If they can't see atoms how do they get chemical formulas?

Seeing as how no one has ever seen an atom, how do they know the exact structures of molecules? Also, if the main proofs of atoms are math and brownian motion (which could be any number of things, not just 'atoms'), then when they updated the size of the neutron a few years back and made it much larger, does that mean all chemistry based on math was flawed and needs to be redone, or that those scientists were just trying to cover their own faulty math? Does any one have the experiment to prove chemical composition of various substances?