The mathematics studied by mathematicians, logicians, and philosophers is a way of expressing intrinsic, fundamental laws and relations upon which reality is constructed. Without mathematics as a field of human study, there can certainly be existence. However, I believe your question is referring to the intrinsic, fundamental laws I mentioned above. These laws and relations constitute the semantic portion of a string of mathematical expressions written on paper. So, to answer your question directly: No, reality would simply be impossible without them.
In fact, you can't even conceive of a world that is devoid of these laws and relations because your mind, i.e. your reality, is constructed upon them. Every action, thought, and feeling is dependent on inherent mental 'categories' (as Immanuel Kant called them) -- space, time, etc. -- which are responsible for organizing data received by means of the senses. These mental categories are sort of like templates, and are, according to Kant, already present at the time of birth, but not yet fully developed until maturity. My theory, although lacking in concrete evidence but still valuable speculation, is that these categories of the mind, when thought of as templates for constructing reality, are made possible because there exists an external world that requires them.