I don't know shit about math or physics but, if atoms cannot be perceived, their existence is doubtful to say the least. If i watch water turn gaseous whenever it's temperature increases, i can say that heat is the cause of this effect. If i watch something melting when its solid, I say heat + solidity is the cause of the effect. After a lot of facts observed I can come up with this law: when something is liquid, it will turn gaseous if heat is continuously apply to it. But i can check the presence of the conditions (liquidity + heat) for this to happen by observation. Say I find a liquid that does not turn gaseous when I heat it up, the law will be proven wrong. But with atoms this cannot happen because I can't see an atom, i can see liquidity, but not atoms. If I say (and this is completely fictional) that liquids turn gaseous because when atoms are electrically charged, their electrons start spinning faster and wider and the push each other apart, and i find a way to transmit energy to water but the water does not turn gaseous, i can say that atoms are still there, but the electrons didn't move because they don't when X thanks to property Y that we just discovered, or i can say that electricity didn't reach the atom for whatever reason, or i can say that the electrons didn't pushed each other becuase they all started spinning in a way they in which they didn't touch each other. Since i cannot see the atom, i can adapt it's properties to be coherent with observable phenomena. If this is in fact what happens, it is entirely plausible that atoms don't actually exist and are just a laborious adaptation of from immense amount of observable phenomena accumulated through years.