In Late Middle Age, the position of the stars in navigation maps was programmatically out of sync with the Ptolemaic predictions. Further refinements in observations led to the abandonment of the geocentric picture altogether. Get the priority right: navigation needs implied a review of geocentric superstitions.
Take modern financial markets. Observing the open outcry system at the Bourse de Paris, the early 20th century work by Bachelier led to the introduction of the Brownian motion into the modelling space. Similarly, algorithmic (i.e. machine intermediated ) trading in early 21st century has led to refined granularity: hence mathematicians started talking about fractional Brownian motion. Again, get the priority right: modelling needs forced a revision of mathematical abstractions.
Take now the woodcut “Day and Night” (1938) by Mauritius Cornelius Escher below:
The black and white pattern – so intrinsic to the visual & conceptual structure of the composition – was forced upon him by the technique he used. Woodcut and its symmetries outgrew their material immediacy, they implied a conceptual outcome – so neatly realized by M.C. Escher.
As another example, take the second Wittgenstein – and his insistence on language games, on usage, on habits: would the shift of focus from the earlier “Tractatus” have been possible without the crucial experience as a school teacher in rural Austria in the 1920ies?
Q: All right, but the imaginary unit was discovered by mathematicians before Maxwell used it in his equations of electromagnetic field so neatly. And that was totally disconnected from subsequent application.
A: Are we sure? Who says that solving second order algebraic equations with negative determinant is disconnected from practical applications? Who says the imaginary unit was not a practical discovery?
The whole argument is in a sense close to the materialistic epistemology which I have already (briefly) discussed here.
“At the Beginning was the Action”, as Goethe says in Faust.