With his knowledge of physical principles like leverage and stress, along with anatomy, he all but invented the modern style of folkstyle wrestling.
Overall in his wrestling coaching career at Oklahoma A&M, his teams went 136–5–4, including 19 undefeated seasons and 11 NCAA titles.
In 1976, Gallagher was inducted into the inaugural class of the National Wrestling Hall of Fame as a Distinguished Member.
In 1908, he ran for a 99-yard touchdown against Kansas State, which still stands as a school record for longest run from scrimmage.
However, by the second year, Gallagher's wrestlers competed in three duals, winning two (against Emporia State and Texas) and tying with Arkansas.
The streak was broken in the last dual meet of the 1930–31 season against cross-state rival, the University of Oklahoma Sooners.
Bobby Pearce and Jack VanBebber both won gold medals at the 1932 Los Angeles Olympics.
At the 1936 Berlin Olympics, Frank Lewis won the gold, while teammate Ross Flood earned silver.
This structure has since been renamed Gallagher-Iba Arena to honor both Gallagher and Henry Iba, long-time basketball coach at Oklahoma A&M/State.
In 1976, Gallagher was inducted into the inaugural class of the National Wrestling Hall of Fame as a Distinguished Member.
The following table shows Gallagher's wins as coach at Oklahoma A&M: # denotes interim athletic director