Final answer:
Karl Barth is recognized as the most prolific and important theologian of the twentieth century, significantly influencing Christian theology amidst the era's philosophical and existential challenges.
Step-by-step explanation:
The most prolific and arguably the most important theologian of the twentieth century is A) Karl Barth. His influential work in theology during a tumultuous time period that saw both World War I and World War II has left a lasting impact on Christian theology. Barth's approach was characterized by a rejection of liberal theology that was prevalent at the time, and his emphasis on the sovereignty of God and the centrality of Jesus Christ. This perspective provided a counterpoint to the skepticism and atheist philosophies that emerged with thinkers like Karl Marx and Friedrich Nietzsche. Barth's work fundamentally shaped Protestant theology and continues to be studied and debated in theological circles even today.