Her thesis, titled The extension of Galois theory to linear differential equations, earned her a master's degree in 1904.

She obtained a second graduate degree one year later from Radcliffe College, where she took courses from Maxime Bôcher and William Fogg Osgood.

[1][3][4] In 1905 she won an Alice Freeman Palmer Fellowship from Wellesley College to spend a year at the University of Göttingen, where she studied under David Hilbert, Felix Klein, Hermann Minkowski, and Karl Schwarzschild.

[3][4] This trip posed a significant threat to Pell's life, since he was a former Russian double agent whose real name was Sergey Degayev.

[3] After the wedding, the Pells returned to Vermillion, South Dakota, where she taught classes in the theory of functions and differential equations.

She moved with her husband to Chicago, where she worked with E. H. Moore to finish her dissertation, Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations, and received a Ph.D. in 1909.

[4][7] Wheeler was instrumental in bringing German mathematician Emmy Noether to Bryn Mawr in 1933, after the latter's expulsion from the University of Göttingen by the Nazi government.

Anna Johnson Pell Wheeler conducted investigations in a branch of functional analysis that she referred to as "linear algebra of infinitely many variables" [2]