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Barrett was the 25th Secretary of the Air Force. In addition to the Smithsonian, she advises presidents and prime ministers of democracies around the world as a board member of the Global Leadership Foundation. She is vice chairman of Caltech and vice president of the Horatio Alger Association. Before the Air Force, she was four-term Chairman of the Board of The Aerospace Corporation. Earlier, Barrett was interim president of Thunderbird School of Global Management, Ambassador to Finland, CEO of the American Management Association, Deputy Administrator of the Federal Aviation Administration, Vice Chairman of the Civil Aeronautics Board, and an executive with two Fortune 200 companies. She served on the governing boards of RAND, Mayo Clinic, Raytheon, Exponent Corporation, and the Space Foundation, among others. She taught leadership as a Fellow at Harvard.