Claimed is one thing, recognized by the NCAA is another. Before the AP poll in 1936, which became the gold standard, there was a free-for-all by pundits, newspapers, magazines, and a Dr. Dickenson, a professor at Illinois who began a math system for national champion in 1926, then back-dated it to 1924 at Knute Rockne's request so Notre Dame could win that year. Notre Dame donated the Rissman Trophy, which Notre Dame retired in 1930, with its third win. Then the Rockne Trophy was retired by Minnesota in 1941 (third win) and the UM donated the Williamson Trophy, but after 1935 the trophies didn't count for much because of the AP poll. The AP football writer (one man) in 1935 chose a triple winner: Minnesota, Southern Methodist and Princeton. In 1934, of the recognized pundits/selectors then active, Alabama and Minnesota each had three (they also each had three men on the official All-America team) - a co-championship would make sense, but the NCAA goes with Minnesota for that year. The majority of these free lancers went with Minnesota in '35, hence the NCAA-recognized Bierman three-peat, 1934-35-36, despite that Dickenson went with Southern Methodist. Before 1920, there are no real champions because all the selections are retroactive by modern "foundations," and individuals. In 1950, the coaches' poll became official, too, so some years there were two champions if the polls differed. Alabama leads with a huge number, including 1973 when they lost in the national championship game (Sugar Bowl) to Notre Dame, but the coaches' poll (UPI) hadn't switched yet to a post-bowl vote so Alabama claims a co-championship for that year. Bear Bryant won six, then, and Nick Saban has added six more. Notre Dame would have 11, Oklahoma 8, Nebraska 5, Minnesota 6. The coaches and AP polls were the arbiters in 1960 and the Gophers finished no. 1 in both, though losing in the Rose Bowl (it was fairly common for national champs to lose in a bowl game). But in recent years, the NCAA has gummed up the works by adding the Football Writers Association, a small number of writers with their own trophy - it went to Mississippi in 1960, so Ole Miss is co-champion now with Minnesota, but I can guarantee that at the time it meant little, and the two polls were everything. The BCS and playoffs have settled the issue since 1998.