How dark was the medieval dark age?

                                                                     (God the Geometer)

The medieval dark age (5th–15th century) in Europe was not that dark. The hypothesis that the Catholic Church was against science (search "conflict thesis") is a very simplistic view of the complex realities of the time period.
 
The Catholic Church, in fact, actively pursued science. It established many learning institutions, including those in Bologna and Oxford. I would go as far as saying that the foundation of modern (European) science was laid by clergymen when they declared that God designed the world according to mathematical principles (see the attached image), though it was not a very original idea. That very idea was, in fact, the main motivation behind most European scientists, including Galileo and Newton (yes, both were devout Christians).
 
Nevertheless, the conflict thesis holds grains of truth. Science did not progress much during the medieval period. Why? The Church actively discouraged induction or observation-based science because human sensory experience was considered fallible. The only method accepted as valid was deduction or pure logical reasoning based on fundamental laws, of course, approved by the Church.
 
The Renaissance (14th–17th century) was nothing but a gradual acceptance of inductive reasoning. Early Renaissance scientists did their work cautiously, as evidenced by Leonardo da Vinci’s statement: “It is true that nature begins by reasoning and ends by experience; but, nevertheless, we must take the opposite route: as I have said, we must begin with experience and try through it to reason.” Note that Leonardo never published his works; he was probably very much aware of the consequences. Bruno was burned alive for his views. Galileo’s life was spared only after he agreed to recant his views upon seeing the instruments of torture.
 
With time, science and Catholicism drifted apart. Today, most people believe that science and religion are mutually exclusive. Most scientists identify as atheists. It is interesting how perspectives change with time.
 
For more details: Biswal, Troubles in the Newtonian Paradise: Hydrology Responds to no God Equation and the Rise of Machines