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Abraham A. Ungar
ABRAHAM A. UNGAR grew up in Sde-Ilan, Israel, and attended the Hebrew University in Jerusalem as an undergraduate, earning his B.Sc. and M.Sc. in 1965 and 1967. He completed his doctorate in mathematical geophysics at Tel-Aviv University in 1973 under the supervision of Zepora Alterman. After being a postdoctoral fellow at the University of Toronto, Department of Physics, he took faculty positions at the National Research Institute for Mathematical Sciences (Pretoria, South Africa), Rhodes University (Grahamstown, South Africa), Simon Fraser University (Vavcouver, Canada), and North Dakota State University in Fargo, where he currently teaches. His interest in understanding why Einstein velocity addition law of relativistically admissible velocities is seemingly structureless, being neither commutative nor associative, led him to the discovery of the gyrocommutative gyrogroup structure that Einstein velocity addition and Möbius addition encode. Both Einstein addition and Möbius addition thus turn out to be gyrocommutative gyrogroup operations, just as the common vector addition is a commutative group operation.