Compared to other branches of natural sciences, mathematics arguably raised more philosophical questions. Since ancient times, philosophers and mathematicians have been debating questions about the nature of mathematics. In this seminar, we join their debate and look at questions about the nature of mathematics related to both ontology and epistemology. For example, What is the nature of mathematical truth? Do mathematical objects and facts exist independently of human consciousness? Are theorems invented or discovered? How does one explain the unreasonable usefulness of mathematics? Do we really need more and more abstract mathematical concepts?