Alex Baumann showed his potential as a world-class swimmer at a young age. Under coach Jeno Tihanyi, Baumann won 10 age-group events and set 9 records during his first year of competition. His abilities became widely recognized and several American universities subsequently sought him out. But Baumann chose to stay in Canada and attend Laurentian University while continuing his training with Tihanyi. In 1978 he won the 200 m individual medley (IM) at the Darmstadt International meet (butterfly, breaststroke, backstroke, freestyle) and won numerous national and international meets in the 200 IM, 400 IM, freestyle, backstroke and butterfly before setting a Commonwealth record in the 400 m IM 28 July 1981 and a world record in the 200 m IM the next day.
Forced out of swimming for 10 months because of a chronic shoulder problem, he returned to lower the Commonwealth record in the 400 m IM and the world record in the 200 m IM at the Commonwealth Games in Brisbane, Australia, in October 1982. He won the 400 m and 200 m IM events at the World University Games in Edmonton July 1983, and lowered the 400 m IM world record to 4:17.53 at the Olympic trials.
Alex Baumann's 2 gold medals at the Los Angeles Olympics (200 m IM, world record 2:01.42; 400 m IM, world record 4:17.41) made him one of only 6 Canadians to win 2 Olympic gold medals (along with George Hodgson, Percy Williams, Gaëtan Boucher, Carolyn Waldo) and Marc Gagnon. He continued competitive swimming, winning 2 gold medals (400 m IM, 200 m IM) at the 1986 Commonwealth Games and recording a world best in 1987 (200 m IM), but in October 1987 he announced his retirement from competitive swimming. Shortly after his retirement, Alex Baumann moved to Australia, where he is currently the CEO of Queensland Swimming, one of the most important development links in Australia's aquatics program. He is an Officer of the Order of Canada and has a place in Canada's Sports Hall of Fame.