He was educated at Sir George Monoux Grammar School in Walthamstow and read mathematics at Brasenose College, Oxford from 1924 to 1930.
Cowling found an error in the paper that invalidated Chapman's results.
Joseph Larmor had worked in this area, arguing that sunspots regenerate themselves through a dynamo effect.
During the 1930s, Cowling also worked on stellar structure involving radiation and convection, at the same time as Ludwig Biermann but independently of him.
Cowling retired from his chair at Leeds in 1970 with the title Emeritus Professor.