1637 (MDCXXXVII) was a common yearstarting on Thursday of the Gregorian calendarand a common year starting on Sunday of the Julian calendar, the 1637th year of the Common Era (CE) and Anno Domini (AD) designations, the 637th year of the 2ndmillennium, the 37th year of the 17thcentury, and the 8th year of the 1630s decade. As of the start of 1637, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.

• February 3 – Tulip mania collapses in the United Provinces (now the Netherlands) by government order
• February 15 – Ferdinand III becomes Holy Roman Emperor
• December 17 – Shimabara Rebellion erupts in Japan
• Pierre de Fermat makes a marginal claim to have proof of what would become known as Fermat's last theorem.
• France places a few missionaries in the Côte d'Ivoire, a country it would come to rule more than 200 years later.
• England wages war against the Mashantucket Pequots
• First opera house, Teatro San Cassiona, opens in Venice
• René Descartes – Discours de la Methode
• Elizabeth Poole becomes the first woman to have founded a town (Taunton, Massachusetts) in the Americas.