Philosophy of Mathematics

Mathematics is one of humankind’s greatest cognitive endeavors, yet it raises many puzzling questions. Unlike much of our other knowledge, most mathematical knowledge is not established by gathering empirical evidence. So how is mathematical knowledge possible? Unlike most other things we consider to be real, mathematical objects are not physical objects. So in what sense do mathematical objects, such as numbers, exist? What are the foundations of mathematics? Do some mathematical proofs provide greater understanding than others? No prior knowledge of mathematics or philosophy is required.