Before you begin to answer that you must be clear on what do you mean by real? Is anything you can think of isn't real and what you observe out there is? What is the domain where you define reality and separate it from fiction? If you consider fiction or thoughts and ideas to be equally real as the screen you are looking at then there is no problem to begin with.
What I wanted to show is that this question has a history of confusion behind it and one must be careful before asking this question by having an expectation of what answer should look like.
One way of talking about math is that its just fiction (in our heads alone) that we use, like language, to label certain objects and that the way these objects interplay with each other, giving rise to new structures or behavior that wasn't there before, so you give it a new label, a product of an operation. Math also has the characteristic of being logical, which not surprisingly is deduced from our observations of the environment around us. We build our intuition using the world in which, we expect that if I have two apples and someone gives me a third I should say I have three apples. This can be readily transformed into a mathematical statement. And just like language is prone to lingual paradoxes, mathematics by its very nature, inherits those same kinds of paradoxes. If you believe that reality should be free of paradoxes, then you are right in saying that mathematics is an abstraction of the human mind.
To counter this idea you might propose mathematical realism or the kind of idea Max Tegmark likes to believe that reality IS math and not the other way around. But then reality(math) must have to be discovered and it seems the only way of doing so is using complex language and symbols and simulating the symbols using paper and pen. Then there is no surprise that nature seems very mathematical because guess what, it is math.
But what is common to either argument is that you cannot separate the similarities between language and math which implies math is not without paradoxes and this is the issue I have with mathematical realism. Paradoxes should exist as a feature of reality if math has to be reality. Math as fiction doesn't have this problem because it is free from carrying the burden of describing reality. I can conjure up a new set of rules for a set of objects and then I can describe totally bonkers of behavior, like a funny video game, that I should never expect to see in the world but it is still valid as an abstraction because I can play the video game! Again the answer boils down to what you will throw out or keep in your domain of reality. The confusion begins there.