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Max received his Bachelor of Science degree from Miami University in Oxford, Ohio and his Medical Doctorate from the University of Cincinnati, College of Medicine. He began his medical career by serving in the United States Air Force from 1953-1974 and retired as a Colonel. During his years in the military, he served as Chief of Pediatrics at Chanute AFB, Illinois; Chief of Pediatrics and Pediatric Consultant for Europe in Weisbaden, Germany; and Chief of Allergy and Immunology Service at Willford Hall, San Antonio, Texas. He was the recipient of the Legion of Merit Award in 1974.

After retirement from the Air Force, he became the Co-Director of the Allergy and Immunology Fellowship Program at the UT Health Science Center in San Antonio, Texas. In 1978, he opened his private medical practice in Allergy and Immunology until his retirement in 1998. He was a member of the American Board of Pediatrics; American Board of Pediatrics – Allergy; and American Board of Allergy and Immunology.