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Leonidas Alaoglu (March 19, 1914 – August 1981) was a Canadian-American mathematician, most famous for his widely-cited result called Alaoglu's theorem on the weak-star compactness of the closed unit ball in the dual of a normed space, also known as the Banach-Alaoglu theorem.

Life and work

Alaoglu was born in Red Deer, Alberta to Greek parents. He received his BS in 1936, Master's in 1937, and PhD in 1938 (at the age of 24), all from the University of Chicago. His thesis, written under the direction of Lawrence M. Graves was entitled Weak topologies of normed linear spaces. His doctoral thesis is the source of Alaoglu's theorem. The Bourbaki-Alaoglu theorem is a generalization of this result by Bourbaki to dual topologies.

After some years teaching at Pennsylvania State College, Harvard University and Purdue University, in 1944 he became an operations analyst for the United States Air Force. In his last position, from 1953 to 1981 he worked as a senior scientist in operations research at the Lockheed Corporation in Burbank, California. In this latter period he wrote numerous research reports, some of them classified.

During the Lockheed years he took an active part in seminars and other mathematical activities at Caltech, UCLA and USC. After his death in 1981 a Leonidas Alaoglu Memorial Lecture Series was established at Caltech. Speakers have included Paul Erdős, Irving Kaplansky, Paul Halmos and Hugh Woodin.

How to improve your calculus textbook

Saunders Mac Lane tells a story about Leon Alaoglu at Harvard, where he was teaching a beginning calculus class. Mac Lane and Alaoglu shared a low opinion of William F. Osgood's calculus book. This scene took place in the early 1940s:

"I [had] recommended the appointment of one Leonidas Alaoglu, Ph.D. Chicago, whose merits were known to me... So on one late October day Leon came to his class in Sever Hall, 'Gentlemen, we now come to Chapter IV, differentials and infinitesimals. Take pages 138 to 184 between the thumb and fingers of the right hand. Tear them from the book!' He did so."

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