Don't be so sure. If there were unthinkable things, then we would be incapable of thinking about them, so we would never know.

Just as language allows us to not only communicate, but to think about highly subtle concepts, and mathematics helps us to model complex relationships, it is not inconceivable that there may be aspects of reality whch may require symbol systems we have not developed yet, or which may be beyond the capability of the human mind to develop. For obvious reasons, I can't give you an example, but just consider how difficult it would be able to talk precisely about Newtonian physics without calculus, or quantum mechanics without probability theory. Some physical environments, such as hydrodynamics, require partial differential equations to be properly understood.

I will concede the mind is clever at work-arounds, a surfer may not know any math, but he is certainly an expert on non-laminar fluid flow. And even sea lions know how to surf very well. It isn't necessary to know classical mechanics to be a good baseball pitcher or a decent billiards player. In cases like this, we learn to "think" with our bodies, which is as good a definition of "athlete" or "dancer" as I can come up with. But the body has physical limitations too.