From 2016-2018 he was a member of Dartmouth College's Society of Fellows, before beginning a lectureship in the History of Science at the University of Edinburgh. He studies how modern societies produce abstract knowledge and how that knowledge reshapes those societies in turn. While such abstractions often seem universal, Barany's work focuses on their personal and idiosyncratic underpinnings, and the complex and
resource-intensive means by which they move across the world. His current research topics include the globalization of the 20th-century mathematics profession and the global history of the blackboard in modern science, education, and culture.
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