Can We Truly See the Structures of Compounds in Chemistry and Physics?

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lewis198
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hey guys, I was thinking about the history of chemistry/physics and thought:

Ok, we know from experimentation that there is matter that cannot be easily reduced, i.e. elements.

However the way we are taught about (in)organic chemistry at school assumes that the structure is a given. How does one tell the structure of a compound, without actually looking at it? Ok, salt would be easy, and metals, but what process would take place?

Does AFM, STM and other forms of microscopy hold promise of 'seeing' actual structures? Because it seems that many structures are just theory and can be falsified.
 
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for example the structure of DNA was not actually 'seen', it was just a model based on the experiments and theory of other physicists.
 
What's seeing if not just bouncing photons off and back-inferring from the scattering pattern? Replace photons with electrons... or with neutrons... and you do the back-inferring on a computer... what's the difference?