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|Centuries:||16th century – 17th century – 18th century|
|Decades:||1600s 1610s 1620s – 1630s – 1640s 1650s 1660s|
|Years:||1634 1635 1636 – 1637 – 1638 1639 1640|
- 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.