.  However, if all we need to do is see the block of wood as just a hard, physical object devoid of shape and we need not use our emotions to conceptualize it, is mathematics even necessary to our existence as the acknowledgement of the physical and the emotional are?  Food for thought!