This book presents high-quality papers on the History of Mathematical Sciences, focusing on Portugal and East Asia, a testament to ongoing international collaboration in uncovering the rich, interwoven histories of science, culture, and diplomacy across continents. This volume explores the profound impact of mathematical and scientific exchanges between Europe, and in particular, Portugal, and East Asia, emphasizing how time, space, and cosmological understanding were shaped and transformed through intercultural contact. Chapters range from Jesuit mechanical clocks in Japan to reinterpretations of Euclidean logic in Chinese translations, from the mapping of early Portuguese planispheres to Qing dynasty astronomical reform. Featuring contributions by leading historians of science, this collection sheds light on the individuals?Jesuits, scholars, artisans?who bridged cultures and shaped knowledge across early modern Eurasia. It offers a unique lens into how mathematics and cosmology were not only tools of measurement but also vehicles of cross-cultural dialogue and power. This book is essential for historians of science, mathematics, and East-West relations.