Yes, in chemistry it is common to guess equations to match experimental data. This never occurs in physics.
The first glimpse at the unsolvable occurs in calculus, where not every antiderivative can be found in terms of elementary formulae.
Then a course on differential equations teaches us that only very few nonlinear equations have solutions in terms of formulae.
Then a course on algebra teaches us that it is impossible to find a formula the roots of a general polynomial of degree greater then 5.
Then a course on set theory teaches us that there are propositions (such as the continuum hypothesis) that are nether true or false.