Final answer:
Pope Paul III came to grips with the problem of Protestantism in a positive fashion during the 1540s by approving the establishment of the Society of Jesus, also known as the Jesuits.
Step-by-step explanation:
The pope who came to grips with the problem of Protestantism in a positive fashion during the 1540s was Pope Paul III.
Paul III recognized the need for reform within the Catholic Church and took steps to address the concerns raised by the Protestant Reformation. In 1540, he approved the establishment of the Society of Jesus, also known as the Jesuits.
The Jesuits played a crucial role in countering the spread of Protestantism and promoting Catholic teachings.