Final answer:
Blaise Pascal was motivated to create a mechanical digital calculator to help his father with tax calculations, leading to his invention, the Pascaline, despite early restrictions on his mathematics education.
Step-by-step explanation:
The motivation of Blaise Pascal to create a calculating machine stemmed from his desire to assist his father, a tax collector, in managing the tedious calculations required for his work. Despite being home-schooled and initially forbidden to study mathematics, Pascal's curiosity led him to teach himself geometry by the age of 12. His invention of the first mechanical digital calculator, known as the Pascaline, was a groundbreaking development in the mathematical world, allowing for quicker and more accurate calculations. Beyond the calculator, Pascal made significant contributions to probability theory, number theory, and geometry, as well as fluid statics through the application of Pascal's Principle in hydraulic systems.