The Renaissance was a time of dramatic cultural change that included a rise in the acquisition of knowledge for the sake of learning, as opposed to more occupational or utilitarian motivations. The idea of empowerment through knowledge helped define the era.
Embodying this sentiment was a host of famous polymaths, or individuals with a wide-spectrum of talents and knowledge. One of the most famous polymaths from this time was Leonardo da Vinci, whose paintings, drawings, sketches, observations and ideas proved to be, at times, centuries ahead of the curve. An outline of just a few of his varied accomplishments would include discoveries in human anatomy (Biology), engineering advanced machinery (Physics), and geological insights (Environmental Science), as well as volumes of artistic masterpieces.
Leonardo’s capacity for invention knew no bounds, and his interests would often overlap and complement one another to a certain degree. For example, it would make sense that an innate understanding of the human skeletal structure would help in an artistic recreation of the human form.
However, there are many other crossover connections: the laws of Geometry, for example, are closely related to one of Leonardo’s most famous paintings, and studies in bird anatomy would certainly play a role in the invention of a few of his flying machines. Finally, Leonardo’s unflinching powers of observation, a common trait amongst artists, would play a huge role in his continued exploration of the world around him, scientifically, artistically, and otherwise.
Of course, nowadays, anyone with an Internet connection has an unprecedented amount of information available at their fingertips at all times. But does that mean it’s harder to really shine as a polymath? One might make the argument that it is easier to invent and discover in a time of great ignorance simply because there is more to be discovered or invented.
Others, however, would state that the rise of information technology brings with it greater prospects for polymath-like achievements thanks to copious cross-disciplinary collaboration opportunities. With a few keystrokes, someone could go from studying painting techniques to discussing mathematical engineering.
If you want to become a polymath, pursue what you like. Try to learn as much as you possibly can on a subject and then relate it back to other areas of interest. While finding a niche specialization might sound tempting, competence (and even mastery) in several different disciplines is now possible thanks to the technologies of the information age. Forget the limits and there's no telling what you may find!