Graduates wear square caps, often referred to as mortarboards, as part of the academic dress tradition that has been in practice for centuries. Here are the main reasons behind this custom:

1. Historical Origins: The mortarboard hat has its roots in medieval Europe, where scholars and clerics wore similar headgear. The shape and design evolved over time, but the flat square top with tassels dates back to the 14th and 15th centuries. The board-like shape is sometimes said to resemble the slab used by stonemasons to hold mortar, hence the term “mortarboard.”
2. Symbolism: The mortarboard is a symbol of scholarly achievement and intellectual pursuit. It signifies that the wearer has completed a significant level of education and is now joining the ranks of learned individuals. The tassel hanging from the mortarboard typically starts on the right side and is moved to the left once the degree is conferred, signifying the completion of studies.
3. Uniformity and Respect: Academic regalia, including the mortarboard, creates a sense of uniformity among graduates and faculty, emphasizing the shared commitment to learning and scholarship. It also adds a formal and respectful atmosphere to graduation ceremonies.
4. Tradition and Ceremony: The wearing of academic regalia, including the mortarboard, is a longstanding tradition that connects today’s graduates with past generations of scholars. It is a visible representation of the continuity and importance of higher education across centuries.
5. Cultural Significance: Across different countries and institutions, variations of the mortarboard and other components of academic dress are worn, reflecting local academic traditions and the history of the institution.

In essence, the mortarboard hat is a ceremonial accessory that marks the milestone of completing a degree program and honors the academic journey and accomplishments of the graduate.