Question

In the early seventeenth century, Johannes Kepler attempted to fit the orbit of Mars into a scheme of nested Platonic solids. When precise observational data from Tycho Brahe resisted this geometric ideal, Kepler did not abandon his search for mathematical harmony; instead, he relentlessly calculated and recalculated the planetary positions. His eventual discovery that Mars moves in an ellipse rather than a circle was not merely a victory of empirical persistence, but a moment where he famously had to tilt at windmills of ancient cosmological dogma. Historians often note that Kepler’s intellectual courage lay in recognizing that the long-cherished paradigm of uniform circular motion was an illusory adversary, built on aesthetic preference rather than physical reality. By relinquishing this ingrained belief, Kepler cleared the path for modern celestial mechanics.

In the context of the passage, the phrase 'tilt at windmills' primarily serves to convey that Kepler had to: