Carter died of a "sudden cardiac event" on Monday night in Boston.
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He served as secretary of defense under former President Barack Obama from February 2015 to January 2017.
Carter graduated from Abington Senior High School in Montgomery County.
He earned bachelor's degrees in physics and medieval history from Yale University and received his doctorate in theoretical physics from Oxford University, where he was a Rhodes Scholar.
He also served on the advisory boards of MIT's Lincoln Laboratories and the Draper Laboratory.
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"I like dusty archives, learning to decipher manuscripts in medieval script, and learning all the languages necessary to read the primary and secondary historical literature, especially Latin," he wrote in a 2007 autobiographical sketch published by Harvard University when he was on the faculty of the Kennedy School of Government.
Carter served as the Pentagon's second-ranking official from 2011 to 2013, spent two years as the department's technology and weapons-buying chief and was assistant secretary of defense for international security policy during Bill Clinton's administration.
He preferred to be called Ash rather than his given name, Ashton.
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ABC News contributed to this report.