The limit to human understanding

Another thought that intrigues me.
Is there a limit to our understanding ?

Suppose there is a system that behaves accroding to logical rules. This encompasses the brain, if you believe in science like me. Then, is this logical system understandable for the human brain, whatever its complexity ?

In other words, is man smart enough to understand anything and everything that is understandable ?

What does it mean, to "understand" ? To be able to enunciate all rules ? To predict the system ? These are not operational concepts since the rules could be given at any level of aggregation or abstraction (example : for the brain, the physical and chemical laws are not enough to understand the brain. Also, the "initial conditions", or the data to define the "state of the brain" will most probably never be fully available to allow prediction).

Consider also that the capacity of the brain has been built over many millennia, from the small capacity of the australopithecus, and that we have no way of telling if the brain would not continue its evolution in the next millenia.

Considering also the large variation in the capacity of understanding among the present human species, I think that it must be concluded certainly that certain systems are not understandable to everyone.

But still, are there certain systems or phenomena that no human can understand ? We could even extend the question to say that man collectively cannot understand ?

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Think about chess : the computer has beaten the world's best player. Certainly, our brain is limited.