To the educated lay person, G del's undecidability theorem may be the single most widely-known mathematical result of the 20th century. G del's theorem is just one of numerous impossibility results established in the last 60 years stating what cannot be done. Another famous negative result, due to the British genius, Alan Turing, states that you cannot tell in advance if a certain abstraction of a digital computer called a Turing machine will ever halt with the correct answer. Now, what all these impossibility results have in common is that they are about the manipulation of symbols, that is, they are about mathematics. I've spent some of my time for most of a decade asking myself what does this tell us about the unknowable in science.
Science is about understanding the universe and everything in it.
Note that there are, a priori, no mathematical models that accompany these questions. Science uses mathematics, but it is also very different from mathematics. The known is taught in the schools and universities and is exhibited in the science museums. But scientists are excited by the unknown. The unknown and the unknowable form the boundary of science.