Over my semester in John Golden's Nature of Mathematics course, the connections between mathematical fields were presented directly to me in a very valuable way. Not only how the actual mathematics within the field were connected, but how these fields are connected historically.
Since this course was taught in chronological order, it was very clear to me how mathematical concepts were initiated, developed, and transformed into new ones. This view of the field that I have learned so much about shows mathematics as growing and dynamic. Seeing this development makes math seem much more personal and approachable. Mathematics in a historical context is much more human than the mathematics that is presented in a classroom. Topology wasn't created overnight and Lagrange multipliers weren't developed in a 50 minute block like they are taught.
Another important thing that I've learned during my semester in Golden's class is that mathematics isn't an individual activity. Sure I had done group lab assignments in Calc 3 or met up with my classmates to finish delta-epsilon proofs, but the field in general appeared to be one clever person solving a clever problem in a clever way.
This course taught me that development in mathematics is the result of multiple sources of man power. For example: Fremat's Last Theorem. The BBC documentary on the solution to Fermat's Last Theorem that I watched as an assignment in Golden's class made me realize how many individuals it takes to make intellectual progress. Although the film focused on Andrew Wiles, the man who finally solved the proof, it also gave an overview of the people and efforts that contributed to the solution. This sort of collaboration wasn't presented in my previous math courses.
Overall, taking John Golden's course has placed mathematics into a context that is more approachable and more enjoyable than before. This class made me excited to continue my mathematics education.