Is it true that all of the physical laws and mathematics needed to describe chemistry are known? This question comes from a rather famous quote by Paul Dirac which goes like this,


  The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.
  -Paul M. Dirac


I have seen this quote a number of times and it never struck me as being peculiar because to my knowledge the actual physical laws describing everything we care about in chemistry are known. However, I was recently at a talk (it was a presentation to one of my classes, but the speaker gave a talk about his research) about density functional theory, and this quote was shown as a sort of introduction for why density functional theory was developed and is applied as a form of approximation. After showing this quote, the speaker said "well that's not strictly speaking true..." and then moved on and didn't say anything else.

I meant to ask what he meant by this after the talk, but I forgot because I was asking about something else.

So, to expand on this:

Are there any physical laws which are unknown (or believed to be unknown) which directly relate to chemistry?

Are there any mathematics which have not been developed which are necessary to fully describe some aspect of known chemistry?
First, it is one thing to know the basis for a "law", and quite another to mathematically calculate the effects of that law. Consider just carbon, for example... chains may be made of thousands of atoms, with various functional groups attached to each. Though, as Dirac stated, it helps to have "shortcuts" to computation such as Fast Fourier transforms, there are still problems that cannot be solved in a "reasonable" time.

Second, if there are unknown laws, how would we know about it (not to quote Rumsfeld on unknown unknowns)?

And finally, even if all physical laws were known and understood, it would still be impossible to predict everything: Kurt Gödel's incompleteness theorems show that in a complex system (it does not have to be very complex; basic grammar-school mathematics qualifies), questions can be asked that cannot be proved true or false. This extends to chemistry and physics.