What advances were made in mathematics during the Renaissance?

During the Renaissance, the term 'Advancements in Mathematics' tends to blur with other advancements during the time. The surviving works of famous Renaissance Men indicate that they considered science to be an umbrella-topic over the other topics (art and mathematics)

Using Science, for example, the calculated with Math to find new medicines and to correct and apply the proper dosage for these new medicines.

But, the most important advances were the concept of '0', from the Hindus, which slowly migrated into the Renaissance. Another is the movement towards helio-centric models (meaning the sun is the center of the Solar System, not the Earth) and away from previous Greek traditions. In addition, the conceptual art for the first working flying machine was conceived by Leonardo da Vinci, which employed multiple new mathematical concepts.

Many advancements in algebra were also made, especially formulas for irregular shapes, as well as patterns between these shapes.

P.S.
The Church resisted many of these changes, because they claimed it was damaging to the gods, but in reality, probably felt that it was a threat to their power.