Who is primarily associated with the development of non-Euclidean geometry?

The development of non-Euclidean geometry is primarily attributed to Bernhard Riemann, who made significant contributions that challenged the traditional notions of geometry established by Euclid. In the early 19th century, mathematicians like Nikolai Lobachevsky and János Bolyai also explored the concepts of geometry where the parallel postulate, a key element of Euclidean geometry, does not hold. Riemann’s work in particular laid the groundwork for understanding curved surfaces and spaces that diverge from Euclidean principles, which reshaped the field of mathematics.

Riemann's ideas were revolutionary as they proposed that space could be understood in various forms, emphasizing that geometry is not limited to a flat plane but can also include geometries on surfaces that are curved, thus giving rise to the concepts in differential geometry and eventually leading to applications in physics, such as general relativity. This shift opened up new avenues of mathematical thought and demonstrated the flexibility of geometric principles, which is why Riemann is recognized as a pivotal figure in the development of non-Euclidean geometry.