Cordes was born in Naperville, Illinois in 1993, the son of Bill and Kristin Cordes. He is a 2011 graduate of Neuqua Valley High School and currently attends the University of Arizona, where is he majoring in physiology. Swimming for the Arizona Wildcats, he is a six-time NCAA individual national champion, winning the 100-yard breaststroke four years in a row and the 200-yard breaststroke in 2013 and 2014. Cordes is the 2013 and 2014 NCAA Swimmer of the Year.
At the 2012 United States Olympic Trials, the qualifying meet for the 2012 Olympics, Cordes missed the Olympic team by finishing third in the 100-meter breaststroke (1:00.58) and twelfth in the 200-meter breaststroke (2:13.26).
At the 2012 FINA Short Course World Championships in Istanbul, his first major international competition, Cordes won one gold and bronze medal. His gold came as a member of the 4×100-meter medley relay, swimming the breaststroke leg in 57.15 (the fastest in the field). In the individual [2012 FINA World Swimming Championships (25 m) – Men's 100 meter breaststroke|100-meter breaststroke], Cordes placed third with a time of 57.83.
At the 2013 US National Championships, Cordes qualified to swim in three individual events, the 50-, 100- and 200-meter breaststroke, and the 4×100-meter medley relay at the 2013 World Aquatics Championships. At the National Championships, he was first in the 100- and 200-meter breaststroke, and finished second behind University Of Arizona teammate Kevin Steel in the 50-meter breaststroke.
At the 2013 World Aquatics Championships, Cordes competed in three individual events and the 4x100-meter medley relay. In his first event, the 100-meter breaststroke, Cordes got a personal best time of 59.78 in the semifinal. In the finals however, he faded away and touched 7th with a time of 1:00.02. In the 50-meter breaststroke, Cordes did not advance past the prelims, posting a time of 27.69 and finishing 21st overall. In his final individual event, the 200-meter breaststroke, Cordes did not advance past the semifinals, finishing with a time of 2:10.03. In the 4x100-meter medley relay, Cordes, as the breaststroke leg, was responsible for disqualifying the United States by diving 0.04 of a second early.
At the 2014 Pan Pacific Swimming Championships, Cordes won gold as a member of the 4x100-meter medley relay with the team finishing with a time of 3:29.94. Swimming the breaststroke leg, Cordes recorded a split of 58.64. In the 100-meter breaststroke, Cordes was disqualified for taking off his goggles midway through the race after they filled with water. In the 200-meter breaststroke, Cordes scratched from the final after posting a time of 2:10.01 in the heats in order to concentrate on the medley relay.
Cordes trained in Singapore with, former Bolles Swimming Head Coach, Sergio Lopez.
At the 2016 US Olympic Swimming Trials, Cordes placed first in the 100m breaststroke, qualifying him for the Olympic Team.As of July 31, 2017