Final answer:
In 1820, the discovery of Non-Euclidean Geometry occurred, which was a significant mathematical breakthrough, rejecting common Euclidean principles and greatly impacting future scientific theories, including Einstein's general relativity.
Step-by-step explanation:
In 1820, the significant event that occurred was the discovery of Non-Euclidean Geometry. Calculus was co-invented by Isaac Newton and Gottfried Wilhelm Leibniz well before 1820. The development of Abstract Algebra and the establishment of Topology came later as well. Non-Euclidean geometry is a type of geometry that rejects the common Euclidean postulate that only one line can be drawn parallel to a given line through a point not on the line.
This discovery changed the course of mathematics by opening up a new field of study; it was a huge leap in understanding the nature of space and eventually contributed to Einstein's theory of general relativity.